Benchmark quantities: Difference between revisions
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Revision as of 07:35, 6 March 2024
Benchmark quantities are numbers that can help people gain perspective for any type of measurement. For example, people know that a million miles (or kilometers) is a very long distance. But what familiar thing is it comparable to? A person may know that it's larger than a typical continent, or than Earth itself. But is it comparable to the distance to the Moon, or perhaps to the Sun? Or to the nearest star other than the Sun? Or perhaps to the size of our galaxy, or to the distance to the nearest galaxy? Likewise, one millionth of an inch (or of a centimeter) is certainly small, but is it most comparable to the size of an atomic nucleus, a whole atom, a virus, or perhaps a single-celled organism? Similar questions can be asked about very fast or very slow speeds, very large or small masses, or time spans, or temperatures, ... and many other types of physical quantities.
Every quantity listed in this article is given in terms of the International System of Units (SI), which are metric units. In some cases, alternative units are given if they are in common use. For example, the distance between Earth and the Sun, besides being given in meters, is also one Astronomical Unit (AU) by definition, and the AU is commonly used for distances to other objects within the solar system as well. Still larger distances are better represented by using light-years.
Note: This article uses the U.S. convention for naming the numbers 109 and larger. For example, 1 billion denotes 109 ("1" followed by 9 zeroes), 1 trillion denotes 1012, and 1 quadrillion denotes 1015.
Acceleration
Acceleration is the rate at which an object's velocity changes. The SI unit of acceleration is meters per second squared (m/s2), or, equivalently, "meters per second, per second." Alternative units are in terms of the acceleration g of objects falling due to gravity on Earth, where g is 9.8 m/s2.
| Value, in meters per second squared | Alternative Units | Description |
|---|---|---|
| 1 x 10-5
10 millionths |
1 millionth of 1 g | Variation in gravitational acceleration for 3 m (10 foot) change in elevation near Earth
or, variation in g aboard an orbiting space ship/station |
| 0.0027 | 0.028% of g | Gravitational acceleration of the Moon due to Earth's gravitational field |
| 0.0059 | 0.060% of g | Gravitational acceleration of Earth or the Moon due to the Sun's gravitational field |
| 0.05 | 0.5% of g | Variation in gravitational acceleration on Earth (equater vs. poles, at sea level) |
| 1.6 | g/6 | Gravitational acceleration on the Moon |
| 9.8 | 1 g | Gravitational acceleration on Earth |
| 50 | 5 g | Acceleration at which humans typically lose consciousness |
| 450 | 46 g | Highest acceleration survived by a human
Don't try this at home! People have also not survived at lower accelerations than this! |
| 10,000-30,000 | 1000-3000 g | Typical lab centrifuge |
Density
Density is a measure of how compact a material substance is. It is calculated by dividing the total mass of a material sample by the sample's volume. Density can be thought of as a combined effect between how close together the atoms in a material are, as well as how massive the individual atoms are. In solids and liquids, the atoms or molecules are closer together than in a gas, so are considerably denser than gases such as air or helium.
There is a limit to how closely atoms can be packed together under normal conditions, so there is a limit to how high a normal material density can be. Achieving higher densities then requires special conditions, for example, those found in the core of a star, or, going even more extreme, inside an atomic nucleus or neutron star.
The SI unit of density is kilograms per cubic meter (kg/m3). Alternative units are grams per cubic centimeter (g/cm3). Since water has a density of 1 g/cm3, using these units also gives the ratio of a material's density to that of water.
Quick scale: While the Sun is, on average, only 40% denser than water, its core is 160 times denser than water. Common metals such as steel, copper, and lead are around 10 times denser than water, which is 800 times denser than air. Helium is roughly 1/7 the density of air.
Quick scale for exotic matter: Atomic nuclei and neutron stars are about 100 trillion times denser than water, which is about 2 septillion times denser than dark matter in our galaxy. (100 trillion is 1 followed by 14 zeroes. 2 septillion is 2 followed by 24 zeroes.) These differences are considerably greater than the ratio between the densest solids and the lightest gas, which is about 250,000 for osmium vs. hydrogen at atmospheric pressure and room temperature.
| Value, in kilograms per cubic meter | Alternative Units | Description |
|---|---|---|
| 2.2 x 10-27 | Dark matter, average for universe | |
| 4-5 x 10-22 | Dark matter, near solar system | |
| 6 x 10-22 | Dark matter, in Milky Way halo | |
| 1 x 10-12
1 trillionth |
Air, ultra-high vacuum conditions (10-9 mbar or 10-12 atm) | |
| 0.18 | Helium, 20 C and atmospheric pressure | |
| 1.2 | Air, 20 C and atmospheric pressure | |
| 9.0 | Compressed air, 20 C, 96 psig (111 psia or 7.5 atm abs.) | |
| 250 | 0.25 g/cc | Balsa wood |
| 534 | 0.534 g/cc | Lithium, the lowest-density solid element |
| 1000 | 1 g/cc | Water |
| 1400 | 1.4 g/cc | Sun (average) |
| 2200-3400 | 2.2-3.4 g/cc | Typical rocks |
| 2700 | 2.7 g/cc | Aluminium |
| 5500 | 5.5 g/cc | Earth (average) |
| 8000, 9000, 11,400 | 8, 9, 11.4 g/cc | Steel, copper, lead, respectively |
| 13,000 | 13 g/cc | Earth's inner core |
| 22,600 | 22.6 g/cc | Osmium, the densest element |
| 160,000 | 160 g/cc | The sun's core (est.) |
| ~1 x 109 | White dwarf star | |
| ~1 x 1017 | Neutron star or atomic nucleus |
Dimensionless values
A dimensionless value is simply a pure number. Examples include the fraction of air molecules that are oxygen (0.21 or 21%), the number pi (3.14159...), and Avogadro's number (6.02 x 1023. A dimensionless value might represent a fraction or percentage of some total, a ratio between two quantities such as the masses of the proton and the electron, or a total count (e.g., the population of a country, or the number of molecules in a glass of water).
Being a pure number, a dimensionless value or quantity has no associated units such as meters or kilograms. For large numbers that represent a total count, the number can alternatively be represented as a multiple of another number, for example two dozen (2x12 or 24), four score (4x20 or 80), a gross (144), or a mole (6.02 x 1023). For small numbers, alternate units can be given in terms of percent (%), parts per million (ppm), parts per billion (ppb), or parts per trillion (ppt).
Quick scale: Loosely speaking, numbers can be classified as either very small compared to the number 1, comparable to 1, or very large compared to 1.
| Value | Alternative Units | Description |
|---|---|---|
| Composition of air | ||
| 0.0004 | 0.04%, 400 ppm | Fraction of air molecules that are carbon dioxide (0% humidity) |
| 0.009 | 0.9% | Fraction of air molecules that are argon (0% humidity) |
| 0.006, 0.023, 0.073 | 0.6%, 2.3%, 7.3% | Fraction of air molecules that are water vapor at 100% humidity
and temperatures of 0, 20, 40 C (32, 68, 104 F), respectively |
| 0.21 | 21% | Fraction of air molecules that are oxygen (0% humidity) |
| 0.78 | 78% | Fraction of air molecules that are nitrogen (0% humidity) |
| 0.25-0.3 | 25-30% | Efficiency of a typical thermodynamic heat engine |
| 1 | 100% | One. Unity. The multiplicative identity. |
| 3 (approx.) | The numbers pi (3.14159...) and e (2.71828...) | |
| 3 | The number of quarks in a proton or neutron | |
| 8 | The number of planets in the solar system | |
| 22-23 | The number of revolutions the Sun has made around the galaxy | |
| 208 | The number of protons and neutrons, combined, in
a nucleus of lead-208, the heaviest stable atomic nucleus | |
| 4.6 x 106
4.6 million |
Median population of a state in the U.S.A.
2023: average of Louisiana and Kentucky, the 25th- and 26th-most populous states, respectively [1] | |
| 3.7 x 107
37 million |
Population of Tokyo (2018), the most populous city in the world | |
| 3.1 x 108
310 million |
Population of the USA (2010 census) | |
| 7.9 x 109
7.9 billion |
Population of the world (2021)[2] | |
| 1 to 4 x 1011
100 to 400 billion |
Estimated number of stars in the Milky Way galaxy | |
| 6 x 1023 | 1 mole | Avogadro's number
The number of hydrogen atoms in 1 gram, or the number of carbon-12 atoms in 12 grams |
| 9.9 x 1024 | 16 moles | The number of molecules in 10 fluid ounces (300 ml) of water |
| 10100 | 1 googol: The number 1 followed by 100 zeros. | |
Distance, length, height
Distance, length, and height are what may typically come to mind upon hearing the phrase "take a measurement".
The SI unit of length is the meter (m). Alternative units include:
- Angstroms
- Inches
- Feet
- Miles
- Astronomical units (AU)
- Light years
- Parsecs
Regarding distances that might be described as "far away," we typically use miles or kilometers to describe distances on Earth, astronomical units for distances within the solar system, and either light years or parsecs for distances to objects outside the solar system.
Quick scale: The Sun's diameter is about 100 times that of Earth, which is about 8 million times bigger than the height of a typical person. A person's height is about 250 times the size of a housefly, which in turn is about 60 million times bigger than the diameter of an atom of hydrogen.
| Value, in meters | Alternative Units | Description |
|---|---|---|
| 1.8 x 10-15 | Diameter of a proton (hydrogen nucleus) | |
| 1-1.2 x 10-14 | 10-12 fm | Diameter of nucleus for heavy atoms |
| 5.3 x 10-11
53 trillionths |
0.53 Angstroms | Radius of hydrogen atom (Bohr model) |
| 3 x 10-8
30 billionths |
30 nm | rhinovirus (cold virus) diameter |
| 0.8-1.2 x 10-7
80 to 120 billionths |
80-120 nm | Influenza virus diameter |
| 0.2-3 x 10-7
20 to 300 billionths |
20-300 nm | Virus diameter (typical range) |
| 4-7 x 10-7
400 to 700 billionths, or around half of one millionth |
400-700 nm | Wavelength range of visible light |
| 0.1-600 x 10-6
0.1 to 600 millionths |
Bacterium | |
| 1-2 x 10-5
10 to 20 millionths |
0.01-0.02 mm, 0.0004-0.0008 inches | Amoeba (typical) |
| 1 x 10-4
100 millionths |
0.1 mm, 0.004 or 1/250 inch | Human hair thickness (typical) |
| 6-7 x 10-3 | 6-7 mm, 1/4 inch | Housefly length (typical) |
| 1.5-1.8 | 5-6 feet | Human height (typical) |
| 25 | 82 feet | Blue whale length |
| 527 | 1729 feet | Sears Tower height (to top of antenna) |
| 8800 | 29,000 feet, 5.5 miles | Mount Everest, height above sea level |
| 9000-13,000 | 30,000-42,000 feet, 6-8 miles | Cruising altitude for commercial aircraft |
| 4 x 106
4 million |
4000 km, 2500 miles | North America, width at approx. 40 degrees North latitude;
Los Angeles-to-New York distance |
| 1.3 x 107
13 million |
13,000 km, 7900 miles | Earth's diameter |
| 3.0 x 108
300 million |
190,000 miles | One light-second, the distance that light travels in one second |
| 3.8 x 108
380 million |
240,000 miles | Earth-Moon distance |
| 1.4 x 109
1.4 billion |
870,000 miles | The Sun's diameter |
| 1.5 x 1011
150 billion |
1 Astronomical Unit (AU)
93 million miles 150 million km |
Earth-Sun average distance |
| 4.5 x 1012
4.5 trillion |
30 AU | Sun-Neptune distance |
| 9.46 x 1015 | 1 light-year
63.2 thousand AU |
The distance that light travels in one year |
| 3.09 x 1016 | 3.26 light years | 1 parsec |
| 4.0 x 1016 | 4.2 ly | Sun-Proxima Centauri distance |
| 8.6 x 1017 | 91 light years | Geometric mean of distances to 20 brightest stars, excluding the Sun
(One measure of a "typical" distance to the brighter stars in the sky) |
| 3.2 x 1018 | 340 light years | Mean of distances to 20 brightest stars, excluding the Sun
(Another measure of a "typical" distance to the brighter stars in the sky) |
| 9.5 x 1020 | 100,000 light years | Diameter of our galaxy, the Milky Way |
| 1.5 x 1021 | 160,000 light years | Distance to Large Magellanic Cloud |
| 2.4 x 1022 | 2.5 million light years | Distance to Andromeda galaxy |
Electric current
Electric current is a measure of the movement of electric charges in an electronic circuit. It represents the amount of charge, per unit time, that moves past a fixed location in a circuit.
The SI unit of electric current is the ampere (A) or amp, which is equivalent to 1 coulomb per second. I.e., one amp represents one coulomb of charge moving past a fixed location every second. One milliamp (mA) is one one-thousandth of an amp.
| Value, in amps | Alternative Units | Description |
|---|---|---|
| 0.01 | 10 mA | Current through typical LED indicator light |
| 0.5 | Current in 60 W, 120 V light bulb | |
| 15 | Current limit in typical household circuit breaker (U.S.A) | |
| Several hundred | Current to start an automobile |
Electric field
Electric field can be thought of in two ways. Ultimately, it is tied to the force exerted on charged objects by other charged objects.
One way to think of electric field is the amount of force exerted per unit of charge in a region of space. So, if the field is 5 newtons per coulomb in some region of space, then an object with a charge of 1 coulomb would experience a net force of 5 newtons (a little over 1 pound) from other charged objects. An object with a charge of 2 coulombs would experience twice the force of an object with 1 coulomb.
A more common way to express electric fields is in terms of the change in electrostatic potential per unit of distance. As such, the same 5 newtons-per-coulomb field can also be expressed as 5 volts per meter. In other words, the electric potential changes by 5 volts over a distance of 1 meter. However, as fields are rarely uniform over distances as large as a meter, it is more common to use smaller distances to express the field, such as volts per centimeter (V/cm) or, in a rare mix of SI and Imperial units, volts per mil, where 1 mil is 0.001 inches.
The SI unit of electric field can be expressed as either volts per meter (V/m) or newtons per coulomb (N/C), though it is more common to use V/m. Alternative units of V/cm or V/mil are also commonly used.
Quick scale: In the Bohr model of the hydrogen atom, the electric field is nearly 200,000 times higher than the breakdown field in air (field required to cause sparking or arcing). This in turn is 30,000 times higher than the electric field normally found near Earth's surface -- which helps explain why most of the time we are not experiencing a lightning storm.
| Value, in volts per meter | Alternative Units | Description |
|---|---|---|
| 100 | 1 V/cm | Typical field near Earth's surface |
| 9000 | Field (rms) between prongs of 120 V plug | |
| 3 x 106
3 million |
80 V/mil | Breakdown field for air at 1 atmosphere pressure |
| 1 to 3 x 107
10 to 30 million |
300 to 800 V/mil | Typical dielectric strengths of plastics |
| 5 x 1011
500 billion |
Field due to the proton on the electron in a hydrogen atom (Bohr model, ground state) |
Electric potential difference, a.k.a. voltage
Electric potential difference, or voltage, is the difference in electrical potential between two points, such as the positive and negative poles of a battery or other device that generates a flow of electrons, or between a point in a device and an electrical ground.
The SI unit of electric potential difference is the volt (V). This unit is used almost universally. Another unit, the statvolt, is used in some textbooks on electricity and magnetism.
Quick scale: A typical Van de Graaff generator has a voltage over 1000 times that of a household outlet, which has a voltage of roughly 10 to 100 times that of typical batteries.
| Value, in volts | Alternative Units | Description |
|---|---|---|
| 1.5 | Alkaline battery (AAA, AA, C, D cells) | |
| 12 | Automobile battery (Six 2-volt cells) | |
| 120 (AC) | Household wall outlet (U.S.) | |
| Several hundred thousand | Typical Van de Graaff generator |
Energy
Energy can have many different forms, for example heat, light, and sound. Kinetic energy is the energy an object has by virtue of its motion; the more massive or faster an object is, the more kinetic energy it has.
The SI unit of energy is the joule (J). Alternative units include:
- electron-volts (eV)
- megaelectron-volts (MeV)
- calories and Calories (with lowercase or uppercase "c")
- british thermal units (BTU)
- kilowatt-hours (kW-h)
| Value, in joules | Alternative Units | Description |
|---|---|---|
| 9.4 x 10-25 | 5.9 x 10-6 eV | Hyperfine energy difference in the ground state of a hydrogen atom |
| 6.1 x 10-21 | 0.038 eV | Energy of cesium-133 hyperfine transition used to define the second |
| 1.60 x 10-19 | 1 eV | One electronvolt |
| 2.8 x 10-19 | 1.8 eV | Low energy of visible-light photon (red, 700 nm wavelength) |
| 5.0 x 10-19 | 3.1 eV | High energy of visible-light photon (violet, 400 nm wavelength) |
| 2.2 x 10-18 | 13.6 eV | Energy to ionize a hydrogen atom |
| 8.2 x 10-14 | 0.5110 MeV | Electron rest-mass energy |
| 1.5 x 10-10
150 trillionths |
938.3 MeV | Proton rest-mass energy |
| 5 x 10-5
50 millionths |
Kinetic energy of housefly flying (12 mg, 3 m/s) | |
| 4.2 | 1 calorie (with lowercase "c") | One calorie, or the energy needed to raise
the temperature of 1 gram of water by 1 C. |
| 70 | Kinetic energy of human walking (80 kg, 1.3 m/s or 3 mph) | |
| 1055 | 1 BTU | One British thermal unit |
| 2400 | Kinetic energy of 0.22 caliber long-rifle bullet (40 g, 346 m/s) | |
| 4200 | 1 Calorie (with uppercase "C")
or 1000 calories (with lowercase "c") |
One "food Calorie", or the energy needed to raise
the temperature of 1 kilogram of water by 1 C. |
| 4300 | Kinetic energy of human world-class sprinter (80 kg, 10.4 m/s) | |
| 11,000 | 0.003 kW-h | Electrical energy in a battery: AA cell (1.5 volts, 2000 mA-hours) |
| 0.99 x 104
99,000 |
Energy to melt "10 fluid ounces" (300 g) of ice
Note: 10 fluid ounces of water are produced after melting. | |
| 1.2 x 105
120,000 |
Energy to heat 10 fluid ounces (300 g) of liquid water from 0 C to 100 C (32 F to 212 F) | |
| 6.7 x 105
670,000 |
Energy to boil 10 fluid ounces (300 g) of water | |
| 3.6 x 106
3.6 million |
1 kW-h | One kilowatt-hour
A good example benchmark to answer the question: How small is one joule of energy? |
| 2.2 x 108
220 million |
Energy consumed by 60 W filament lightbulb in 1000 hours lifetime. | |
| 3.7 x 109
3.7 billion |
Potential energy of satellite-Earth system: 1000 kg satellite at 400 km altitude | |
| 2.9 x 1010
29 billion |
Kinetic energy of 1000 kg satellite in 400 km altitude low-Earth orbit
This is roughly eight times the potential energy of raising the satellite to this altitude. | |
| 9.0 x 1016 | Rest-mass energy of one kilogram of mass | |
| 1 x 1019 | Annual electrical consumption of USA (1999) | |
| 1.8 x 1032 | Difference in kinetic energy of Earth at perihelion and aphelion (relative to the Sun)
Difference in potential energy of Earth-Sun system at perihelion and aphelion | |
| 2.65 x 1033 | Kinetic energy of Earth, in the Sun's rest frame | |
| -5.30 x 1033 | Gravitational potential energy of the Sun and Earth, relative to infinite separation |
Force
Force is an interaction between two objects, and quantifies how strongly two objects either push or pull on each other. Two objects always push (or pull) on each other with the same amount of force -- a fact that can be difficult to fully grasp, but is in fact the third law in Newton's three laws of motion.
The SI unit of force is the newton (N). Alternative units are pounds-force (lbf), not to be confused with pounds, which are a unit of mass.
Quick scale: The force of gravity between the Sun and Earth is about 6 x 1019 times the weight of a typical person, i.e. the force of gravity between Earth and a person. A typical person's weight is about 8 billion times stronger than the force between an electron and proton in a hydrogen atom.
| Value, in newtons | Alternative Units | Description |
|---|---|---|
| 8.2 x 10-8 | Force between an electron and proton in a hydrogen atom (Bohr model) | |
| 450-1100 | 100-240 lb (force) | Typical person's weight |
| 2.0 x 1020 | Gravitational force between Earth and the Moon | |
| 3.5 x 1022 | Gravitational force between Earth and the Sun |
Frequency
Frequency is the repetition rate at which cyclical (repetitive) phenomena repeat.
This section is for cyclical or periodic phenomena other than those involving rotations or revolutions, which are covered in the section "speed, angular or rotational"
The SI unit of frequency is the hertz, which is the number of cycles per second of the repeating phenomenon, for example the 50 or 60 cycles per second used for common household electricity. Alternatively, it can be expressed in terms of the repeat-time period, for example "once every 12 hours and 25 minutes" in the case of ocean tides.
Quick scale: The frequency of a visible light wave is about 4 to 7 million times greater than that of a typical FM radio wave, which is about 500 thousand times greater than that of household electricity, which in turn is near the low end of audible sound frequencies.
| Value, in hertz | Alternative Units | Description |
|---|---|---|
| 2.2 x 10-5
22 millionths |
Once every 12 hours and 25 minutes | Ocean tides |
| 50 or 60 | Household electrical outlet | |
| 20 - 20,000 | Audible sound | |
| 1 x 106
1 million |
1000 kHz AM radio frequency | |
| 1 x 108
100 million |
100 MHz FM radio frequency | |
| 2.45 x 109
2.45 billion |
Microwave oven frequency | |
| 9.19 x 109
9.19 billion |
Frequency of cesium-133 hyperfine transition used to define the second | |
| 4.3-7.5 x 1014
430 to 750 trillion |
Frequency of visible light (700-400 nm wavelength) |
Magnetic field (a.k.a. magnetic flux density)
Most of us are familiar with magnets in our everyday lives. This section lists the strengths of various magnetic phenomena.
The SI unit of magnetic field strength is the tesla (T). Alternative units are in gauss (G).
Quick scale: The magnetic field strength used for an MRI is between 50 to 300 times stronger than a common household refrigerator magnet, which in turn is 300 times stronger than Earth's magnetic field.
| Value, in tesla | Alternative Units | Description |
|---|---|---|
| 2.5 to 6.5 x 10-5
25 to 65 millionths |
0.25 to 0.65 G | Earth's magnetic field at Earth's surface (0.25 G near the equator, 0.65 G near the poles) |
| 0.01 | 100 G | Common household refrigerator magnet |
| 0.5 to 3 | Field used for MRI | |
| 45 | Highest human-made magnetic field, continuous use [3] | |
| 100 | Highest human-made magnetic field, repeatable pulses (0.015 second pulse duration) |
Mass
Mass is the quantity of matter that comprises an object. Strictly speaking, mass is different than weight, which is the strength of the force (or "pull") of gravity on an object. A person standing on the Moon has the same mass, but less weight, than they do when standing on Earth. This is because a person has the same amount of matter wherever they are, but the Moon pulls on them with less gravitational force than Earth does.
The SI unit of mass is the kilogram (kg). Alternate units include:
- milligrams (mg)
- grams (g)
- avoirdupois ounces (oz), not to be confused with fluid ounces
- pounds (lbs)
- solar masses
Quick scale: The Sun's mass is about 300,000 times that of Earth, which is of order 1023 -- i.e., 1 followed by twenty-three 0s -- times that of a typical person. A typical person is about 6 million times more massive than a housefly, which in turn is of order 1022 times more massive than an atom of hydrogen.
| Value, in kilograms | Alternative Units | Description |
|---|---|---|
| 9.1 x 10-31 | Electron | |
| 1.7 x 10-27 | 1836 times the mass of the electron | Proton, or hydrogen atom |
| 3.5 x 10-25 | Lead-208, the heaviest stable atomic isotope | |
| 1.2 x 10-5
12 millionths |
12 mg | Housefly |
| 0.040 | 40 g | Standard-velocity 0.22 caliber bullet |
| 0.30 | 300 grams, 10.4 ounces | 10 fluid ounces of water |
| 4-8 | 10-20 lbs | House cat |
| 75 | 165 lbs | Human (typical) |
| 1-2 x 105
100,000 to 200,000 |
200,000-400,000 lbs, 100-200 tons | Blue whale |
| 6 x 109
6 billion |
13 billion lbs | Great Pyramid at Giza, Egypt |
| 6 x 1010
60 billion |
130 billion lbs | Three Gorges Dam, Hubei province, China |
| 5 x 1018 | 1 x 1019 lbs | Earth's atmosphere |
| 1.4 x 1021 | 3 x 1021 lbs | Earth's oceans |
| 7.3 x 1022 | The Moon | |
| 6.0 x 1024 | Earth | |
| 1.9 x 1027 | Jupiter | |
| 2.0 x 1030 | 1 solar mass | The Sun |
| 1.5 x 1031 | 7.5 solar masses | Betelgeuse, a supergiant star |
| 1.3 x 1032 | 65 solar masses | Total mass of binary black hole system in first-ever detection of gravitational waves (2015) |
| 8.2 x 1036 | 4.1 x 106 solar masses | Black hole at center of Milky Way galaxy |
| 1 x 1040 | 6-7 x 109 solar masses | Black hole in M87, the first black hole ever imaged (2019) |
| 1 x 1042 | 5 x 1011 solar masses | Milky Way galaxy (our galaxy) |
| 2-3 x 1042 | Local group of galaxies | |
| 2-3 x 1045 | Local (Virgo) supercluster of galaxies |
pH
The pH of an aqueous (water) solution is a measure of the degree of acidity of the solution. It is generally assumed that the solution is near room temperature, or more specifically at 25 degrees Celsius (77 degrees Fahrenheit).
pH is indicated by a numerical scale, with "7" indicating a neutral solution. Acidic solutions have a pH less than 7, while basic solutions have a pH greater than 7.
pH is a measure of the concentration of hydrogen ions. This concentration, in moles per liter of solution, can be found by raising 10 to the power of the negative of the pH value. For example, a pH of 2 indicates a hydrogen ion concentration of 10-2, or 0.01, moles per liter. A pH of 6 indicates a hydrogen ion concentration of 10-6, or one millionth, moles per liter.
A more extensive version of the following table appears in the main pH article.
| pH value | Alternative Units
moles/liter |
Description |
|---|---|---|
| 2 | 0.01
1 hundredth |
Lemon juice, vinegar |
| 3 | 0.001
1 thousandth |
Orange juice |
| 5 | 0.00001
10 millionths |
Black coffee |
| 7 | 0.0000001
1 tenth of 1 millionth |
Distilled water, neutral solutions |
| 11 | Household ammonia | |
| 14 | Drain cleaner |
Power
Power can be thought of as the rate at which energy is either produced or consumed. Strictly speaking, energy can be neither created nor destroyed, so in reality power is the rate at which energy is converted from one form into another.
The SI unit of power is the watt (W), equivalent to the production or consumption of one joule of energy every second. Alternate units include the horsepower (1 hp = 746 W) and the british thermal unit per hour (1 BTU/hr = 0.293 W).
Quick scale: The total power radiated by the Sun, if converted to electricity with 100% efficiency, would be enough to power several quadrillion (1015) large cities of 1 million people each. A city that size consumes the equivalent of 20-30 million traditional lightbulbs in electricity, or 20-30 bulbs per person.
| Value, in watts | Alternative Units | Description |
|---|---|---|
| 0.001 | 1 mW | Power in beam of a typical laser pointer |
| 0.5 - 1.0 | Power output of a small DC electric motor (12 V, 0.1 - 0.2 A) | |
| 60 | Traditional incandescent lightbulb power | |
| 250 | 0.33 hp | Power output of a moderate-sized (1/3 horsepower) electric motor |
| 1000-1500 | Typical power consumption of a microwave oven, toaster oven, or electric heater | |
| 90,000 | 120 hp | Power output of a small (120 horsepower) car engine |
| 1-2 x 109
1-2 billion |
Typical electrical power consumption for a large U.S. city (pop. 1 million) | |
| 2 x 1017
200 quadrillion |
Power radiated by the Sun that reaches Earth
(About 1/2 of 1 billionth of the total power radiated by the Sun) | |
| 4 x 1026 | Total power radiated by the Sun |
Pressure
Pressure can loosely be thought of as a measure of the force exerted by a gas or liquid on objects in contact with the gas or liquid. It is actually the force per area that is exerted.
The SI unit of pressure is the pascal (Pa), equivalent to one newton of force distributed over an area of one square meter. Other common units are the standard atmosphere (atm), pounds per square inch (psi), millimeters of mercury (mm Hg) or equivalently Torr, and millibar (mbar).
Pressure values can be expressed as either absolute pressure or gauge pressure. Absolute pressure is the actual force-per-area exerted by the gas or liquid. Gauge pressure is the difference of the absolute pressure minus the surrounding atmospheric pressure. Gauge pressure is useful in that it gives the next force (per area) exerted on a container wall with the gas or liquid of interest on one side and the ambient atmosphere on the other, or can also be used to express deviations of air pressure from standard atmospheric pressure. The units for a gauge-pressure measurement in psi are written as "psig," to distinguish it from an absolute pressure measurement.
Quick scale: The pressure used to make synthetic diamond is several hundred million times that of the atmosphere. The pressure in a good laboratory vacuum system is around one trillionth of that of the atmosphere.
| Value, in pascals | Alternative Units | Description |
|---|---|---|
| 1 x 10-7 | 1 x 10-12 atm
1 x 10-9 mbar |
Laboratory ultra-high vacuum conditions |
| 600 | 0.006 atm | Atmospheric pressure on Mars |
| 34,000 | 1/3 atm | Air pressure at summit of Mt. Everest (8849 m or 29,032 ft above sea level) |
| 91,000 | 0.90 atm (-0.10 atm gauge pressure)
910 mbar |
Typical category-5 hurricane |
| 98,000 | 0.97 atm (-0.03 atm gauge pressure)
980 mbar |
Typical category-1 hurricane |
| 100,000 | 1.0 atm
15 psi, 760 mm Hg, 1013 mbar |
Atmospheric pressure |
| 700,000 to 800,000 | 7-8 atm
100-120 psi |
Typical workshop air compressor |
| 21 million | 200 atm
3000 psi |
Standard scuba tank pressure |
| 5 to 6 billion | 50 to 60 thousand atm | Pressure used to make synthetic diamond |
Speed
In addition to representing the rate at which something moves, speed can also represent the rate at which two objects either approach each other or separate, as in the case of Africa and South America.
The SI unit of speed is meters per second (m/s), and alternative units can be based on any alternative units for time and/or distance. Extremely fast speeds can be given in comparison to the speed of light c, e.g. (2/3)c for two-thirds as fast as the speed of light.
Quick scale: The speed of light is 30 million times faster than a fast human sprinter, and a fast sprinter is 5 billion times faster than the speed at which Africa and South America are moving apart from one another.
| Value, in meters per second | Alternative Units | Description |
|---|---|---|
| 2 x 10-9
2 billionths |
6 cm or 2 inches per year | Rate of separation of Africa and South America |
| 1 x 10-7
100 billionths |
3 inches per week | Rate at which grass grows (est.) |
| 7 x 10-6
7 millionths |
Tip of hour hand on a wall clock (2" length) | |
| 2 x 10-4 or 0.0002
200 millionths |
Tip of minute hand on a wall clock (4" length) | |
| 0.01 | 1 cm or 0.4 inches per second | Tip of second hand on a wall clock (4" length) |
| 0.03 | 1 inch per second | Insect walking |
| 1.3 | 3 miles per hour (mph) | Human walking |
| 6.7 | "4-minute mile"
15 mph |
Fast human distance runner |
| 10 | 100 meters in 10 seconds
22 mph |
Fast human sprinter |
| 27 | 60 mph | Automobile highway speed |
| 107 | 240 mph | Approx. top speed of Indy race car |
| 343 | 767 mph | Speed of sound (dry air, atmospheric pressure, 20 C temperature)
Standard muzzle velocity of 0.22 caliber long rifle |
| 460 | 1000 mph | Speed of Earth's surface at equator |
| 510 | 1100 mph | Speed (rms) of air molecule at around room temperature (27 C, 300 K) |
| 1020 | 2280 mph | The Moon (relative to Earth) |
| 2700 | 6000 mph | Speed (rms) of a hydrogen atom at around room temperature (27 C, 300 K) |
| 3100 | 6900 mph | Satellite in geosynchronous orbit (rela. to Earth) |
| 4700 | 10,500 mph | Pluto (rela. to the Sun) |
| 7670 | 17,200 mph | Satellite in low-Earth orbit (400 km altitude) |
| 30,000 | 67,000 mph | Earth (rela. to the Sun) |
| 48,000 | 110,000 mph | Mercury (rela. to the Sun) |
| 200,000 | c/1500
450,000 mph |
The Sun (rela. to the center of our galaxy |
| 2.2 x 106
2.2 million |
c/137, or roughly 1% of the speed of light | Speed of electron in hydrogen ground state (Bohr model) |
| 2 x 108
200 million |
(2/3)c | Speed of light in glass
Speed of electronic signal in typical coaxial cable |
| 2.6 x 108
260 million |
0.87c | Speed of an object when its kinetic energy is equal to its rest mass energy mc2 |
| 3 x 108
300 million |
186,000 miles per second | The speed of light, c |
Speed, angular or rotational
This section is for rotational (spinning) motion or the revolution (orbiting) of an object about another object. For periodic phenomena that do not involve rotation or revolution, see the frequency section.
Values are given in terms of cycles (rotations or revolutions) per second. Revolutions per minute (rpm) are used as well.
Quick scale: Air molecules at room temperature spin roughly 100 billion times faster than a car engine, which in turn spins one to ten million times faster than Earth about its axis.
| Value, in cycles per second (hertz) | Alternative Units | Description |
|---|---|---|
| 3.17 x 10-8
317 billionths |
Once per year | Revolution of Earth about the Sun |
| 1.16 x 10-5
11.6 millionths |
Once every 23 hours, 56 minutes, and 4 seconds,
or roughly once per day |
Rotation of Earth about its axis |
| 0.0167 or 1/60 | 1 rpm | One revolution per minute |
| 0.556, 0.75, 1.3 | 33-1/3, 45, 78 rpm | Phonograph records
The progression from 78 to 33-1/3 rpm records is a mid-20th-century, analog example of increasing data storage density. |
| 12.5 | 750 rpm | Car engine, idling |
| 83-100 | 5000-6000 rpm | Car engine, typical maximum speed |
| ~1012 to 1013
1 to 10 trillion |
Typical rotation speed of an air molecule at room temperature |
Temperature
While Celsius and Fahrenheit are two commonly used temperature scales, for comparison purposes it is best to use an absolute temperature scale, so Kelvins (K) are the main units in the listings below.
| Value, in Kelvins | Alternative Units | Description |
|---|---|---|
| 0 | -273 C, -460 F | Absolute zero |
| 2.7 | Cosmic microwave background | |
| 4.2 and less | Liquid helium | |
| 20 and less | Liquid hydrogen | |
| 77 and less | Liquid nitrogen | |
| 90 and less | Liquid oxygen | |
| 184 | -89 C, -128 F | Coldest recorded (natural) temperature on Earth
(Vostok Station, Antarctica, on July 21, 1983) |
| 195 and less | -78 C, -109 F | "Dry ice", frozen carbon dioxide |
| 273 | 0 C, 32 F | Water freezes, or cold weather |
| 293-296 | 20-23 C, 68-73 F | Room temperature, or mild weather |
| 310 | 37.0 C, 98.6 F | Human body temperature, or very hot weather |
| 373 | 100 C, 212 F | Water boils |
| 450 | 177 C, 350 F | Moderately hot household oven |
| 530 | 260 C, 500 F | Very hot household oven |
| 770 | 500 C, 930 F | Faintly red-hot object |
| 970 | 700 C, 1300 F | Moderately red-hot object |
| 2800 | 2500 C, 4600 F | Tungsten lightbulb filament (typical), a white-hot object |
| 5800 | 5500 C, 9900 F | The Sun's surface |
| 10,000 | 9700 C, 17,500 F | Surface of a blue-hot star.
Examples: Sirius is 9940 K. Rigel is 11,000 K. |
| 1.5 x 107
15 million |
1.5 x 107 C, 2.7 x 107 F | The Sun's center |
Thermal conductivity
Thermal conductivity is a measure of the ability of a material to conduct heat.
The SI unit of thermal conductivity is watts per meter-kelvin, or W/(m•K). This is equivalent to W/(m•°C) since it is differences in temperature that are relevant in calculations that involve thermal conductivity, so kelvins are then interchangeable with degrees Celsius. Alternative units are W/(cm•K) and BTU/(hr•ft•°F).
Quick scale: The thermal conductivity of copper is about 20 times that of a poor metal conductor like stainless steel, which is about 20 times that of glass. Glass is about 40 times more conductive than air.
Values given are for near-room-temperature conditions.
| Value, in watts per meter-kelvin | Alternative Units | Description |
|---|---|---|
| 0.025 | Air (1 atm pressure) | |
| 0.12-0.33 | Common plastics | |
| 0.6 | Water | |
| 1 | Glass | |
| 16-20 | Stainless steel | |
| 166-237 | Aluminium: 237 is for pure aluminium. 166-200 is for alloys typically used in aluminium heat sinks. Other alloys can be outside the stated range. | |
| 400 | Copper | |
| 2000 | Diamond |
Time
Note, the repeat periods of cyclical phenomena, like the cycle time of a typical sound frequency, are not generally included here. Doing so would simply repeat information that can be found in the frequency section of this article. An exception is made for the period of rotation or revolution of astronomical bodies such as Earth or the Moon, since these have historically served as standard definitions of time intervals like the day or the year.
The SI unit of time is the second. Alternative units are minutes, hours, days, weeks, months, and years.
Quick scales: The age of the solar system, and by extension Earth, is roughly 60 million human lifetimes. A typical human lifetime is 25 to 30 thousand days or 2 to 2-1/2 billion seconds. One year is roughly π x 107 seconds, or, more precisely, 31.56 million seconds.
| Value, in seconds | Alternative Units | Description |
|---|---|---|
| 1.1 x 10-10
110 trillionths |
Period of cesium-133 hyperfine transition used to define the second | |
| 1.6 x 10-9
1.6 billionths |
Lifetime of the first excited state of a hydrogen atom | |
| 0.2 | Human reaction time (typical) | |
| 1.3 | Light travel time, Earth to the Moon (one-way) | |
| 500 | 8.3 minutes | Light travel time, Earth to the Sun (one-way) |
| 5500 | 92 minutes | Orbital period of satellites at 400 km altitude, a typical low-Earth orbit. |
| 86,400 | 1 Day | One day |
| 2.36 x 106
2.36 million |
27.3 days | Orbital period of the Moon |
| 2.55 x 106
2.55 million |
29.5 days | Synodic period of the Moon, or period of the Moon's phases |
| 3.16 x 107
31.6 million |
1 Year | Orbital period of Earth |
| 2.4 x 109
2.4 billion |
76 years | Human lifetime (typical) |
| 7.8 x 109
7.8 billion |
248 years | Orbital period of Pluto |
| 1.2 x 1013
12 trillion |
380,000 years | Age of the universe when neutral hydrogen atoms formed |
| 6.2 x 1015 | 200 million or 0.20 billion years | Orbital period of the Sun around the galaxy |
| 1.4 x 1017 | 4.5 billion years | Age of the solar system |
| 4.3 x 1017 | 13.7 billion years | Age of the universe |