Benchmark quantities

	Main Article	Discussion	Related Articles  [?]	Bibliography  [?]	External Links  [?]	Citable Version  [?]
	This editable Main Article is under development and subject to a disclaimer. [edit intro]

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[edit]

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.

Density[edit]

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.

Dimensionless values[edit]

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.

Distance, length, height[edit]

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.

Electric current[edit]

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.

Electric field[edit]

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.

Electric potential difference, a.k.a. voltage[edit]

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.

Electrical resistivity[edit]

Energy[edit]

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)

Force[edit]

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.

Frequency[edit]

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.

Magnetic field (a.k.a. magnetic flux density)[edit]

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.

Mass[edit]

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.

pH[edit]

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.

Power[edit]

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.

Pressure[edit]

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.

Speed[edit]

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.

Speed, angular or rotational[edit]

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.

Temperature[edit]

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.

Thermal conductivity[edit]

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.

Time[edit]

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.