An absolute constant is a number that has the same value wherever it appears. Examples:

• π (pi) has the value 3.14159… at all times. The … means that I’ve given up at giving you ALL the decimal places of pi. As you probably know, these decimals go on forever.
• e(Euler’s number) has the value 2.71828… at all times.
• Same deal on the …, the decimals go on forever with no sign of a repeating pattern.
• c (the speed of light in a vacuum) has the value 186,232 miles per second at all times.

Some constants are bare numbers, like pi and e. They are just numbers and don’t have units of measurement attached to them. Other constants are physical constants, for example, c (the speed of light). A physical constant describes the size of something in the physical universe, so it must have a unit of measurement attached. In the case of c, it’s miles per second for us stubborn Americans, and meters per second for most others in the world.

The same absolute constant may pop up in different parts of nature and in different parts of mathematics. Take, for example, the number pi. When it is multiplied times the diameter of a circle, the result is the circumference of the circle. That is the context in which the ancient Greeks first noticed pi over 2,000 years ago. But pi appears in nature and mathematics in other contexts. For example, pi is multiplied times energy and momentum to find the strength of gravity in Einstein’s Theory of General Relativity.

Pi also appears in equations regarding the behavior of quantum particles as well as equations for calculating probabilities in statistical analyses. In mathematics, it is found in equations about prime numbers. Pi pops up in physics and math more than any number has a right to, but other absolute constants also can surprise with the unexpected places that they show up.

The term “absolute constant” is not a commonly used. Usually, people just say “constant.” You can use the term “absolute constant” however, to distinguish it from other types of constants: 1) constants in an algebra equation (algebraic constants) or 2) constants of nature that vary with the situation.

Constants of nature that vary with the situation. The term “absolute constant” would also be used if one wanted to distinguish it from a type of constant that actually has variation in it. For example, one of the equations for the behavior of gases includes a constant of this type. It’s the equation for the amount of kinetic energy in a box of gas given its pressure, volume, and temperature. The amount of kinetic energy varies depending upon how many gas molecules are in the box. The more molecules, the more kinetic energy is in the box.

But the amount of kinetic energy is said to be a constant for any particular number of molecules. The type of gas doesn’t matter. For example, a certain number of oxygen molecules in a box will generate the same amount of kinetic energy as would carbon dioxide molecules.

For you among us who are not faint of heart, here’s the equation: (PV )/T =nk where P = pressure; V = volume; T = temperature in Kelvin; n = number of molecules; and k = Boltzmann’s constant. One can say that (PV )/T is a constant. However, it is not an absolute constant. It varies depending on the number of molecules in the box. There is an absolute constant in this equation: Boltzmann’s constant. It is the average amount of kinetic energy per molecule of gas at a specified temperature (1.3807 x 10^-23 joules per kelvin).