Constants

Package: CONSTANTS_PACKAGE. Registered by createEngine(); for a slimmer engine, register it explicitly (see choosing packages).

Reach for a well-known constant by name instead of typing the digits. Where a constant has a unit, it arrives as a proper quantity, so it converts and multiplies like any other measurement.

Dimensioned constants

The speed of light and the acceleration of gravity carry their units:

speed of light // 299,792,458.00 m/s
gravity // 9.81 m/s²

Because they are real quantities, they take part in the arithmetic. Gravity times a mass is a force, and it reads out in newtons through the named derived units:

gravity * 70 kg as N // 686.47 N
speed of light in km/h // 1,079,252,848.80 km/h

Mathematical constants

tau is a full turn, 2π, and the golden ratio (also phi) is the proportion that appears throughout art and nature. pi and e are already built in.

tau // 6.28
golden ratio // 1.62

Each is a number with a name, exactly as pi is, so it goes anywhere a number does. An amount written straight before one multiplies it, the way 2pi is two times pi, and an equation or a function can hold one:

2tau // 12.57
3 golden ratio // 4.85
(1 + 1)tau // 12.57
solve(x^2 = tau, x) // [-2.51, 2.51]
solve(x^2 = 2tau, x) // [-3.54, 3.54]
der(tau*x^2, x) // 12.5663706144x

A constant with a unit goes into a function or a map the same way, and the answer keeps its unit. A function here is a formula you name once and use again, f(m) = m * gravity read as “the weight of a mass m”; a map works an expression out for each item of a list.

f(m) = m * gravity // f(m) defined
f(70 kg) as N // 686.47 N

map(x * gravity, [1, 2]) // [9.81 m/s², 19.61 m/s²]

The boundary is the dimensioned constants. A bare amount before gravity or speed of light is not read as a product, since 2 gravity could as well mean two of something measured in gravities; write the *. And an equation, a derivative or an integral works on a formula, which is algebra on plain numbers and has nowhere to keep a unit, so a constant with a unit there is refused for its unit, and the line says which:

solve(x = gravity * 2, x) // A formula keeps no units, so combining "x" with an amount in m/s² would drop the m/s². Give "x" a value on a line above, or write the formula without the unit.

A constant in a unit the engine cannot write yet (planck, avogadro) is a plain number, so an equation takes it as it takes any number.

Physical constants (values)

These are precise scientific values. Avogadro’s number is large enough to show in full; the others are so small that the default display rounds them, so they are listed here with their proper values and units:

avogadro // 602,214,076,000,000,000,000,000

constant	value	unit
planck	6.62607015 × 10⁻³⁴	J·s
boltzmann	1.380649 × 10⁻²³	J/K
elementary charge	1.602176634 × 10⁻¹⁹	C
gas constant	8.314462618	J/(mol·K)
avogadro	6.02214076 × 10²³	mol⁻¹
electron mass	9.1093837015 × 10⁻³¹	kg
proton mass	1.67262192369 × 10⁻²⁷	kg

electron mass and proton mass carry their kilograms, and boltzmann its joules per kelvin, so they convert and combine like the other dimensioned constants: the Boltzmann constant times a temperature is an energy.

boltzmann // 1.38e-23 J/K
boltzmann * 300 K // 4.14e-21 J

The rest are in units the engine cannot write yet: a joule-second, a coulomb (the unit of electric charge), and anything per mole (the chemist’s count of particles). Each of them is a plain number, and scaling one by a plain number works as it always has. What is refused is meeting a quantity, since a plain number takes the other side’s unit and the answer would be labelled wrongly: Planck’s constant times a frequency is an energy, not a number of hertz.

planck * 5e14 // 3.31e-19
avogadro * 2 // 1,204,428,152,000,000,000,000,000
planck * 5e14 Hz // A constant measured in J·s and a quantity in Hz cannot be multiplied: the engine cannot spell J·s yet, so the answer would wrongly be in Hz. Leave the unit off the other side and read the result in the unit it should have.

The refusal applies to the constant itself, as written or held in a variable. A value already worked out from one, planck * 2, is an ordinary number.