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### IMSL_CONSTANT

IMSL_CONSTANT

The IMSL_CONSTANT function returns the value of various mathematical and physical constants.

The names allowed are listed in the table that follows. Values marked with (mp) are exact (to machine precision). The references in the right-hand column are indicated by code numbers: (1) for Cohen and Taylor (1986), (2) for Liepman (1964), and (3) for precomputed mathematical constants. The supported units are listed below.

 Name Description Value Ref. amu atomic mass unit 1.6605655 x 10–27 kg 1 ATM standard atm. pressure 1.01325 x 105 N/m2 (mp) 2 AU astronomical unit 1.496 x 1011 m Avogadro Avogadro’s number, N 6.022045 x 1023 1/mole 1 Boltzman Boltzman’s constant, k 1.380662 x 10–23 J / K 1 C speed of light, c 2.997924580 x 108 m/s 1 Catalan Catalan’s constant 0.915965... (mp) 3 E base of natural logs, e 2.718... (mp) 3 ElectronCharge electron charge, e 1.6021892 x 10–19 C 1 ElectronMass electron mass, me 9.109534 x 10–31 kg 1 ElectronVolt electron volt, ev 1.6021892 x 10–19 J 1 Euler Euler’s constant, γ 0.577... (mp) 3 Faraday Faraday constant, F 9.648456 x 104 C/mole 1 FineStructure fine structure, α 7.2973506 x 10–3 1 Gamma Euler’s constant, γ 0.577... (mp) 3 Gas gas constant, R0 8.31441 J/mole/K 1 Gravity gravitational constant, G 6.6720 x 10–11 N m2 / kg2 1 Hbar Planck’s constant / 2π 1.0545887 x 10–34 J s 1 PerfectGasVolume std. vol. ideal gas 2.241383 x 10–2 m3 / mole 1 Pi Pi, π 3.141... (mp) 3 Planck Planck’s constant, h 6.626176 x 10–34 J s 1 ProtonMass proton mass, Mp 1.6726485 x 10–27 kg 1 Rydberg Rydberg’s constant, Rinfinity 1.097373177 x 107 /m 1 Speedlight speed of light, c 2.997924580 x 108 m/s 1 StandardGravity standard g 9.80665 m/s2 (mp) 2 StandardPressure standard atm. pressure 1.01325 x 105 N/m2 (mp) 2 StefanBoltzman Stefan-Boltzman, σ 5.67032 x 10–8 W/K4 /m2 1 WaterTriple triple point of water 2.7316 x 102 K 2

The units allowed are as follows:

 Unit Description time day, hour = hr, min = minute, s = sec = second, year frequency Hertz = Hz mass AMU, g = gram, lb = pound, ounce = oz, slug distance Angstrom, AU, feet = foot, in = inch, m = meter = metre, micron, mile, mill, parsec, yard area acre volume l = liter = litre force dyne, N = Newton energy BTU, Erg, J = Joule work W = watt pressure ATM = atmosphere, bar temperature degC = Celsius, degF = Fahrenheit, degK = Kelvin viscosity poise, stoke charge Abcoulomb, C = Coulomb, statcoulomb current A = ampere, abampere, statampere voltage Abvolt, V = volt magnetic induction T = Tesla, Wb = Weber other units l, farad, mole, Gauss, Henry, Maxwell, Ohm

The metric prefixes listed in the next table can be used with the previous units. The one- or two-letter prefixes can only be used with one-letter unit abbreviations.

 Prefix Definition Value a atto 10–18 f femto 10–15 p pico 10–12 n nano 10–9 u micro 10–6 m milli 10–3 c centi 10–2 d deci 10–1 dk deca 102 k kilo 103 myria 104 mega 106 g giga 109 t tera 1012

There is no one-letter unit abbreviation for myria or mega since m means milli.

## Examples

### Example 1

In this example, Euler’s constant γ is obtained and printed. Euler’s constant is defined to be as follows:

`PM, IMSL_CONSTANT('gamma')`
`0.577216`

### Example 2

In this example, the speed of light is obtained using several different units.

`c1 = IMSL_CONSTANT('SpeedLight', 'meter/second')`
`c2 = IMSL_CONSTANT('SpeedLight', 'mile/second')`
`c3 = IMSL_CONSTANT('SpeedLight', 'cm/ns')`
`PM, 'speed of light = ', c1, c2, c3, \$`
`  Title =' meters/second ' + \$`
`  'miles/second cm/ns'`

IDL prints:

`meters/second miles/second cm/ns`
`speed of light = 2.99792e+008 186282. 29.9792`

## Syntax

Result = IMSL_CONSTANT(Name[, Units]] [, /DOUBLE])

## Return Value

By default, returns the desired constant. If no value can be computed, NaN (Not a Number) is returned.

## Arguments

### Name

Scalar string specifying the name of the desired constant. The case of the characters is not relevant when specifying name, i.e., character strings “PI”, “Pi”, “pI”, and “pi” are equivalent. Spaces and underscores are allowed and ignored.

### Units (optional)

Scalar string specifying the units of the desired constant. If empty, then Systeme International d’Unites (SI) units are assumed. The case of the characters is not relevant when specifying units, i.e., character strings “METER”, “Meter”, and “meter” are equivalent. Parameter units has the form “U1*U2*...*Um/V1/.../Vn,” where Ui and Vi are the names of basic units or the names of basic units raised to a power. Basic units must be separated by * or /. Powers are indicated by ^, as in “m^2” for m2. Examples are “METER*KILOGRAM/SECOND”, “M*KG/S”, “METER”, or “M/KG^2”.

## Keywords

### DOUBLE (optional)

If present and nonzero, double precision is used.

## Errors

### Warning Errors

MATH_MASS_TO_FORCE: Conversion of units-of-mass to units-of-force required for consistency.

## Version History

 6.4 Introduced

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