The DimensionEngine calculator includes numerous built-in functions for advanced analyses.
Clicking on any function here will automatically insert it under the Input tab.
Search below by category or use the alphabetical listing.
Categories
- Constants
- Basic Functions
- Trigonometric Functions
- Advanced Mathematical Functions
- Vector Functions
- Functions of User-Defined Functions
- Other Functions
Constants
- Boltzmann() = 1.3806504e-23 J / degK
- CLight() = 299792458.0 m/s (speed of light)
- euler() = 0.5772156649015328606065120900824024310422
- gas() = 8.31434 J / mol / degK = kg m^2 / s^2 degK mol
- GEarth() = 6.67428e11 m^3 / kg s^2 (Earth's gravitational constant)
- grav() = 9.806652 m / s^2
- pi() = 3.1415926535897932384626433832795028841972
- Planck() = 6.62606896e-34 kg m^2 / s (Planck's constant)
- StefanBoltzmann() = 5.670400e-8 W m^2 / degK^4
Basic Functions
- abs(x) = absolute value of x
- ceil(x) = round x up to nearest integer
- exp(x) = exponential of x
- floor(x) = round x down to nearest integer
- int(x) = round x down to nearest integer
- LinInterp(x1, y1, x2, y2, x) = y1 + (x - x1) * (y2 - y1) / (x2 - x1)
- ln(x) = natural logarithm of x
- log(x) = natural logarithm of x
- log10(x) = log base 10 of x
- mod(x, y) = floating point remainder of y / x
- Normsdist(z) = standard normal cumulative distribution (mean = 0, stdev = 1)
- Normsinv(z) = inverse of the standard normal cumulative distribution (mean = 0, stdev = 1)
- Number(x, units) = dimensionless value of x in units
- round(x) = round x to nearest (up or down) integer
- sign(x) = sign of x
- sqrt(x) = square root of x
Trigonometric Functions
- acos(x) = arccosine of x
- acot(x) = arccotangent of x
- acsc(x) = arccosecant of x
- asec(x) = arcsecant of x
- asin(x) = arcsine of x
- atan(x) = arctangent of x
- atan2(y, x) = arctangent in correct quadrant of y/x
- cos(x) = cosine of x
- cosh(x) = hyperbolic cosine of x
- cot(x) = cotangent of x
- coth(x) = hyperbolic cotangent of x
- csc(x) = cosecant of x
- csch(x) = hyperbolic cosecant of x
- sec(x) = secant of x
- sech(x) = hyperbolic secant of x
- sin(x) = sine of x
- sinh(x) = hyperbolic sine of x
- tan(x) = tangent of x
- tanh(x) = hyperbolic tangent of x
Advanced Mathematical Functions
- AiryAi(x) = Airy function Ai(x)
- AiryBi(x) = Airy function Bi(x)
- BesselI(n, x) = modified Bessel function of the first kind, I(n, x)
- BesselJ(n, x) = Bessel function of the first kind, J(n, x)
- BesselK(n, x) = modified Bessel function of the second kind, K(n, x)
- BesselY(n, x) = Bessel function of the second kind, Y(n, x)
- BetaFunc(z, w) = beta function B(z, w)
- EllipticE(phi, k) = Legendre elliptic integral of the second kind, E(phi, k)
- EllipticF(phi, k) = Legendre elliptic integral of the first kind F(phi, k)
- EllipticPi(phi, n, k) = Legendre elliptic integral of the third kind, Pi(phi, n, k)
- Erf(x) = error function
- Erfc(x) = complimentary error function
- ExpInt(x) = exponential integral E(1, x)
- ExpIntEi(x) = exponential integral Ei(x)
- ExpIntN(n, x) = exponential integral E(n, x)
- GammaFunc(x) = gamma function of x
- GammaPFunc(a, x) = incomplete Gamma function P(a, x)
- GammaQFunc(a, x) = incomplete Gamma function Q(a, x) = 1 - P(a, x)
- IncBetaFunc(a, b, x) = incomplete Beta function I(a, b, x)
- JacobiCN(u, kc) = Jacobian elliptic function, cn(u, kc)
- JacobiDN(u, kc) = Jacobian elliptic function, dn(u, kc)
- JacobiSN(u, kc) = Jacobian elliptic function, sn(u, kc)
- LogGammaFunc(x) = natural log of the gamma function of x
Vector Functions
- angle(x, y) = angle between vectors x and y
- component(x, n) = the nth componet of a vector x
- cross(x, y) = cross product of vectors x and y
- dot(x, y) = dot product of vectors x and y
- mag(x) = magnitude of vector x
- PolarAngle(x) = atan2(x[2], x[1]) = atan2(component(x, 2), component(x, 1))
- PolarVec(f, q) = [cos(q), sin(q), 0] * f
Functions of User-Defined Functions
- fmax(y, x1, x2, ...) = choose x1, x2, ... to maximize y
- fmin(y, x1, x2, ...) = choose x1, x2, ... to minimize y
- func(x1, val1, x2, val2, ...) = evaluate func(x1 = val1, x2 = val2, ...)
- solve(y1, y2, ..., x1, x2 ... ) = choose x1, x2, ... such that y1 = y2 = ... 0
Other Functions
- BEGIN = marks the start of a user-defined function
- cgs(e1, e2, ...) = use centimeter-gram-second default units with exceptions e1, e2, ... (args are optional)
- DefUnit(name, x) = user defined unit 'name' set = x
- END = marks the end of a user-defined function
- FPS(e1, e2, ...) = use Foot-Pound-Second default units with exceptions e1, e2, ... (args are optional)
- IPS(e1, e2, ...) = use Inch-Pound-Second default units with exceptions e1, e2, ... (args are optional)
- MKS(e1, e2, ...) = use Meter-Kilogram-Second default units with exceptions e1, e2, ... (args are optional)
- PrintFunc = print the currently defined user-function