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All-in-one calculator: Arithmatics, Trigonometry, Physics, Probability, Statistics, Combinatorics and Matrix.

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Examples

1.2 * (2 + 4.5) = 7.8 8 % 3 = 2 sin(45 deg)^2 = 0.5 abs(-2.3)+min(1,2) = 3.3
sqrt(3^2 + 4^2) = 5 2^4+log(8,2)+log10(100) = 21 3 inch + 2 cm = 3.7874 inch 90 km/h to m/s = 25 m / s
det([-1, 2; 3, 1]) = -7 pow(2,10) = 1024 var(1,2,3,4,5) = 2.5 9.81 m/s^2 * 100 kg * 40 m = 39.24 kJ

Reference

Arithmetic functions

Function Description
abs(x) Calculate the absolute value of a number.
add(x, y) Add two or more values, x + y.
cbrt(x [, allRoots]) Calculate the cubic root of a value.
ceil(x) Round a value towards plus infinity If x is complex, both real and imaginary part are rounded towards plus infinity.
cube(x) Compute the cube of a value, x * x * x.
divide(x, y) Divide two values, x / y.
dotDivide(x, y) Divide two matrices element wise.
dotMultiply(x, y) Multiply two matrices element wise.
dotPow(x, y) Calculates the power of x to y element wise.
exp(x) Calculate the exponent of a value.
fix(x) Round a value towards zero.
floor(x) Round a value towards minus infinity.
gcd(a, b) Calculate the greatest common divisor for two or more values or arrays.
hypot(a, b, …) Calculate the hypotenusa of a list with values.
lcm(a, b) Calculate the least common multiple for two or more values or arrays.
log(x [, base]) Calculate the logarithm of a value.
log10(x) Calculate the 10-base logarithm of a value.
mod(x, y) Calculates the modulus, the remainder of an integer division.
multiply(x, y) Multiply two or more values, x * y.
norm(x [, p]) Calculate the norm of a number, vector or matrix.
nthRoot(a) Calculate the nth root of a value.
pow(x, y) Calculates the power of x to y, x ^ y.
round(x [, n]) Round a value towards the nearest integer.
sign(x) Compute the sign of a value.
sqrt(x) Calculate the square root of a value.
square(x) Compute the square of a value, x * x.
subtract(x, y) Subtract two values, x - y.
unaryMinus(x) Inverse the sign of a value, apply a unary minus operation.
unaryPlus(x) Unary plus operation.
xgcd(a, b) Calculate the extended greatest common divisor for two values.
arg(x) Compute the argument of a complex value.
conj(x) Compute the complex conjugate of a complex value.
im(x) Get the imaginary part of a complex number.
re(x) Get the real part of a complex number.

Trigonometry functions

Function Description
acos(x) Calculate the inverse cosine of a value.
acosh(x) Calculate the hyperbolic arccos of a value, defined as acosh(x) = ln(sqrt(x^2 - 1) + x).
acot(x) Calculate the inverse cotangent of a value, defined as acot(x) = atan(1/x).
acoth(x) Calculate the hyperbolic arccotangent of a value, defined as acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2.
acsc(x) Calculate the inverse cosecant of a value, defined as acsc(x) = asin(1/x).
acsch(x) Calculate the hyperbolic arccosecant of a value, defined as acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1)).
asec(x) Calculate the inverse secant of a value.
asech(x) Calculate the hyperbolic arcsecant of a value, defined as asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x).
asin(x) Calculate the inverse sine of a value.
asinh(x) Calculate the hyperbolic arcsine of a value, defined as asinh(x) = ln(x + sqrt(x^2 + 1)).
atan(x) Calculate the inverse tangent of a value.
atan2(y, x) Calculate the inverse tangent function with two arguments, y/x.
atanh(x) Calculate the hyperbolic arctangent of a value, defined as atanh(x) = ln((1 + x)/(1 - x)) / 2.
cos(x) Calculate the cosine of a value.
cosh(x) Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 * (exp(x) + exp(-x)).
cot(x) Calculate the cotangent of a value.
coth(x) Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x).
csc(x) Calculate the cosecant of a value, defined as csc(x) = 1/sin(x).
csch(x) Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1 / sinh(x).
sec(x) Calculate the secant of a value, defined as sec(x) = 1/cos(x).
sech(x) Calculate the hyperbolic secant of a value, defined as sech(x) = 1 / cosh(x).
sin(x) Calculate the sine of a value.
sinh(x) Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 * (exp(x) - exp(-x)).
tan(x) Calculate the tangent of a value.
tanh(x) Calculate the hyperbolic tangent of a value, defined as tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1).

Probability functions

Function Description
combinations(n, k) Compute the number of ways of picking n possibilities.
factorial(n) Compute the factorial of a value Factorial only supports an integer value as argument.
gamma(n) Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values.
kldivergence(x, y) Calculate the Kullback-Leibler (KL) divergence between two distributions.
multinomial(a) Multinomial Coefficients compute the number of ways of picking a1, a2, .
permutations(n [, k]) Compute the number of ways of obtaining an ordered subset of n elements.
pickRandom(array) Random pick one or more values from a one dimensional array.
random([min, max]) Return a random number larger or equal to max using a uniform distribution.
randomInt([min, max]) Return a random integer number larger or equal to max using a uniform distribution.

Statistics functions

Function Description
mad(a, b, c, …) Compute the median absolute deviation of a matrix or a list with values.
max(a, b, c, …) Compute the maximum value of a matrix or a list with values.
mean(a, b, c, …) Compute the mean value of matrix or a list with values.
median(a, b, c, …) Compute the median of a matrix or a list with values.
min(a, b, c, …) Compute the maximum value of a matrix or a list of values.
mode(a, b, c, …) Computes the mode of a set of numbers or a list with values(numbers or characters).
prod(a, b, c, …) Compute the product of a matrix or a list with values.
quantileSeq(A, prob[, sorted]) Compute the prob order quantile of a matrix or a list with values.
std(a, b, c, …) Compute the standard deviation of a matrix or a list with values.
sum(a, b, c, …) Compute the sum of a matrix or a list with values.
var(a, b, c, …) Compute the variance of a matrix or a list with values.

Matrix functions

Function Description
concat(a, b, c, … [, dim]) Concatenate two or more matrices.
cross(x, y) Calculate the cross product for two vectors in three dimensional space.
det(x) Calculate the determinant of a matrix.
diag(X) Create a diagonal matrix or retrieve the diagonal of a matrix When x on the diagonal will be returned.
dot(x, y) Calculate the dot product of two vectors.
eye(n) Create a 2-dimensional identity matrix with size m x n or n x n.
filter(x, test) Filter the items in an array or one dimensional matrix.
flatten(x) Flatten a multi dimensional matrix into a single dimensional matrix.
forEach(x, callback) Iterate over all elements of a matrix/array, and executes the given callback function.
inv(x) Calculate the inverse of a square matrix.
kron(x, y) Calculates the kronecker product of 2 matrices or vectors.
map(x, callback) Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.
ones(m, n, p, …) Create a matrix filled with ones.
partitionSelect(x, k) Partition-based selection of an array or 1D matrix.
range(start, end [, step]) Create an array from a range.
reshape(x, sizes) Reshape a multi dimensional array to fit the specified dimensions.
resize(x, size [, defaultValue]) Resize a matrix.
size(x) Calculate the size of a matrix or scalar.
sort(x) Sort the items in a matrix.
squeeze(x) Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
subset(x, index [, replacement]) Get or set a subset of a matrix or string.
trace(x) Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.
transpose(x) Transpose a matrix.
zeros(m, n, p, …) Create a matrix filled with zeros.

Units

Base Unit
Length meter (m), inch (in), foot (ft), yard (yd), mile (mi), link (li), rod (rd), chain (ch), angstrom, mil
Surface area m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil, acre, hectare
Volume m3, litre (l, L, lt, liter), cc, cuin, cuft, cuyd, teaspoon, tablespoon
Liquid volume minim (min), fluiddram (fldr), fluidounce (floz), gill (gi), cup (cp), pint (pt), quart (qt), gallon (gal), beerbarrel (bbl), oilbarrel (obl), hogshead, drop (gtt)
Angles rad (radian), deg (degree), grad (gradian), cycle, arcsec (arcsecond), arcmin (arcminute)
Time second (s, secs, seconds), minute (mins, minutes), hour (h, hr, hrs, hours), day (days), week (weeks), month (months), year (years), decade (decades), century (centuries), millennium (millennia)
Frequency hertz (Hz)
Mass gram(g), tonne, ton, grain (gr), dram (dr), ounce (oz), poundmass (lbm, lb, lbs), hundredweight (cwt), stick, stone
Electric current ampere (A)
Temperature kelvin (K), celsius (degC), fahrenheit (degF), rankine (degR)
Amount of substance mole (mol)
Luminous intensity candela (cd)
Force newton (N), dyne (dyn), poundforce (lbf), kip
Energy joule (J), erg, Wh, BTU, electronvolt (eV)
Power watt (W), hp
Pressure Pa, psi, atm, torr, bar, mmHg, mmH2O, cmH2O
Electricity and magnetism ampere (A), coulomb (C), watt (W), volt (V), ohm, farad (F), weber (Wb), tesla (T), henry (H), siemens (S), electronvolt (eV)
Binary bit (b), byte (B)

Prefixes

Name Abbreviation Value
deca da 1e1
hecto h 1e2
kilo k 1e3
mega M 1e6
giga G 1e9
tera T 1e12
peta P 1e15
exa E 1e18
zetta Z 1e21
yotta Y 1e24
Name Abbreviation Value
deci d 1e-1
centi c 1e-2
milli m 1e-3
micro u 1e-6
nano n 1e-9
pico p 1e-12
femto f 1e-15
atto a 1e-18
zepto z 1e-21
yocto y 1e-24

Physical Constants

Universal constants

Name Symbol Value Unit
speedOfLight c 299792458 m · s-1
gravitationConstant G 6.6738480e-11 m3 · kg-1 · s-2
planckConstant h 6.626069311e-34 J · s
reducedPlanckConstant h 1.05457172647e-34 J · s

Electromagnetic constants

Name Symbol Value Unit
magneticConstant μ0 1.2566370614e-6 N · A-2
electricConstant ε0 8.854187817e-12 F · m-1
vacuumImpedance Z0 376.730313461 Ω
coulomb κ 8.9875517873681764e9 N · m2 · C-2
elementaryCharge e 1.60217656535e-19 C
bohrMagneton μB 9.2740096820e-24 J · T-1
conductanceQuantum G0 7.748091734625e-5 S
inverseConductanceQuantum G0-1 12906.403721742 Ω
magneticFluxQuantum f0 2.06783375846e-15 Wb
nuclearMagneton μN 5.0507835311e-27 J · T-1
klitzing RK 25812.807443484 Ω

Atomic and nuclear constants

Name Symbol Value Unit
bohrRadius a0 5.291772109217e-11 m
classicalElectronRadius re 2.817940326727e-15 m
electronMass me 9.1093829140e-31 kg
fermiCoupling GF 1.1663645e-5 GeV-2
fineStructure α 7.297352569824e-3 -
hartreeEnergy Eh 4.3597443419e-18 J
protonMass mp 1.67262177774e-27 kg
deuteronMass md 3.3435830926e-27 kg
neutronMass mn 1.6749271613e-27 kg
quantumOfCirculation h / (2me) 3.636947552024e-4 m2 · s-1
rydberg R∞ 10973731.56853955 m-1
thomsonCrossSection 6.65245873413e-29 m2
weakMixingAngle 0.222321 -
efimovFactor 22.7 -

Physico-chemical constants

Name Symbol Value Unit
atomicMass mu 1.66053892173e-27 kg
avogadro NA 6.0221412927e23 mol-1
boltzmann k 1.380648813e-23 J · K-1
faraday F 96485.336521 C · mol-1
firstRadiation c1 3.7417715317e-16 W · m2
loschmidt n0 2.686780524e25 m-3
gasConstant R 8.314462175 J · K-1 · mol-1
molarPlanckConstant NA · h 3.990312717628e-10 J · s · mol-1
molarVolume Vm 2.241396820e-10 m3 · mol-1
sackurTetrode -1.164870823 -
secondRadiation c2 1.438777013e-2 m · K
stefanBoltzmann σ 5.67037321e-8 W · m-2 · K-4
wienDisplacement b 2.897772126e-3 m · K

Adopted values

Name Symbol Value Unit
molarMass Mu 1e-3 kg · mol-1
molarMassC12 M(12C) 1.2e-2 kg · mol-1
gravity gn 9.80665 m · s-2
atm atm 101325 Pa

Natural units

Name Symbol Value Unit
planckLength lP 1.61619997e-35 m
planckMass mP 2.1765113e-8 kg
planckTime tP 5.3910632e-44 s
planckCharge qP 1.87554595641e-18 C
planckTemperature TP 1.41683385e+32 K