Developer Utilities
Small developer utilities that save a trip to a random website. Encode and decode Base64, explain a regex, build UTM links, generate QR codes and vCards, and more — the everyday helpers. Free in your browser, and available by API when you need them in a script.
Developer Utilities
Spring constant calculator
k = F/x, free in browser
POST /mech/spring-constant$0.002Developer Utilities
Terminal velocity calculator
mass, drag, density and area free
POST /mech/terminal-velocity$0.002Developer Utilities
Torque calculator
τ = rF sin(θ) in newton-metres
POST /mech/torque$0.002Developer Utilities
Work done calculator
W=Fd cos θ in joules free
POST /mech/work-done$0.002Developer Utilities
Aliquot sum calculator
proper divisors, perfect / deficient / abundant
POST /numth/aliquot-sum$0.002Developer Utilities
Amicable numbers checker
test if two integers form an amicable pair
POST /numth/amicable-numbers$0.002Developer Utilities
Armstrong number checker
narcissistic numbers, digit power sum
POST /numth/armstrong-number$0.002Developer Utilities
Automorphic number checker
does n² end with n, free
POST /numth/automorphic-number$0.002Developer Utilities
Digit sum calculator
sum digits in any base, free
POST /numth/digit-sum$0.002Developer Utilities
Digital root calculator
repeated digit sum and additive persistence
POST /numth/digital-root$0.002Developer Utilities
Number of divisors calculator
tau(n) from prime factors
POST /numth/divisor-count$0.002Developer Utilities
Sum of divisors calculator
sigma(n) from prime factors
POST /numth/divisor-sum$0.002Developer Utilities
Euler's totient φ(n)
count coprimes from prime factors
POST /numth/euler-totient$0.002Developer Utilities
Extended Euclidean calculator
gcd and Bézout coefficients x, y
POST /numth/extended-euclidean$0.002Developer Utilities
Factorial prime factorization
n! factors via Legendre formula
POST /numth/factorial-prime-factors$0.002Developer Utilities
Happy number checker
sum of squares of digits until 1 or a cycle
POST /numth/happy-number$0.002Developer Utilities
Jacobi symbol calculator
(a/n) via quadratic reciprocity
POST /numth/jacobi-symbol$0.002Developer Utilities
Legendre symbol (a/p)
quadratic residuosity mod odd prime
POST /numth/legendre-symbol$0.002Developer Utilities
Mersenne number checker
compute 2^p−1 and Lucas-Lehmer primality
POST /numth/mersenne-number$0.002Developer Utilities
Modular exponentiation calculator
base^exp mod m (fast BigInt)
POST /numth/modular-exponentiation$0.002Developer Utilities
Modular multiplicative inverse
a⁻¹ mod m via extended Euclidean
POST /numth/modular-inverse$0.002Developer Utilities
Next prime after n
smallest prime strictly greater than n
POST /numth/next-prime$0.002Developer Utilities
Pandigital number checker
each base digit once, missing digits
POST /numth/pandigital-checker$0.002Developer Utilities
Previous prime finder
largest prime strictly less than n
POST /numth/prev-prime$0.002Developer Utilities
Prime counting function π(n)
count primes ≤ n by sieve
POST /numth/prime-counting$0.002Developer Utilities
Quadratic residue checker
is a a square mod m, list residues
POST /numth/quadratic-residue$0.002Developer Utilities
Radix converter
change integer bases 2–36, free
POST /numth/radix-convert$0.002Developer Utilities
Factorial trailing zeros
count zeros of n! via powers of five
POST /numth/trailing-zeros-factorial$0.002Developer Utilities
Twin prime checker
test (n, n+2) and list pairs up to a limit
POST /numth/twin-primes$0.002Developer Utilities
Brewster angle calculator
polarization angle from n₁, n₂, free
POST /optics/brewster-angle$0.002Developer Utilities
Critical angle calculator
total internal reflection from two indices
POST /optics/critical-angle$0.002Developer Utilities
Diffraction grating calculator
angle from d, λ, order m, free
POST /optics/diffraction-grating$0.002Developer Utilities
F-stop calculator
f-number from focal length and aperture diameter, free
POST /optics/f-number$0.002Developer Utilities
Lens magnification calculator
linear m = −v/u for lenses and mirrors, free
POST /optics/lens-magnification$0.002Developer Utilities
Lens power calculator
diopters from focal length (m), free
POST /optics/lens-power$0.002Developer Utilities
Mirror equation calculator
image distance & magnification from f and do
POST /optics/mirror-equation$0.002Developer Utilities
Single-slit diffraction calculator
angular position of minima from a, λ and order m, free
POST /optics/single-slit-diffraction$0.002Developer Utilities
Snell's law calculator
refraction angle from n1, n2 and incidence, free
POST /optics/snell-law$0.002Developer Utilities
Telescope magnification calculator
angular M from objective & eyepiece
POST /optics/telescope-magnification$0.002Developer Utilities
Beat frequency calculator
f_beat = |f1 − f2| free, rejects negative Hz
POST /phys/beat-frequency$0.002Developer Utilities
Doppler effect calculator
observed frequency and frequency shift, free
POST /phys/doppler-effect$0.002Developer Utilities
Doppler shift sound calculator
perceived frequency from relative speed
POST /phys/doppler-sound$0.002Developer Utilities
Period to frequency calculator
convert T↔f (Hz) free, rejects zero
POST /phys/period-frequency$0.002Developer Utilities
Pipe resonance calculator
open/closed pipe fundamental and harmonics
POST /phys/pipe-resonance$0.002Developer Utilities
Sound intensity calculator
I = P / (4πr²) in W/m², free
POST /phys/sound-intensity$0.002Developer Utilities
Decibel calculator
sound intensity level L=10·log₁₀(I/I₀) free, rejects non-positive I
POST /phys/sound-intensity-db$0.002Developer Utilities
Speed of sound calculator
dry air from temperature (m/s)
POST /phys/speed-of-sound-air$0.002Developer Utilities
Standing wave calculator
nodes and wavelength from harmonic number and string length, free
POST /phys/standing-wave$0.002Developer Utilities
Wave speed on a string calculator
v = √(T/μ), free
POST /phys/wave-on-string-speed$0.002Developer Utilities
Wave speed calculator
v=fλ from frequency and wavelength (or solve any)
POST /phys/wave-speed$0.002Developer Utilities
Birthday paradox calculator
shared day probability for n people
POST /prob/birthday-paradox$0.002Developer Utilities
Coin flip probability
exactly k heads in n flips, free
POST /prob/coin-flip$0.002Developer Utilities
Conditional probability calculator
P(A|B) and independence test
POST /prob/conditional-probability$0.002Developer Utilities
Dice sum probability
every total for k dice with s sides
POST /prob/dice-sum$0.002Developer Utilities
Dice roll probability
exact or at-least target sum with k s-sided dice
POST /prob/dice-target$0.002Developer Utilities
Expected value calculator
mean, variance and standard deviation
POST /prob/expected-value$0.002Developer Utilities
Geometric distribution calculator
P(first success on trial k) and E[X]
POST /prob/geometric-distribution$0.002Developer Utilities
Hypergeometric probability
k successes in n draws, free
POST /prob/hypergeometric$0.002Developer Utilities
Odds to probability converter
a to b, percent, free
POST /prob/odds-converter$0.002Developer Utilities
Poisson probability calculator
P(X=k), CDF, mean and variance
POST /prob/poisson-distribution$0.002