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
Parallel axis theorem calculator
find I with I_c + md²
POST /mech/parallel-axis-theorem$0.002Developer Utilities
Power to overcome drag calculator
P = F_d × v at steady speed
POST /mech/power-to-overcome-drag$0.002Developer Utilities
Rolling down incline calculator
acceleration with inertia
POST /mech/rolling-down-incline-acceleration$0.002Developer Utilities
Rotational work calculator
W=τθ in joules free
POST /mech/rotational-work$0.002Developer Utilities
Spring launch speed calculator
v from k, compression, and mass
POST /mech/spring-launch-speed$0.002Developer Utilities
Graphing quadratic inequalities
boundary roots and shaded solution region
POST /math/graphing-quadratic-inequalities$0.002Developer Utilities
Belt and pulley speed calculator
find driven pulley RPM
POST /mech/belt-speed$0.002Developer Utilities
Orbit total energy calculator
circular satellite energy
POST /mech/circular-orbit-energy-total$0.002Developer Utilities
Orbital angular momentum calculator
specific h from r, v, and path angle
POST /mech/orbital-angular-momentum$0.002Developer Utilities
Specific orbital energy calculator
ε = −μ/(2a) free
POST /mech/specific-orbital-energy$0.002Developer Utilities
Surface gravity from density calculator
g = (4/3)πGρr free
POST /mech/surface-gravity-from-density$0.002Developer Utilities
Gravitational binding energy two masses calculator
U = −Gm₁m₂/r free
POST /mech/two-mass-gravitational-pe$0.002Developer Utilities
First-class lever calculator
find the required effort force
POST /mech/lever-first-class$0.002Developer Utilities
Friction for rolling without slipping
μ_min from angle and inertia factor
POST /mech/rolling-friction-needed$0.002Developer Utilities
Seconds pendulum length calculator
two-second period from gravity
POST /mech/seconds-pendulum$0.002Developer Utilities
SHM displacement calculator
amplitude, frequency and phase
POST /mech/shm-displacement$0.002Developer Utilities
SHM total energy calculator
E = ½kA² for mass-spring oscillators
POST /mech/shm-total-energy$0.002Developer Utilities
Force to Tip an Object Calculator
POST /mech/toppling-force$0.002Developer Utilities
Vertical spring stretch calculator
δ = mg/k for a hanging mass
POST /mech/vertical-spring-stretch$0.002Developer Utilities
Apparent weight in fluid calculator
subtract buoyant force
POST /mech/apparent-weight-submerged$0.002Developer Utilities
G-force calculator
convert acceleration to standard gravity
POST /mech/g-force-acceleration$0.002Developer Utilities
Ladder equilibrium calculator
min friction and reactions
POST /mech/ladder-against-wall$0.002Developer Utilities
Moment of a force calculator
M = F × d in newton-metres
POST /mech/moment-of-force$0.002Developer Utilities
Pulley system effort calculator
force to lift a block and tackle load
POST /mech/pulley-system-effort$0.002Developer Utilities
Stokes drag force calculator
F = 6πηrv for a sphere in viscous fluid
POST /mech/stokes-drag$0.002Developer Utilities
Weight at latitude calculator
Earth rotation, free
POST /mech/weight-at-latitude$0.002Developer Utilities
All primitive roots modulo n
complete generator list
POST /numth/all-primitive-roots$0.002Developer Utilities
Cipolla modular square root
√a mod odd prime p
POST /numth/cipolla-algorithm$0.002Developer Utilities
Fermat's little theorem checker
compute a^(n−1) mod n
POST /numth/fermat-little-check$0.002Developer Utilities
Hensel lifting calculator
lift a polynomial root modulo p^k
POST /numth/hensel-lift$0.002Developer Utilities
Modular division calculator
a ÷ b mod n via inverse
POST /numth/modular-division$0.002Developer Utilities
Pisano period calculator
Fibonacci cycle length modulo m
POST /numth/pisano-period$0.002Developer Utilities
Pocklington primality test
certify n from a partial factorization of n−1
POST /numth/pocklington-test$0.002Developer Utilities
Difference of squares factorization
find a² − b² for odd n
POST /numth/difference-of-squares-factor$0.002Developer Utilities
Euler-Jacobi pseudoprime checker
a^((n-1)/2) ≡ (a/n)
POST /numth/euler-pseudoprime-check$0.002Developer Utilities
Integer nth root floor calculator
exact k-th root
POST /numth/integer-nth-root$0.002Developer Utilities
Liouville function calculator
compute λ(n) from prime factors
POST /numth/liouville-function$0.002Developer Utilities
Lucas primality test
verify a prime certificate
POST /numth/lucas-primality-test$0.002Developer Utilities
Powerful part calculator
split n into powerful × squarefree
POST /numth/powerful-part$0.002Developer Utilities
Prime factor count with multiplicity
big omega Ω(n)
POST /numth/prime-factor-multiplicity$0.002Developer Utilities
Abundancy index calculator
sigma(n)/n exact fraction, free
POST /numth/abundancy-index$0.002Developer Utilities
Aliquot sequence calculator
iterate proper-divisor sums
POST /numth/aliquot-sequence$0.002Developer Utilities
Calkin–Wilf sequence term
n-th positive rational fraction
POST /numth/calkin-wilf-term$0.002Developer Utilities
Continued fraction convergents
sequence of h/k from partial quotients
POST /numth/convergents-from-cf$0.002Developer Utilities
Deficient number checker
compare the proper divisor sum with n
POST /numth/deficient-number-check$0.002Developer Utilities
Pell equation solver
find the fundamental x and y
POST /numth/pell-equation-solver$0.002Developer Utilities
Proper divisors list
all divisors of n excluding n itself
POST /numth/proper-divisors$0.002Developer Utilities
Sum of totatives
n·φ(n)/2 for n>1, free calculator
POST /numth/sum-of-totatives$0.002Developer Utilities
Engel Expansion Calculator for Positive Fractions
POST /numth/engel-expansion$0.002Developer Utilities
Frobenius number for two coins
largest unmakeable amount
POST /numth/frobenius-number$0.002Developer Utilities
Gaussian integer multiplication calculator
multiply a + bi
POST /numth/gaussian-integer-multiply$0.002Developer Utilities
Odd parts partition count
distinct partition calculator
POST /numth/partitions-distinct-odd$0.002Developer Utilities
Pythagorean triple generator
Euclid formula a=m²−n², b=2mn, c=m²+n²
POST /numth/pythagorean-triple-generator$0.002Developer Utilities
Sum of two squares checker
is n = a² + b² by prime factors?
POST /numth/sum-two-squares-check$0.002Developer Utilities
Taxicab number representations as sums of two positive cubes
POST /numth/taxicab-representations$0.002Developer Utilities
Woodall number generator
n-th Woodall number n·2^n−1
POST /numth/woodall-number$0.002Developer Utilities
Integer compositions count
number of ordered sums of n
POST /numth/compositions-count$0.002Developer Utilities
Digitadition generators
find all m with m + digit sum = n
POST /numth/digitadition-generators$0.002Developer Utilities
Moran number checker
test digit-sum prime quotients
POST /numth/moran-number$0.002Developer Utilities
Pernicious number checker
test prime binary one count
POST /numth/pernicious-number$0.002