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
Identity matrix generator
I_n with ones on the diagonal, free
POST /algebra/identity-matrix$0.002Developer Utilities
2×2 matrix inverse calculator
adjugate over det, free
POST /algebra/matrix-inverse-2x2$0.002Developer Utilities
Row echelon form calculator
forward Gaussian elimination
POST /algebra/matrix-row-echelon$0.002Developer Utilities
Interior and exterior triangle angles calculator
from two known angles
POST /math/interior-and-exterior-triangle-angles$0.002Developer Utilities
Interval notation converter
bounds and inclusivity to interval form
POST /math/interval-notation$0.002Developer Utilities
Absolute value equation two solutions calculator
|ax+b|=c both roots
POST /algebra/absolute-value-two-solutions$0.002Developer Utilities
Compound rule of three calculator
mixed direct and inverse
POST /algebra/compound-rule-of-three$0.002Developer Utilities
Collinear points checker
three points on one line, shared slope
POST /algebra/collinear-points-check$0.002Developer Utilities
Linear combination of two numbers
find x, y for ax + by = c
POST /algebra/linear-combination$0.002Developer Utilities
Nested absolute value equation solver
solve ||ax+b|+c|=d for x
POST /algebra/solve-absolute-value-equation-nested$0.002Developer Utilities
Circular orbit speed calculator
v = √(μ/r) from μ and radius
POST /astro/circular-orbit-speed$0.002Developer Utilities
Orbital radius from vis-viva calculator
solve r from v, a, μ
POST /astro/vis-viva-radius$0.002Developer Utilities
Semi-major axis from apsides
a = (ra + rp) / 2
POST /astro/semimajor-from-apsides$0.002Developer Utilities
Orbital mean motion calculator
n = √(μ/a³) from μ and a
POST /astro/mean-motion$0.002Developer Utilities
Semi-major axis from period calculator
a from T and μ (Kepler)
POST /astro/sma-from-period$0.002Developer Utilities
Orbital period with both masses
Kepler T from m1, m2 and a
POST /astro/kepler-two-masses$0.002Developer Utilities
Characteristic energy C3 calculator
C3 = v∞² launch energy
POST /astro/characteristic-energy-c3$0.002Developer Utilities
Radial/transverse orbital velocity
v_r and v_⊥ from e, ν, h
POST /astro/orbital-velocity-vector$0.002Developer Utilities
Hohmann second burn Δv calculator
circularize at the outer orbit
POST /astro/hohmann-deltav2$0.002Developer Utilities
Launch window phase angle calculator for Hohmann transfers
POST /astro/launch-window-phase-angle$0.002Developer Utilities
Magnitude Difference to Brightness Ratio Calculator
POST /astro/magnitude-diff-to-ratio$0.002Developer Utilities
Two-body reduced mass calculator
calculate reduced mass in kilograms
POST /astro/reduced-mass$0.002Developer Utilities
Rigid body Roche limit calculator
radius and density ratio
POST /astro/roche-limit-rigid$0.002Developer Utilities
Total magnitude of equal stars calculator
combine stellar brightness
POST /astro/cluster-total-magnitude$0.002Developer Utilities
Radial Velocity from Doppler Shift Calculator
POST /astro/radial-velocity-doppler$0.002Developer Utilities
White dwarf radius from mass calculator
Nauenberg relation
POST /astro/white-dwarf-radius$0.002Developer Utilities
Wien peak wavelength calculator
blackbody temperature to metres
POST /astro/wien-peak-wavelength$0.002Developer Utilities
CMB Temperature at Redshift Calculator
T(z) = T0(1 + z)
POST /astro/cmb-temperature-at-z$0.002Developer Utilities
Critical density of the universe calculator
from the Hubble constant
POST /astro/critical-density$0.002Developer Utilities
Photon Flux from Luminosity Calculator
Photons per Second
POST /astro/photon-flux-from-power$0.002Developer Utilities
Central mass from moon orbit calculator
Kepler's third law
POST /astro/central-mass-from-moon$0.002Developer Utilities
Hubble constant from velocity and distance calculator
POST /astro/hubble-constant-from-velocity$0.002Developer Utilities
Focal ratio and f-number calculator from focal length and aperture
POST /astro/focal-ratio$0.002Developer Utilities
Seasonal Solar Declination Range Calculator
POST /astro/planet-axial-tilt-season$0.002Developer Utilities
Planet orbital speed around a star calculator
POST /astro/planet-orbital-speed$0.002Developer Utilities
True field of view calculator
telescope eyepiece degrees
POST /astro/true-field-of-view$0.002Developer Utilities
Julian Date to Gregorian date and time calculator
POST /astro/datetime-from-julian-date$0.002Developer Utilities
Pixel Sampling and Resolution Check Calculator
POST /astro/pixel-sampling$0.002Developer Utilities
Star trail length calculator
exposure time and declination
POST /astro/star-trail-length$0.002Developer Utilities
Azimuth from equatorial coordinates calculator
POST /astro/azimuth-equatorial$0.002Developer Utilities
Day of year calculator from a calendar date
POST /astro/day-of-year$0.002Developer Utilities
Equation of time approximation calculator
solar time offset
POST /astro/equation-of-time$0.002Developer Utilities
Orbital radius from period in days calculator
semi-major axis in AU
POST /astro/orbital-radius-from-period-days$0.002Developer Utilities
Black hole evaporation time calculator
Hawking lifetime
POST /astro/black-hole-lifetime$0.002Developer Utilities
Orbital altitude from period and body calculator
POST /astro/orbital-altitude-from-period$0.002Developer Utilities
Orbital speed in kilometres per second calculator
POST /astro/orbital-velocity-kms$0.002Developer Utilities
Reflected-Light Planet Apparent Magnitude Calculator
POST /astro/apparent-magnitude-planet$0.002Developer Utilities
Stellar luminosity in solar units calculator
POST /astro/stellar-number-density$0.002Developer Utilities
Add minutes to a datetime
deterministic ISO UTC calculator
POST /date/add-minutes$0.002Developer Utilities
Add quarters to a date
three-month date calculator with clamping
POST /date/add-quarters$0.002Developer Utilities
Date difference in years, months and days
exact calendar breakdown
POST /date/diff-breakdown-ymd$0.002Developer Utilities
Working days remaining in month
exclude weekends and holidays
POST /date/workdays-remaining-month$0.002Developer Utilities
Days remaining in the month
calculate days until month end
POST /date/days-remaining-month$0.002Developer Utilities
Start and end of decade
find first and last year from a date
POST /date/decade-start-end$0.002Developer Utilities
Fraction of year elapsed
UTC year progress calculator
POST /date/fraction-of-year-elapsed$0.002Developer Utilities
First and last day of year
find calendar year boundaries
POST /date/year-start-end$0.002Developer Utilities
End of next month calculator
find the exact date
POST /date/end-of-next-month$0.002Developer Utilities
Nth weekday after a date
find the next chosen weekday occurrence
POST /date/nth-weekday-from-date$0.002Developer Utilities
Weekday of the first of the month from an ISO date
POST /date/weekday-of-first-of-month$0.002Developer Utilities
Julian–Gregorian day offset calculator by date year
POST /date/julian-gregorian-offset$0.002