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
Gravity balance point distance calculator between two masses
POST /astro/l1-gravity-balance$0.002Developer Utilities
L4 and L5 Lagrange Point Geometry Calculator
POST /astro/lagrange-l4-l5-geometry$0.002Developer Utilities
Brightness ratio to magnitude difference calculator
POST /astro/ratio-to-magnitude-diff$0.002Developer Utilities
Rocket final mass calculator
dry mass from Δv, ve, and m₀
POST /astro/rocket-final-mass$0.002Developer Utilities
Orbital semi-latus rectum calculator
p = a(1−e²) from a and e, free
POST /astro/semilatus-rectum$0.002Developer Utilities
Sphere of influence calculator
patched-conic r_SOI = a(m/M)^(2/5)
POST /astro/sphere-of-influence$0.002Developer Utilities
Rocket structural coefficient calculator
dry and propellant mass
POST /astro/structural-coefficient$0.002Developer Utilities
Rocket thrust from mass flow
F = ṁ·ve in newtons, free
POST /astro/thrust-from-mass-flow$0.002Developer Utilities
Rocket thrust-to-weight ratio calculator
thrust, mass and gravity
POST /astro/thrust-to-weight$0.002Developer Utilities
Differential tidal force calculator
Δa = 2GML/r³ inverse-cube free
POST /astro/tidal-force$0.002Developer Utilities
True anomaly from eccentric anomaly calculator
half-angle formula, free
POST /astro/true-anomaly-from-eccentric$0.002Developer Utilities
Blackbody radiant exitance calculator
Stefan-Boltzmann law
POST /astro/blackbody-flux$0.002Developer Utilities
Bolometric magnitude calculator
apply a bolometric correction
POST /astro/bolometric-magnitude$0.002Developer Utilities
Atmospheric extinction magnitude calculator
magnitudes lost
POST /astro/extinction-magnitude$0.002Developer Utilities
Mass ratio from barycenter calculator
m₁/m₂ = r₂/r₁
POST /astro/mass-ratio-from-barycenter$0.002Developer Utilities
Proper motion calculator
arcsec/yr from tangential velocity and distance
POST /astro/proper-motion-from-velocity$0.002Developer Utilities
Surface brightness calculator
magnitude per square arcsecond
POST /astro/surface-brightness$0.002Developer Utilities
Combined magnitude of two stars
total apparent magnitude from flux sum
POST /astro/combined-magnitude$0.002Developer Utilities
Planet equilibrium temperature calculator
stellar flux and albedo
POST /astro/equilibrium-temperature$0.002Developer Utilities
Main-sequence lifetime calculator
τ ≈ 10¹⁰ · (M/L) years, free
POST /astro/main-sequence-lifetime$0.002Developer Utilities
Stellar lifetime energy calculator
total radiant energy in joules
POST /astro/stellar-energy-output$0.002Developer Utilities
Stellar flux at planet calculator
luminosity and orbital distance
POST /astro/stellar-flux-at-planet$0.002Developer Utilities
Chandrasekhar mass limit calculator
5.83/μe² solar masses
POST /astro/chandrasekhar-mass$0.002Developer Utilities
Hubble time calculator
expansion timescale t_H = 1/H0 in years, free
POST /astro/hubble-time$0.002Developer Utilities
Simple lookback time calculator
low-redshift estimate
POST /astro/lookback-time-lowz$0.002Developer Utilities
Matter density at redshift calculator
rho(z) from present density
POST /astro/matter-density-at-z$0.002Developer Utilities
Scale factor from redshift calculator
a = 1/(1 + z)
POST /astro/scale-factor-from-redshift$0.002Developer Utilities
Stellar angular diameter calculator
mas from radius and distance
POST /astro/stellar-angular-diameter$0.002Developer Utilities
Stellar surface escape velocity calculator
mass and radius
POST /astro/stellar-escape-velocity$0.002Developer Utilities
Universe age from Hubble constant
matter-dominated flat age t=(2/3)/H0
POST /astro/age-from-hubble$0.002Developer Utilities
Low-redshift luminosity distance calculator
d_L ≈ cz/H0 in Mpc
POST /astro/luminosity-distance-lowz$0.002Developer Utilities
Planet mass from surface gravity
M = g·R²/G in kilograms, free
POST /astro/mass-from-gravity$0.002Developer Utilities
Moon orbital speed calculator
mean circular-orbit speed
POST /astro/moon-orbital-speed$0.002Developer Utilities
Planet mass from density and radius calculator
POST /astro/planet-mass-from-density$0.002Developer Utilities
Solar Day Length Calculator
Sidereal Rotation and Orbit
POST /astro/solar-day-length$0.002Developer Utilities
Telescope light-gathering power calculator
compare with the human eye
POST /astro/light-gathering-power$0.002Developer Utilities
Minimum useful magnification calculator for telescopes
POST /astro/min-useful-magnification$0.002Developer Utilities
Moon illuminated fraction calculator
from phase angle, free
POST /astro/moon-illumination-fraction$0.002Developer Utilities
Planet year length calculator
orbital year from stellar mass and a
POST /astro/planet-year-length$0.002Developer Utilities
Rayleigh angular resolution calculator
1.22 λ/D
POST /astro/rayleigh-resolution$0.002Developer Utilities
Solar declination by day of year
cosine seasonal model, free
POST /astro/solar-declination-day$0.002Developer Utilities
Airmass from altitude calculator
secant approximation
POST /astro/airmass-from-altitude$0.002Developer Utilities
Aperture from focal ratio calculator
diameter D = f/N in mm, free
POST /astro/aperture-from-focal-ratio$0.002Developer Utilities
Focal reducer calculator
effective focal length and f-ratio
POST /astro/focal-reducer$0.002Developer Utilities
Image scale calculator
arcsec/pixel from pixel size & focal length
POST /astro/image-scale-pixel$0.002Developer Utilities
Modified Julian Date calculator
MJD from Julian Date, free
POST /astro/modified-julian-date$0.002Developer Utilities
Sidereal drift rate calculator
star motion by declination
POST /astro/sidereal-drift-rate$0.002Developer Utilities
Days since J2000 epoch calculator
JD minus 2451545.0
POST /astro/days-since-j2000$0.002Developer Utilities
Declination from horizontal coords
altitude, azimuth, latitude
POST /astro/declination-horizontal$0.002Developer Utilities
Hour angle from LST and right ascension calculator
POST /astro/hour-angle-from-lst$0.002Developer Utilities
Precession of declination calculator
annual Δδ from n·cos(α)
POST /astro/precession-dec$0.002Developer Utilities
Right Ascension from Ecliptic Coordinates Calculator
POST /astro/ra-from-ecliptic$0.002Developer Utilities
Transit altitude from declination calculator
POST /astro/transit-altitude$0.002Developer Utilities
Black hole event horizon area calculator
Schwarzschild formula
POST /astro/event-horizon-area$0.002Developer Utilities
Orbital period in days calculator
Kepler T from AU and solar masses
POST /astro/orbital-period-days$0.002Developer Utilities
Photon sphere radius calculator
from black hole mass
POST /astro/photon-sphere-radius$0.002Developer Utilities
Binary Roche lobe radius calculator
Eggleton approximation
POST /astro/roche-radius-binary$0.002Developer Utilities
Hohmann departure speed calculator
periapsis from radii and μ
POST /astro/transfer-departure-speed$0.002Developer Utilities
Bond albedo from reflected flux calculator
reflected to incident ratio
POST /astro/albedo-from-flux$0.002Developer Utilities
Escape to circular speed ratio calculator
v_esc = √2 · v_circ
POST /astro/escape-to-circular-ratio$0.002