Interactive Astrophysics

Give any two of angular size, physical size, and distance, and get the third using the exact trigonometric relation. The small-angle approximation shown alongside for comparison.

Calculate angular velocity ω from a rotation period, frequency, or rotations-over-time, via ω = 2π/T = 2πf, in rad/s, deg/s, RPM, and rev/s — plus optional tangential velocity v = ωr — with an animated rotating disk and a comparison scale from the Moon to a millisecond pulsar.

Enter one distance in any unit and instantly see its equivalent in meters, kilometers, AU, light-years, parsecs, kiloparsecs, megaparsecs, and gigaparsecs — plus the light-travel time.

Calculate the binary mass function f(M) = PK³/(2πG)(1-e²)^1.5 from an orbital period and radial-velocity semi-amplitude, giving an assumption-free lower bound on an unseen companion's mass — plus an advanced mode that numerically solves for M2 given an inclination and the visible star's mass, with a mass-benchmark ruler and an inclination-dependence chart.

Calculate the idealized Hawking-radiation evaporation time of a Schwarzschild black hole, t = 5120 π G² M³ / (ħ c⁴), and see on a log-log plot why the M³ scaling makes stellar and supermassive black holes essentially eternal while sufficiently tiny ones would already be gone.

Calculate the innermost stable circular orbit (ISCO) around a Schwarzschild or Kerr black hole from its mass and dimensionless spin a*, in gravitational radii, Schwarzschild radii, and kilometers — with a live horizon/ISCO/disk diagram and the accretion efficiency it implies.

Enter a temperature and watch the blackbody spectrum draw itself in real time — Planck's law, Wien's law, Stefan–Boltzmann flux, and the object's true apparent color, computed live.

Calculate how far back in cosmic history you're looking when you observe an object at redshift z, via numerical integration of t_L(z) = (1/H0)∫dz'/[(1+z')E(z')] in a flat ΛCDM cosmology — with standard cosmology presets, a cosmic timeline, and an integral-area chart, validated against Astropy.

Solve for any of apparent magnitude, absolute magnitude, or distance from the other two via m − M = 5log10(d/10 pc) [+ A], with an optional interstellar-extinction term, a distance ladder, and a semi-log distance-modulus chart.

Convert a spectral line's rest and observed wavelengths into radial velocity (or the reverse), using either the classical v/c approximation or the exact relativistic Doppler relation — with a velocity gauge and a chart showing exactly where the two formulas diverge.

Estimate N, the number of detectable communicating civilizations in the Milky Way, from N = R*·fp·nₑ·fl·fi·fc·L — with a slider for every factor, live result, and two visuals that show what most Drake equation tools hide: the last four factors span so many orders of magnitude that the output is a statement about your assumptions, not a measurement of the galaxy.

Calculate an accreting black hole or neutron star's Eddington luminosity from its mass via L_Edd ≈ 1.26×10^38 (M/M_sun) erg/s, and — given an observed luminosity — its Eddington ratio, with a colour-coded ratio meter and a log-log mass-luminosity chart.

Calculate the speed needed to leave a body's gravity for good, v_esc = √(2GM/r), from Earth, the Moon, Mars, Jupiter, the Sun, a white dwarf, or a neutron star — in km/s, m/s, and as a fraction of c — with a log-scale comparison ladder from a small asteroid to a neutron star, and the exact link to this site's Schwarzschild radius calculator.

Estimate a planet's equilibrium temperature from its star's effective temperature and radius, orbital distance, Bond albedo, and heat-redistribution assumption via T_eq = T★√(R★/2a)(1-A)^(1/4) — in K and °C, with absorbed flux, a star-planet diagram, and a temperature gauge comparing it to solar-system planets.

Calculate how much a star's brightness dips when a planet transits it, δ = (Rp/R★)², in fraction, percent, ppm, and millimagnitudes — or work backward from an observed depth to a planet radius — with a to-scale transit diagram and a synthetic light curve.

Estimate the geometric probability that a planet's orbit happens to be aligned for a transit, P ≈ (R★+Rp)/a, with an advanced mode for eccentricity and argument of periapsis — plus a viewing-angle geometry diagram and a distance-versus-probability chart, pairing with the Transit Depth Calculator.

Give any two of an astronomical source's flux, luminosity, and distance, and get the third via the inverse-square law — with optional uncertainty propagation and the isotropic-emission assumption stated explicitly.

Calculate the free-fall time of a uniform-density sphere via t_ff = √(3π/32Gρ), from either a mass density or a molecular-cloud number density, with the exact collapse trajectory and a comparison scale against real cloud, planet, and stellar densities.

Calculate how much light is gravitationally redshifted escaping from radius R around a mass M, z = (1-r_s/R)^(-1/2) - 1, with the observed wavelength, a naive equivalent velocity for comparison, a climbing-photon wavelength-stretch diagram, and a redshift-versus-radius chart that diverges at the horizon.

Calculate the chirp mass of a merging compact binary — the single combination of two masses that a gravitational-wave detector measures most precisely — along with total mass, mass ratio, and an ISCO merger-frequency estimate, visualized as the real upward-sweeping frequency "chirp."

Calculate a star's conservative and optimistic habitable zone boundaries in AU using the real Kopparapu et al. (2013) empirical formulation, and see whether a candidate planet's orbit falls inside it.

Calculate the Hawking temperature of a Schwarzschild black hole, T_H = ħc³/(8π G M k_B), from its mass in solar masses, Earth masses, or kilograms — with a log-log plot of temperature versus mass spanning Planck-scale hypotheticals to supermassive giants, and a CMB reference line marking the boundary between net-absorbing and net-evaporating.

Estimate the Hill sphere — the region where a planet or moon's own gravity dominates over its host's tidal pull — from its mass, its host's mass, orbital distance, and eccentricity, via r_H ≈ a(1-e)(m/3M)^(1/3), in km, AU, and body radii, with a scaled orbit + Hill-sphere diagram.

Solve the linear Hubble law v = H0·d for a nearby galaxy's recession velocity or distance, with an adjustable H0 (60–80 km/s/Mpc), a genuine Hubble diagram plotting your point on the v = H0·d line, and explicit caveats about where the linear approximation breaks down.

Solve Kepler's third law P² = 4π²a³/G(M₁+M₂) for orbital period, semi-major axis, or total system mass from the other two — the general two-body form, not the solar-system shortcut P²=a³ that silently assumes a 1 M☉ central body and a negligible companion — with a log-log chart showing exactly where the two diverge.

Convert between apparent magnitude difference and brightness (flux) ratio using F1/F2 = 10^(-0.4(m1-m2)) — with a two-star visual comparison and a magnitude number line to make the reversed, logarithmic scale intuitive.

Estimate how long a star spends fusing hydrogen on the main sequence from t_MS ≈ 10¹⁰(M/M☉)⁻²·⁵ yr — since fuel scales roughly with mass while burn rate scales with luminosity — with a log-log mass-vs-lifetime chart against a naive 1/M comparison, and a log-scale bar chart comparing red-dwarf and massive-star lifetimes.

Convert between a star's parallax and its distance exactly, watch the geometry that makes it work, and see how measurement uncertainty propagates — and when the simple inversion stops being trustworthy.

Convert between photon energy, wavelength, and frequency instantly — type into any field and the other two update live, from radio waves to gamma rays.

Convert a star's proper motion and distance into its true tangential velocity through space, combine RA/Dec components, and add a radial velocity for the full 3D space speed.

Watch a quantum wave packet evolve in real time under a free particle, square wells, a harmonic oscillator, a step, or a tunneling barrier — an interactive numerical solution of the time-dependent Schrödinger equation.

Give any two of redshift, rest wavelength, and observed wavelength, and get the third exactly — plus the classical and relativistic recession velocities implied by that redshift.

Calculate how close a moon or satellite can orbit a much more massive celestial body (like a planet) before tidal forces overcome its self-gravity, where the moon or satellite is ultimately destroyed.

Calculate the event-horizon radius of an idealized non-rotating black hole from its mass via r_s = 2GM/c² — in kilometers, meters, AU, Earth radii, and solar radii — or work backward from a radius to a mass, with a to-scale event-horizon diagram and a log-log chart showing the genuinely linear mass-radius relation from Earth to M87*.

Compute a radio source's spectral index α from two flux density measurements, classify it as steep, flat, or inverted, and extrapolate the predicted flux at any other frequency — with optional uncertainty propagation.

Estimate a main-sequence star's luminosity from its mass (or the reverse) using a piecewise empirical L ≈ M^α relation with α ranging from about 2.3 to 4 to shallower at high mass — in L☉, watts, and absolute bolometric magnitude, with a log-log mass-luminosity diagram and a linear-scaling comparison.

Calculate a star's surface gravity g = GM/R² from its mass and radius, and the astronomically standard log g (base-10 log of g in cgs units), with a rough dwarf/giant/supergiant/white-dwarf/neutron-star classification, a log g ladder, and a mass-radius diagram with constant-log-g contour lines.

Calculate a telescope's diffraction-limited angular resolution from its aperture and wavelength via the Rayleigh criterion θ = 1.22λ/D, compared against the empirical Dawes limit, in arcseconds, milliarcseconds, degrees, and radians — with a two-stars-resolving filmstrip and a resolution comparison scale.

Calculate telescope magnification (M = F/f), exit pupil, and true field of view from telescope and eyepiece focal length — plus a verdict on whether the setup is actually usable: empty magnification above ~2× the aperture in millimetres, wasted light above a ~7mm exit pupil. With a magnification gauge and a to-scale exit-pupil comparison.

Calculate how close a star can orbit a black hole before tidal forces shred it apart — and find the black hole mass above which the star is swallowed whole instead, producing no observable flare.

Calculate how much actual sky an eyepiece shows — true field ≈ apparent field ÷ magnification, or the more accurate 57.2958 × field stop ÷ telescope focal length when the field stop is known — in degrees and arcminutes, with the Moon, Andromeda Galaxy, Orion Nebula, Pleiades, and the Double Cluster drawn to scale inside the resulting field to answer 'will it fit' directly.

Compute the X-ray hardness ratio HR from soft and hard band counts, with Poisson error propagation. Free interactive tool.