Hohmann Transfer Orbit Calculator

Low Earth orbit to geostationary. A 300 km orbit has r₁ = 6,378.1366 + 300 = 6,678.14 km, and geostationary orbit, whose period is one sidereal day (86,164.09054 s), has r₂ = 42,164.17 km. With μ = 398,600.435507 km³/s², the circular speeds are 7.726 and 3.075 km/s. The transfer ellipse has a = 24,421.15 km, so it leaves at 10.15 km/s and arrives at 1.608 km/s. The burns are 10.15 − 7.726 = 2.426 km/s and 3.075 − 1.608 = 1.467 km/s, 3.893 km/s in total, and half the ellipse takes π√(a³/μ) = 5.275 h.

Earth to Mars. Around the Sun (μ = 1.32712440041279419 × 10²⁰ m³/s²) from 1.00000261 au to 1.52371034 au, the ellipse has a = 1.262 au and e = 0.2075. Leaving takes 2.945 km/s more than Earth’s 29.78 km/s orbital speed, arriving needs 2.649 km/s more to match Mars, and the trip lasts 258.9 days. Mars moves 135.65° in that time, so it must be 44.35° ahead at launch.

The common mistake: using altitudes as orbit radii. Orbital speed depends on the distance from the centre of the planet, not from its surface. Putting 300 km and 35,786 km into the formulas as radii gives a total of 17.79 km/s, more than four times the true 3.893 km/s, because a “300 km” orbit from the centre would be deep inside the Earth. Always add the planet’s radius (6,378.1366 km for Earth) to an altitude first.

The orbit is named after Walter Hohmann, a German civil engineer and city architect of Essen, who worked out in his spare time how a spacecraft could reach other planets with the least fuel. He published the answer in 1925 in Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies), more than thirty years before the first satellite. His transfer rests on Kepler’s third law of 1619, which ties an orbit’s period to the size of its ellipse, and on the vis-viva equation of Newtonian gravity.

The same two-burn idea is still how communications satellites reach geostationary orbit: the launcher leaves them on a geostationary transfer orbit, and the satellite’s own engine makes the final circularising burn at apogee. For interplanetary trips the real paths are refined with the planets’ actual elliptical, tilted orbits and with gravity assists, but the Hohmann figures remain the first estimate of the time and delta-v, and of how often a launch window opens.

Gravitational parameters here are from NASA JPL’s DE440 planetary ephemeris (Park et al., 2021) and planet radii from JPL’s planetary physical parameters and NASA’s planetary fact sheets. Planet orbit sizes are JPL’s mean orbital elements (valid 1800–2050), treated as circles.

This calculator finds the two burns of a Hohmann transfer between any two circular, coplanar orbits around Earth, the Moon, Mars, the Sun or a body you define, with orbits given as altitudes or as distances from the centre in km, miles, metres or au. It works inward as well as outward, gives the transfer ellipse, the speeds before and after each burn, the transit time, the synodic period and the phase angle the target needs at launch, and draws the orbits to scale with the target’s position at departure.

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