Hohmann Transfer Orbit Calculator

Understanding the Hohmann transfer orbit calculator — concept and principle

A Hohmann transfer is the classic two-burn manoeuvre for moving a spacecraft between two circular, coplanar orbits around the same body. This calculator gives the two velocity changes (Δv), their total and the time of the transfer. Mission designers use it as the first estimate of propellant needs, for example raising a satellite from low Earth orbit to geostationary orbit.

Speed up at the low point, coast half an ellipse, speed up again at the top.

How it is calculated

First burn: Δv₁ = √(μ/r₁) × (√(2r₂/(r₁ + r₂)) − 1)
Second burn: Δv₂ = √(μ/r₂) × (1 − √(2r₁/(r₁ + r₂)))
Transfer time: t = π × √(a³/μ), with a = (r₁ + r₂)/2, i.e. half the period of the transfer ellipse.

r₁ and r₂ are orbit radii from the planet's centre (km), μ = GM (km³/s²; Earth 398,600.4418). Δv is in km/s; time is shown in hours.

The principle

The transfer orbit is an ellipse that touches the inner orbit at its closest point and the outer orbit at its farthest point. Its speed at any radius follows the vis-viva equation v² = μ(2/r − 1/a). The first burn raises speed from the circular value √(μ/r₁) to the ellipse's perigee speed; the spacecraft then coasts half an orbit and, at apogee, a second burn raises it to the outer circular speed √(μ/r₂). Both burns are along the direction of motion, which makes this the lowest-Δv two-burn transfer for most radius ratios.

Worked example

Defaults: r₁ = 6,771 km (about 400 km altitude), r₂ = 42,164 km (geostationary radius), μ = 398,600.4418.
Circular speeds: √(μ/r₁) = 7.672599 km/s; √(μ/r₂) = 3.074666 km/s.
Transfer ellipse speeds: perigee 10.072067 km/s, apogee 1.617445 km/s.
Δv₁ = 10.072067 − 7.672599 = 2.399467858 km/s; Δv₂ = 3.074666 − 1.617445 = 1.457221015 km/s.
Total Δv = 3.856688874 km/s. With a = 24,467.5 km, t = π√(a³/μ) = 5.290087793 h.

Each point is the calculator re-run with only “Initial orbit radius (km)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Initial orbit radius (km)	Total Δv (km/s)
1,693	8.153664908
3,386	5.802441222
5,078	4.626239017
6,771	3.856688874
8,464	3.291060437
10,156	2.847510362
13,542	2.180596301

How to read the result

Δv translates into propellant through the rocket equation, so a few hundred m/s can mean a large mass difference. Real launches to geostationary orbit also need a plane change, because launch sites are not on the equator, which adds to the total. If r₂/r₁ is larger than about 11.94, a three-burn bi-elliptic transfer can use less Δv, at the cost of much longer travel time.

Common mistakes

Using altitude instead of radius from the centre (add Earth's radius, about 6,371 km).
Adding the two speeds instead of the speed differences.

Keep in mind: This is an ideal two-body estimate. Finite burn times, plane changes, drag and perturbations change real Δv budgets, so mission planning needs full trajectory analysis.

Frequently asked questions

Can I use it for interplanetary transfers?

Yes, with μ of the Sun and the planets' orbital radii, giving the heliocentric Δv; departure and capture around planets must be added separately.

Why is the second burn smaller than the first here?

Speeds are lower far from Earth, so the gap between the ellipse's apogee speed and the circular speed is smaller.

Is the transfer time fixed?

For a Hohmann transfer, yes; it is always half the ellipse's period, so faster transfers require more Δv.

Sources: Hohmann W., Die Erreichbarkeit der Himmelskörper, Oldenbourg, 1925 · Curtis H.D., Orbital Mechanics for Engineering Students, Elsevier · Vallado D.A., Fundamentals of Astrodynamics and Applications, Microcosm Press

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

Your numbers