Hohmann Transfer Calculator
Calculate the two burns, the total Δv and the transfer time to move between two circular orbits with a Hohmann transfer, from low Earth orbit to geostationary orbit or anywhere else.
The cheapest two-burn route
In 1925 the German engineer Walter Hohmann showed that the most efficient way to move between two circular, coplanar orbits with two engine burns is an ellipse that just touches both. The first burn, made in the direction of travel, raises the far side of the orbit to the target altitude. The spacecraft coasts half an ellipse, and a second prograde burn at the top circularises the new orbit. Each burn changes the speed by the difference between the circular speed and the speed on the transfer ellipse at that point, both from the vis-viva equation. The transfer ellipse has a semi-major axis equal to the average of the two orbit radii, and the coast takes half its period.
From a 400 km orbit to geostationary altitude at 35,786 km around Earth, the transfer ellipse has a semi-major axis of 24,471 km. The spacecraft starts at 7.669 km/s and must speed up to 10.066 km/s, a first burn of 2.397 km/s. It arrives at the top moving at only 1.618 km/s, while geostationary orbit needs 3.075 km/s, so the second burn is 1.456 km/s. The total is 3.854 km/s and the coast takes 5 hours 17 minutes.
Where the real budget differs
Real missions to geostationary orbit pay more because of inclination. A launch from Cape Canaveral reaches an orbit tilted 28.5° to the equator, and the plane must be turned. Doing that alone at geostationary speed would cost about 1.51 km/s; combining it with the circularising burn at the slow apoapsis, where a turn is cheapest, adds only a few hundred metres per second. That is why near-equatorial launch sites such as Kourou are valued for geostationary work. Hohmann transfers are also slow. A faster route with a larger first burn reaches the target sooner, and for very large ratios of radii, above about 11.94, a three-burn bi-elliptic transfer becomes slightly cheaper, though it takes much longer.
Common mistakes
The most frequent is adding the two circular speeds or subtracting them directly. The difference between 7.669 and 3.075 km/s is 4.594 km/s, which is neither burn and is larger than the true total of 3.854 km/s. Another is forgetting that going down costs the same as going up: lowering an orbit from geostationary to 400 km uses the same two magnitudes in reverse, as retrograde burns. A third is entering distances from the centre of the planet into an altitude field, which adds the planet’s radius twice. The calculator asks for altitudes above the surface and adds the radius itself, 6,378.137 km for Earth.
How to use it
- Choose the central body.
- Enter the starting orbit altitude in kilometres. The default is a 400 km low Earth orbit.
- Enter the target orbit altitude. The default 35,786 km is geostationary altitude.
- Read the two burns, the total of 3.854 km/s and the transfer time of 5 h 17 min, together with the speeds before and after each burn.
- Add any plane change and a margin for steering losses separately; the result assumes circular orbits in the same plane and instant burns.
Questions from the flight desk
How much delta-v does it take to get from LEO to GEO?
For a Hohmann transfer from a 400 km circular orbit to geostationary altitude, about 3.85 km/s: 2.40 km/s to enter the transfer orbit and 1.46 km/s to circularise. A launch from Cape Canaveral must also remove a 28.5° inclination, which raises the total to roughly 4.2 to 4.3 km/s when the plane change is combined with the second burn.
How long does a Hohmann transfer take?
Half the period of the transfer ellipse. From 400 km to geostationary orbit that is about 5 hours 17 minutes. From Earth to Mars around the Sun it is about 259 days. The time is fixed by the two orbit sizes, so a quicker trip always needs a larger first burn and usually a larger arrival burn too.
Is a Hohmann transfer always the most efficient?
It is the most efficient two-burn transfer between coplanar circular orbits. When the outer orbit is more than about 11.94 times the radius of the inner one, a three-burn bi-elliptic transfer uses slightly less Δv, at the cost of a much longer flight. Gravity assists and low-thrust spirals follow different rules altogether.
Why are there two burns in a Hohmann transfer?
The first burn changes the circular orbit into an ellipse whose high point reaches the target altitude. Without a second burn the spacecraft would fall back along the ellipse to where it started. The second burn at the high point adds the speed needed to stay at that altitude in a circle.
Disclaimer: Orbital mechanics results are ideal two-body figures with instantaneous burns, computed from the values you enter and the constants stated on each page. They are not mission analysis, flight dynamics or launch safety advice. Real orbits are perturbed by Earth’s oblateness, the Moon, the Sun and atmospheric drag, and real burns carry gravity and steering losses. Never use these numbers to operate a spacecraft or to fly a rocket; follow the safety code of your rocketry association and the advice of qualified engineers.