About the Hohmann Transfer Calculator
This Hohmann transfer calculator works out the most fuel-efficient two-burn manoeuvre between two circular, coplanar orbits. Choose the central body, enter the starting and target orbits as altitudes, radii or astronomical units, and it returns the first and second burn, the total delta-v (Δv) and how long the coast along the transfer ellipse takes.
It is aimed at students of orbital mechanics, space enthusiasts and players of games such as Kerbal Space Program who want real numbers: raising a satellite from low Earth orbit to geostationary orbit, planning an ISS reboost, or estimating an Earth-to-Mars trajectory around the Sun. The chart shows how the spacecraft’s speed changes at each stage.
The model assumes impulsive (instantaneous) burns, perfectly circular starting and final orbits in the same plane, and only the central body’s gravity. Real missions add plane changes, gravity losses, launch windows and the gravity of departure and arrival planets, so treat the results as the ideal minimum.
With the default inputs, the total delta-v is 3.854 km/s. Change any value above to recalculate instantly.
How to use the hohmann transfer calculator
- 1Pick the central body (or enter a custom mass and radius).
- 2Choose whether orbits are given as altitudes, radii in km, or radii in AU.
- 3Enter the initial and target orbits.
- 4Read the two burns, total delta-v and transfer time.
- 5Use the chart to see the speed at each stage of the transfer.
Formula and method
A Hohmann transfer uses an ellipse that just touches both circular orbits: its periapsis is the inner orbit and its apoapsis the outer one, so its semi-major axis is the average of the two radii. Speeds come from the vis-viva equation v = √(μ(2/r − 1/a)). The first burn raises speed from circular velocity √(μ/r₁) to the ellipse’s periapsis speed; the second, at apoapsis, raises it to the new circular speed.
The transfer takes half the ellipse’s orbital period, π√(a³/μ). μ = GM is the central body’s standard gravitational parameter (JPL values); altitudes are added to the body’s equatorial radius. Burns are treated as instantaneous and orbits as circular and coplanar.
- μ
- Standard gravitational parameter GM of the central body (m³/s²)
- r₁, r₂
- Radii of the initial and target circular orbits (m)
- a
- Semi-major axis of the transfer ellipse
- Δv₁, Δv₂
- Velocity changes of the two burns
- t
- Transfer (coast) time
Worked examples
Low Earth orbit (400 km) to geostationary orbit
r₁ = 6,778 km and r₂ = 42,164 km give a transfer ellipse with a = 24,471 km. The first burn adds 2.40 km/s, the second 1.46 km/s at apogee — 3.85 km/s in total — and the coast takes about 5.3 hours.
Earth to Mars around the Sun (1 AU → 1.524 AU)
Starting at Earth’s orbital speed of 29.8 km/s, a 2.95 km/s boost puts the craft on an ellipse reaching Mars’ orbit in about 259 days, where a 2.65 km/s burn matches Mars’ orbit. Escaping Earth and capture at Mars are extra.
ISS reboost from 400 km to 420 km
Raising a 400 km orbit by 20 km takes two tiny burns of about 5.6 m/s each — 11.3 m/s total — and roughly 46 minutes of coasting between them.
Earth to Jupiter’s orbit (1 AU → 5.2 AU)
Reaching Jupiter’s distance needs 8.79 km/s at departure and 5.64 km/s at arrival — 14.4 km/s total — and about 997 days (2.7 years) of coasting, which is why real missions use gravity assists.
Frequently asked questions
What is a Hohmann transfer orbit?+
It is an elliptical orbit that touches both a lower and a higher circular orbit, used to move between them with two engine burns. Walter Hohmann described it in 1925; for most orbit pairs it needs the least delta-v of any two-burn transfer.
How much delta-v does it take to get from LEO to GEO?+
From a 400 km circular orbit, about 3.85 km/s in an ideal coplanar Hohmann transfer. A launch from Cape Canaveral must also remove the 28.5° inclination: done alone at GEO that costs about 1.5 km/s, but combined with the apogee burn it raises burn 2 from 1.46 to about 1.82 km/s, roughly 4.2 km/s in total.
How long does a Hohmann transfer to Mars take?+
About 259 days (8.5 months) for an idealised transfer from 1 AU to 1.524 AU. Real missions take 6–9 months depending on the launch window and the actual, slightly elliptical orbits.
Is a Hohmann transfer always the most efficient?+
Not always. When the outer orbit is more than about 11.94 times the inner one, a three-burn bi-elliptic transfer can save delta-v, and gravity assists or low-thrust trajectories can beat both for interplanetary missions.
Does the spacecraft’s mass affect the delta-v?+
No — delta-v depends only on the orbits and the central body. Mass determines how much propellant is needed to deliver that delta-v, which you can find with the rocket equation calculator.