Hohmann Transfer Calculator

What a Hohmann transfer is and when to use it

A Hohmann transfer is the most fuel-efficient two-burn way to move a spacecraft between two coplanar circular orbits around the same body. The first burn raises the far side of the orbit into an ellipse whose closest point touches the starting orbit and whose farthest point touches the target orbit. The craft coasts half an ellipse, then a second burn at the far point circularizes the orbit.

This calculator gives the size of each burn (delta-v), the total delta-v, and the coasting time. It suits mission-design homework, orbital mechanics study, rough feasibility checks such as low Earth orbit to geostationary orbit, and comparing how expensive different target orbits are. It also works for moving to a lower orbit, in which case both burns act against the direction of motion.

The equations

With the two orbit radii measured from the center of the central body, the transfer ellipse has semi-major axis a = (r₁ + r₂) / 2. The calculator uses the vis-viva equation to find speeds and subtracts:

μ is the gravitational parameter GM of the central body, in km³/s² (Earth about 398,600.4).
r₁, r₂ are the initial and final circular orbit radii in km, measured from the body's center (radius plus altitude).
Δv₁ = |√(μ(2/r₁ − 1/a)) − √(μ/r₁)|, the first burn.
Δv₂ = |√(μ/r₂) − √(μ(2/r₂ − 1/a))|, the second burn.
t = π √(a³/μ), the time to fly half of the transfer ellipse, shown in hours.

Worked example

Transfer from a 300 km parking orbit around Earth (r₁ = 6,378 + 300 = 6,678 km) to geostationary orbit (r₂ = 42,164 km) with μ = 398,600.4418 km³/s², which are the calculator's default inputs.

The semi-major axis is a = (6,678 + 42,164) / 2 = 24,421 km. The circular speeds are √(μ/r₁) = 7.726 km/s and √(μ/r₂) = 3.075 km/s. On the ellipse the speed at perigee is 10.152 km/s and at apogee 1.608 km/s.

So Δv₁ = 10.152 − 7.726 = 2.426 km/s and Δv₂ = 3.075 − 1.608 = 1.467 km/s, for a total of 3.893 km/s. The transfer time is π √(24,421³ / 398,600.4418) ≈ 18,990 s, which the calculator shows as 5.28 h.

Common mistakes and how to interpret the result

Entering altitude instead of radius. The formulas need distance from the body's center. Add the body's radius to the altitude, otherwise the burns will be wrong.
Ignoring plane changes. The Hohmann transfer assumes both orbits are coplanar and circular. Inclination changes cost extra delta-v that this tool does not include.
Mixing units. μ must be in km³/s² when radii are in km. Using meters for radii with this μ gives nonsense.
Treating the answer as a full mission budget. Real missions add gravity losses, finite burn durations, steering losses and margins, so treat the result as the ideal impulsive minimum.

Frequently Asked Questions

Why is the Hohmann transfer efficient?

For two coplanar circular orbits it needs the least total delta-v of any two-impulse transfer. Each burn is applied tangentially at the point where it changes orbital energy most effectively.

Does it work for going to a lower orbit?

Yes. If r2 is smaller than r1 the burns are retrograde. The calculator uses absolute values, so both delta-v figures are shown as positive magnitudes of speed change.

Can I use it for other planets or the Sun?

Yes, provided you enter the correct gravitational parameter and radii. For example, the Sun's mu is about 132,712,440,018 km cubed per second squared, which lets you estimate interplanetary transfers between circular coplanar orbits.

Is a faster transfer possible?

Yes, but it costs more delta-v. A Hohmann transfer takes the longest coast time of the efficient options; bi-elliptic and higher-energy transfers trade fuel or time in different ways.