Hohmann Transfer Calculator
Enter the radius of your starting orbit and target orbit, choose a central body, and get the two delta-v burns, total delta-v, semi-major axis, eccentricity, time of flight, and propellant mass. Supports Earth, the Sun, Moon, Mars, Jupiter, Venus, and custom gravitational parameters. Results update instantly as you type.
What is a Hohmann transfer?
A Hohmann transfer is the most fuel-efficient way to move a spacecraft between two co-planar circular orbits using exactly two engine burns. It was described by German engineer Walter Hohmann in 1925. The spacecraft fires its engine to leave the initial circular orbit, coasts along a transfer ellipse, then fires again at the other end to settle into the target orbit. Because the burns happen at exactly the points where the circles and ellipse are tangent, only the speed changes at each burn, not the direction, which keeps the delta-v (and thus fuel cost) at a minimum for two-impulse transfers. The method is used for everything from raising a satellite from its parking orbit to geostationary orbit to planning interplanetary missions like Voyager, Mars Odyssey, and countless commercial spacecraft.
How to use this calculator
Select a central body (Earth, Sun, Moon, Mars, Jupiter, Venus, or a custom gravitational parameter). Choose whether to enter orbital radii from the body center or altitudes above the surface - the calculator adds the body radius automatically for the altitude option. Enter the starting and target orbital radii or altitudes and click anywhere to see the results. The delta-v breakdown shows both individual burns and the total. Toggle "Calculate propellant mass" to add a specific impulse and spacecraft wet mass, and get the propellant needed for the full maneuver using the Tsiolkovsky rocket equation applied sequentially to both burns.
The key formulas
The transfer ellipse has a semi-major axis a = (r1 + r2) / 2, where r1 and r2 are the radii of the two circular orbits. Velocities on each circular orbit are given by the vis-viva equation simplified for circles: v = sqrt(mu / r). Velocities at the endpoints of the transfer ellipse are found with the full vis-viva equation: v = sqrt(mu * (2/r - 1/a)). The two delta-v values are the absolute differences between the circular orbit speed and the transfer ellipse speed at each endpoint. The time of flight is half the period of the transfer ellipse: t = pi * sqrt(a^3 / mu). Propellant mass follows the Tsiolkovsky rocket equation: mp = m0 * (1 - exp(-delta_v / (Isp * g0))), applied sequentially for each burn because the spacecraft is lighter after the first burn.
When is the Hohmann transfer not the best option?
For very large orbit changes where the radius ratio exceeds about 11.94, a bi-elliptic transfer - which uses three burns - can use less total delta-v. The savings come from burning at a very distant apogee where the spacecraft is moving slowly and small velocity changes produce large orbital changes. For transfers that require a change in orbital plane (inclination change), a combined Hohmann-plus-plane-change maneuver can be more efficient than doing them separately. Low-thrust ion propulsion does not use impulsive Hohmann transfers at all: it continuously spirals from one orbit to the other, spending more time but consuming very little propellant. The Hohmann transfer also assumes circular, co-planar orbits; real-world transfers between elliptical or inclined orbits require more complex trajectory optimization.
Common orbital radii and delta-v reference values
| Mission | Target radius (km) | Approx. altitude (km) | Typical total delta-v (km/s) | Transfer time |
|---|---|---|---|---|
| ISS to MEO | 20,200 | 13,829 | 2.7 | ~5 h |
| ISS to GEO | 42,164 | 35,786 | 3.9 | ~5.3 h |
| ISS to Moon | 384,400 | 378,029 | 3.1 | ~5 d |
| Earth to Mars | 227.9M | - | 5.6 | ~8.5 mo |
| Earth to Venus | 108.2M | - | 3.5 | ~5 mo |
Typical mission profiles for transfers from LEO (6,778 km radius from Earth center). Values are approximate.
Frequently asked questions
What does delta-v mean in a Hohmann transfer?
Delta-v is the change in velocity a spacecraft must execute to move from one orbit to another. In a Hohmann transfer there are two burns: the first injects the spacecraft onto the transfer ellipse, and the second circularizes it at the target orbit. Delta-v directly determines how much propellant is needed, through the Tsiolkovsky rocket equation. A lower total delta-v means a more fuel-efficient transfer.
Why are there two burns, not one?
One burn at the initial orbit gets the spacecraft onto an elliptical path that just touches the target orbit at one end. If no second burn is applied, the spacecraft simply returns to its starting point at the other end of the ellipse. The second burn, applied at the point where the ellipse and target orbit meet, adjusts the speed to match the circular velocity of the target orbit and locks the spacecraft into it.
Can a Hohmann transfer go between any two orbits?
It works best between two circular, co-planar orbits around the same body. If the orbits are elliptical or at different inclinations, the calculation is more complex. Interplanetary missions can use a heliocentric Hohmann transfer where both planetary orbits are treated as circular, which gives a useful approximation even though the real orbits are slightly elliptical.
What units does this calculator use?
All distances are in kilometers (km) and all velocities are in km/s, which are standard units in astrodynamics. The gravitational parameters (mu) for built-in bodies are in km^3/s^2. Time of flight is displayed in days, hours, minutes, and seconds. Propellant mass is in kilograms.
What specific impulse should I use for the propellant calculation?
Specific impulse (Isp) depends on the propulsion system. Chemical rockets typically achieve 300-450 s: solid rockets around 280-310 s, hypergolic bipropellants around 300-340 s, and liquid hydrogen engines around 420-460 s. Hall-effect ion thrusters reach 1,500-3,000 s. A value of 450 s is a good placeholder for a modern cryogenic upper stage. Note that ion engines cannot realistically perform impulsive Hohmann burns - they are better modeled as continuous low-thrust spirals.
What is the gravitational parameter (mu)?
The gravitational parameter mu = G x M is the product of the universal gravitational constant and the mass of the central body. It is used instead of G and M separately because mu is known to much greater precision for most solar system bodies. Earth's mu is 398,600.4418 km^3/s^2, the Sun's is about 1.327 x 10^11 km^3/s^2. You can enter a custom value for any other body when you select the "Custom mu" option.
How accurate is the Hohmann transfer for real missions?
The Hohmann transfer gives the exact minimum delta-v for two-impulse transfers between circular co-planar orbits under the two-body (point mass) assumption. Real missions add corrections for the non-spherical Earth, solar pressure, atmospheric drag at low altitudes, and the gravitational influence of the Moon and Sun. For preliminary mission planning and delta-v budgeting, the Hohmann result is an excellent starting point. High-fidelity trajectory optimization tools then refine it.