A Hohmann transfer is the most fuel-efficient two-burn path between circular orbits: one burn to enter an elliptical transfer orbit, another to circularise. It is used to raise satellites to geostationary orbit and as the basis of interplanetary trajectories.
How to use the Hohmann Transfer Calculator
- Central body
- Initial orbit altitude
- Final orbit altitude
- Initial orbit radius
- Final orbit radius
- Engine specific impulse (s)
- Spacecraft initial mass
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the central body. Around Earth, enter the altitudes; around the Sun, the orbital radii. Add the specific impulse and initial mass to estimate propellant.
Inputs explained
| Field | What to enter |
|---|---|
| Central body | Choose one: Earth (altitudes above the surface), Sun (distances from the Sun) |
| Initial orbit altitude | Units: km, m, mi, nmi, ft |
| Final orbit altitude | Units: km, m, mi, nmi, ft |
| Initial orbit radius | Units: au, km |
| Final orbit radius | Units: au, km |
| Engine specific impulse (s) | A number |
| Spacecraft initial mass | Units: kg, g, mg, t, lb, oz |
What each result means
- First burn Δv₁ = sqrt([mu]÷[R1])×(sqrt(2×[R2]÷([R1] + [R2])) – 1)
- Second burn Δv₂ = sqrt([mu]÷[R2])×(1 – sqrt(2×[R1]÷([R1] + [R2])))
- Total Δv = abs([First burn Δv₁]) + abs([Second burn Δv₂])
- Transfer time = pi×sqrt((([R1] + [R2])÷2)^3÷[mu])
- Propellant needed = [Spacecraft initial mass]×(1 – exp(-[Total Δv]÷([Engine specific impulse (s)]×9.80665)))
Example values
How the main result changes when Initial orbit altitude changes and everything else stays at the example values above:
| Initial orbit altitude (km) | Total Δv (km/s) |
|---|---|
| 150 | 3.9545 |
| 225 | 3.9247 |
| 300 | 3.8952 |
| 375 | 3.8662 |
| 450 | 3.8375 |
| 600 | 3.7813 |
Formula
a = (r₁ + r₂)/2, Δv₁ = √(μ/r₁)·(√(2r₂/(r₁ + r₂)) − 1), Δv₂ = √(μ/r₂)·(1 − √(2r₁/(r₁ + r₂)))
t = π·√(a³/μ), m_prop = m₀·(1 − e^{−Δv/(I_sp·g₀)})
Worked example
Inputs — Central body: Earth (altitudes above the surface); Initial orbit altitude: 300 km; Final orbit altitude: 35,786 km; Engine specific impulse (s): 320; Spacecraft initial mass: 5,000 kg.
Results — First burn Δv₁ = 2.42765 km/s; Second burn Δv₂ = 1.46757 km/s; Total Δv = 3.89523 km/s; Transfer time = 5.27275 h; Propellant needed = 3,554.89832 kg.
Key terms
- Transfer orbit
- Ellipse touching both the initial and final orbits.
Frequently asked questions
Is a Hohmann transfer the fastest?
No – it is the most efficient for two burns, but slow.
How much delta-v to reach GEO from LEO?
About 3.9 km/s (without plane change).
Why does an Earth–Mars transfer take ~8.5 months?
That is half the period of the transfer ellipse.
When is a bi-elliptic transfer better?
When the radius ratio exceeds about 11.94.