# Hohmann Transfer Calculator

URL: https://speedycalculator.com/calculators/physics/hohmann-transfer/
Last updated: 2026-10-30

> The Hohmann transfer calculator finds the two engine burns (Δv₁, Δv₂), the total delta-v, the transfer time and the propellant mass needed to move a spacecraft between two circular orbits around Earth or the Sun.

## Inputs

- Central body
- Initial orbit altitude (km, m, mi, nmi, ft)
- Final orbit altitude (km, m, mi, nmi, ft)
- Initial orbit radius (au, km)
- Final orbit radius (au, km)
- Engine specific impulse (s)
- Spacecraft initial mass (kg, g, mg, t, lb, oz)

## Results

- First burn Δv₁
- Second burn Δv₂
- Total Δv
- Transfer time
- Propellant needed

## 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)})
```

## Explanation

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

FieldWhat to enterCentral bodyChoose one: Earth (altitudes above the surface), Sun (distances from the Sun)Initial orbit altitudeUnits: km, m, mi, nmi, ftFinal orbit altitudeUnits: km, m, mi, nmi, ftInitial orbit radiusUnits: au, kmFinal orbit radiusUnits: au, kmEngine specific impulse (s)A numberSpacecraft initial massUnits: 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)1503.95452253.92473003.89523753.86624503.83756003.7813

## 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.

## FAQ

**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.


## Sources

- [NASA – Planetary fact sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/)
- [NASA – Basics of Space Flight](https://science.nasa.gov/learn/basics-of-space-flight/)