Hohmann Transfer Calculator: Delta-v and Transfer Time Between Circular Orbits
Two-burn transfers between circular orbits.
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How this calculator works
Choose the central body.
Enter the radii of the first and second circular orbits, measured from the centre of the body.
The calculator gives each burn, the total delta-v and the transfer time.
Formulas used
- a = \frac{r_1 + r_2}{2}
- \Delta v_1 = \sqrt{\mu\left(\frac{2}{r_1} - \frac{1}{a}\right)} - \sqrt{\frac{\mu}{r_1}}
- t = \pi\sqrt{\frac{a^3}{\mu}}
Worked example
With the default numbers in the calculator above:
- Speed in the first circular orbit: 7.7258 km/s
- Speed in the second circular orbit: 3.0747 km/s
- First burn, at the first orbit: 2.4258 km/s
- Second burn, at the second orbit: 1.4668 km/s
- Total delta-v of the transfer: 3.8926 km/s
- Transfer time (half of the transfer ellipse): 5.275 hours (0.2198 days)
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is a Hohmann transfer?
The minimum-energy two-burn path between two circular orbits in the same plane. The spacecraft follows half of an ellipse that touches both orbits.
What is the delta-v from low Earth orbit to geostationary orbit?
About 3.9 km/s for a transfer from a 300 km orbit, taking about 5.3 hours.
How do I turn delta-v into fuel?
Use the rocket equation, which links the delta-v, the exhaust speed and the mass ratio.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any orbital mechanics text (the Hohmann transfer).
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