Hohmann Transfer Calculator

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A Hohmann transfer moves a spacecraft between two circular orbits with two engine burns. It is the classic way to raise a satellite, for example from low Earth orbit to geostationary orbit.

Standards:

NGSS HS-ESS1-4
AP1 Unit 2
IB D.1

Our alignment; not reviewed by the standards bodies.

Formulas verified in build: 2026-10-16

The equation

a_t=\frac{r_1+r_2}{2},\quad v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}

\Delta v_1=v_{p}-\sqrt{\tfrac{\mu}{r_1}},\quad \Delta v_2=\sqrt{\tfrac{\mu}{r_2}}-v_{a},\quad t=\pi\sqrt{\frac{a_t^3}{\mu}}

Worked example

Given

Start altitude (km): 300 km
Target altitude (km): 35786 km

Answer

First burn Δv₁: 2.426 km/s
Second burn Δv₂: 1.467 km/s
Total Δv: 3.893 km/s
Transfer time: 5.28 h

Check

LEO at 300 km to GEO needs about 3.89 km/s in total, the standard textbook result (Curtis, ch. 6); the build checks this.

Assumptions

Earth only, circular and coplanar orbits, instant burns (no plane change).

Go deeper

Sources

H. D. Curtis, Orbital Mechanics for Engineering Students, 4th ed., Butterworth-Heinemann (Elsevier), 2020.
D. A. Vallado, Fundamentals of Astrodynamics and Applications, 4th ed., Microcosm Press, 2013.
NASA, Basics of Space Flight.

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