Vis-viva equation
v = √[μ(2/r − 1/a)]
Transfer-orbit velocity at each apsis follows from vis-viva.
Hohmann Transfer Calculator
Estimate the two impulsive burns and coast time for an ideal coplanar transfer between circular orbits around the same body.
Access: Free to use, no installation, and No account required.
Inputs
The model assumes circular, coplanar orbits and instantaneous burns. Plane changes, finite thrust, atmospheric drag, launch geometry, and operational constraints are excluded.
Results
Hohmann transfer model
The transfer orbit is an ellipse tangent to the initial and final circular orbits. The first impulse enters the transfer ellipse; the second impulse circularizes at the opposite apsis.
When this model is not enough
Use the full workbench or Orbital Mechanics Simulator for bi-elliptic transfers, phasing, plane changes, state vectors, perturbations, and propagated maneuvers.
Engineering reference
Hohmann Transfer Calculator: background and worked detail
Use the Hohmann Transfer Calculator to estimate the two impulsive burns, total delta-v, transfer-orbit speeds, semi-major axis, and coast time for an ideal coplanar transfer between two circular orbits around the same central body.
The two-burn minimum-energy transfer
A Hohmann transfer uses half of an ellipse tangent to both circular orbits. The first instantaneous burn moves the spacecraft from the initial circular orbit onto the transfer ellipse; the second burn circularizes at the destination radius.
It is a powerful baseline for comparing propulsion requirements, but it assumes perfectly timed impulses, coplanar circular endpoints, a two-body gravity model, and no finite-burn or perturbation effects.
400 km LEO to geostationary altitude
Select Earth with 400 km initial altitude and 35,786 km final altitude.
- The first burn raises apogee from low Earth orbit to geostationary radius.
- The second burn circularizes at the higher radius.
- The combined ideal delta-v is about 3.85 km/s and the coast time is about 5.3 hours.
Result: The result is an ideal orbital-mechanics baseline and does not include launch-site, plane-change, finite-burn, or station-keeping requirements.
Equations used by this calculator
Transfer semi-major axis
a_t = (r₁ + r₂)/2
The Hohmann ellipse is tangent to both endpoint circles.
Transfer time
t = π√(a_t³/μ)
The coast covers one half of the transfer ellipse.
Why a real mission needs more than this
Assumptions
- Initial and final orbits are circular and coplanar.
- Burns are instantaneous impulses.
- Only the selected central body's point-mass gravity is included.
Limitations
- Does not include inclination changes, launch geometry, atmospheric drag, finite burn duration, Oberth timing errors, or perturbations.
- A Hohmann transfer is not always the globally minimum-delta-v transfer for every radius ratio or mission constraint.
Validation checks
No transfer
Case: Set initial and final altitudes equal.
Expected: Both burn magnitudes and total delta-v should be zero.
Reverse transfer
Case: Swap the initial and final altitudes.
Expected: Total ideal delta-v should be the same magnitude, although burn directions reverse physically.
Hohmann Transfer Calculator FAQ
Is Hohmann transfer always the most efficient?
It is the classic two-impulse optimum for many coplanar circular transfers, but other strategies such as bi-elliptic transfers or combined plane changes can be preferable in some cases.
Why is transfer time half an orbital period?
The transfer trajectory uses exactly half of the transfer ellipse, from one apsis to the opposite apsis.
Does the calculator include plane change?
No. Inclination and plane-change maneuvers require additional delta-v and geometry analysis.
Where this calculation comes from
Shared with the Orbital Mechanics Workbench, which adds plane changes, phasing, and finite-burn effects.
Open the source workbench →Read calculation and source methodology →