Hohmann Transfer Calculator — Orbital Manoeuvre Δv
A Hohmann transfer is the most fuel-efficient two-burn manoeuvre to move a spacecraft between two co-planar circular orbits. Enter the initial and target orbit radii (from the body's centre), choose the central body, and get the delta-v of each burn, total propellant cost, transfer time, and the eccentricity of the transfer ellipse.
Central body
km
km
Sum of both impulsive burns to complete the Hohmann transfer
- 1
Transfer ellipse semi-major axis
a = (6,778 + 42,164) ÷ 2 = 24,471 km - 2
Departure burn Δv₁ (vis-viva)
√(μ × (2 ÷ r₁ − 1 ÷ a)) − √(μ ÷ r₁) = 2.398 km/sDifference between transfer-ellipse periapsis speed and circular speed at r₁. - 3
Arrival burn Δv₂ (vis-viva)
√(μ ÷ r₂) − √(μ × (2 ÷ r₂ − 1 ÷ a)) = 1.457 km/s - 4
Total Δv
|2.398| + |1.457| = 3.854
How does this calculator work?
Hohmann transfer: two tangential burns connect two circular co-planar orbits via a half-ellipse. Δv₁ raises/lowers the trajectory to the target; Δv₂ circularises it. Total Δv = |Δv₁| + |Δv₂|. Transfer time = π√(aₜ³/μ). For LEO (6 778 km) to GEO (42 164 km) around Earth the total Δv is ≈ 3.86 km/s in about 5.3 hours.
Formula
How this is calculated
A Hohmann transfer uses two impulsive burns on opposite ends of an elliptical transfer orbit. The first burn at r₁ raises (or lowers) the apoapsis to r₂, putting the spacecraft on the transfer ellipse. The second burn at r₂ circularises the orbit. Both burns are calculated with the vis-viva equation: v = √(μ·(2/r − 1/a)), where μ is the central body's standard gravitational parameter and a is the semi-major axis of the conic.
Δv₁ is the speed difference between the circular velocity at r₁ (√(μ/r₁)) and the transfer ellipse periapsis velocity. Δv₂ is the difference between the transfer ellipse apoapsis velocity and the circular velocity at r₂. The total Δv is the sum of their absolute values — it represents the minimum propellant cost in the idealised two-impulse model.
The transfer time is exactly half the orbital period of the transfer ellipse: T/2 = π√(aₜ³/μ). Important assumptions: the orbits are circular and co-planar (no plane change manoeuvre); the burns are instantaneous impulses (no finite thrust losses); and the gravitational influence of third bodies (e.g. the Moon) is ignored. Real missions account for all of these with trajectory optimisation tools. The gravitational parameter values used here are the 2023 IAU standards.
Frequently asked questions
It minimises total Δv for two co-planar, circular orbit transfers by aligning both burns with the velocity vector (tangential impulses). Any other two-impulse path between the same two orbits requires more Δv. For very large radius ratios (r₂/r₁ > 11.94) a bi-elliptic transfer can be more efficient, though it requires three burns.
Distance from the centre of the body (radius), not altitude above the surface. To convert: add the mean surface radius (Earth: 6 371 km, Mars: 3 390 km, Moon: 1 737 km) to the altitude. The default r₁ = 6 778 km is the ISS orbit (~407 km altitude above Earth).
No. A pure Hohmann transfer assumes both orbits share the same orbital plane. Combining a plane change with an orbit raise is very expensive in Δv and requires a different optimisation. If you need to change inclination, the most efficient point is typically at the ascending or descending node where the orbits cross.
Also known as
TG we-Calculate Editorial Team. (2026). Hohmann Transfer Calculator — Orbital Manoeuvre Δv [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hohmann-transfer-calculator
TG we-Calculate Editorial Team. "Hohmann Transfer Calculator — Orbital Manoeuvre Δv." TG we-Calculate. 2026. https://we-calculate.com/calculator/hohmann-transfer-calculator.
TG we-Calculate Editorial Team, "Hohmann Transfer Calculator — Orbital Manoeuvre Δv," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hohmann-transfer-calculator
@misc{wecalculate_hohmann_transfer_calculator, title = {Hohmann Transfer Calculator — Orbital Manoeuvre Δv}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hohmann-transfer-calculator}}, year = {2026}, note = {TG we-Calculate} }
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