hohmann transfer calculator

What is a Hohmann transfer?

A Hohmann transfer is the classic two-burn maneuver used to move a spacecraft between two circular orbits in the same plane. It is often the most fuel-efficient impulsive transfer for this specific setup: circular start orbit, circular target orbit, and no plane change.

The idea is simple: perform the first burn to enter an elliptical transfer orbit, coast halfway around that ellipse, then perform a second burn to circularize at the destination orbit.

How this calculator works

This tool takes your central body, its gravitational parameter μ, and two orbit altitudes. It then computes:

• Burn 1 (Δv₁): injection into the transfer ellipse
• Burn 2 (Δv₂): circularization at the destination orbit
• Total Δv: the sum of burn magnitudes
• Time of flight: half the transfer orbit period
• Reference phase angle: useful for rendezvous planning

Core equations (impulsive model)

Let r₁ and r₂ be the initial and final orbit radii from the body center:

• Transfer semi-major axis: a_t = (r₁ + r₂)/2
• Circular speed at r: v_c = √(μ/r)
• Transfer speed at radius r: v_t = √(μ(2/r − 1/a_t))
• Burns: Δv₁ = v_t1 − v_c1, Δv₂ = v_c2 − v_t2
• Transfer time: t = π√(a_t³/μ)

Worked example: LEO to GEO

If you load the built-in Earth example (300 km to 35,786 km), you should see a total Δv near 3.9 km/s and transfer time near 5.3 hours. That aligns with standard mission design approximations for an idealized impulsive transfer.

Important assumptions and limitations

This calculator is intentionally clean and fast, so it uses a simplified model:

• No atmospheric drag
• No non-spherical gravity effects (J2, harmonics)
• No third-body perturbations
• No finite burn losses (instantaneous impulses assumed)
• No plane changes (coplanar transfer only)

For early concept design, this is exactly what you want. For flight-grade mission planning, use high-fidelity trajectory optimization tools.

When a Hohmann transfer is not best

1) Large radius ratio cases

For very large orbit-radius ratios, a bi-elliptic transfer can require less Δv than a direct Hohmann transfer, though it usually takes much longer.

2) Low-thrust propulsion missions

Electric propulsion systems (ion/Hall thrusters) usually follow continuous-thrust spirals rather than two clean impulsive burns.

3) Combined transfer + plane change

If you must change inclination, timing that plane change at a point of low velocity can dramatically alter optimal strategy.

Quick usage tips

• Keep units consistent: this page uses km, km/s, and seconds.
• Use the preset selector for common bodies, then adjust as needed.
• For a descent transfer, the calculator will show negative signed burns; use total Δv magnitude for propellant budgeting.
• Use this as a first-pass estimator before detailed simulation.

Final thought

The Hohmann transfer is one of those elegant results in astrodynamics: minimal math, powerful intuition, and immediate mission value. Whether you are planning a student cubesat scenario or validating a back-of-the-envelope estimate, this calculator gives a fast, reliable starting point.