Interactive Calculator
Assumes ideal two-body dynamics, coplanar circular start/end orbits, and impulsive burns.
What this Hohmann transfer calculator does
This tool estimates the velocity changes (Δv) and transfer time required to move between two circular orbits around the same central body using a classic Hohmann transfer orbit. It is one of the most fundamental maneuvers in orbital mechanics and is widely used for mission planning, sanity checks, and educational work.
Enter your body parameters, initial orbit altitude, and final orbit altitude. The calculator returns:
- Burn 1 Δv at departure (prograde or retrograde)
- Burn 2 Δv at arrival (prograde or retrograde)
- Total Δv budget (sum of magnitudes)
- Time of flight for the half-ellipse transfer
- Useful supporting values like circular and transfer velocities
How a Hohmann transfer works
A Hohmann transfer uses an ellipse tangent to both the initial and final circular orbits. You perform two engine burns:
- Burn 1: Leave the initial circular orbit and enter the transfer ellipse.
- Burn 2: Circularize at the destination orbit when you reach the opposite side of the ellipse.
For coplanar circular orbits, this is usually the lowest-Δv two-impulse transfer.
Equations used by the calculator
Radii from altitude
r2 = R + h2
Circular orbit speeds
Transfer ellipse and velocities (vis-viva)
v_t1 = √( μ (2/r1 - 1/a_t) )
v_t2 = √( μ (2/r2 - 1/a_t) )
Burn magnitudes and transfer time
Δv2 = v_circ2 - v_t2
Δv_total = |Δv1| + |Δv2|
t_transfer = π √(a_t³ / μ)
Example: Low Earth Orbit to Geostationary Transfer Orbit
A common demonstration is moving from about 400 km altitude (LEO) to 35,786 km altitude (GEO radius level). You should see a large first burn, a moderate second burn, and a transfer time of around a few hours. This aligns with practical mission profiles where insertion and circularization are separated by half an orbit.
Assumptions and limitations
What is included
- Two-body gravity model
- Instantaneous impulsive burns
- Coplanar circular initial and final orbits
What is not included
- Plane changes (inclination changes can dominate Δv)
- Finite burn duration and thrust limitations
- Atmospheric drag, J2 perturbation, third-body effects
- Launch windows, eclipse constraints, or operational margins
For real mission design, use this as a first-pass estimate before high-fidelity tools.
Tips for better mission estimates
- Use accurate μ and radius values for your central body.
- Keep units consistent (this calculator expects km and km³/s²).
- Add margin to your total Δv budget for guidance and dispersions.
- Consider bi-elliptic transfers if the radius ratio is very large.
Bottom line
If you need a fast and clean estimate for orbit raising or lowering, a Hohmann transfer is the right place to start. Use the calculator above to compare scenarios quickly, then move to more detailed analysis as mission complexity grows.