What Is a Hohmann Transfer Calculator?

A Hohmann Transfer Calculator is an orbital mechanics tool that estimates the ideal two-burn transfer between two circular, coplanar orbits around the same central body. It calculates the first burn required to enter an elliptical transfer orbit, the second burn required to circularize at the target orbit, the total delta-v, the transfer time, the semi-major axis of the transfer ellipse, and the speeds at both ends of the transfer path.

Hohmann transfers are one of the most important concepts in spaceflight because they show how a spacecraft can move efficiently between two circular orbits. For example, a spacecraft can transfer from low Earth orbit to geostationary altitude, from one circular parking orbit to a higher science orbit, or from one nearly circular heliocentric orbit to another. The same mathematical structure applies whether the central body is Earth, the Moon, Mars, Jupiter, or the Sun, as long as the simplifying assumptions are acceptable.

The transfer is called a “two-burn” maneuver. The first impulse changes the spacecraft’s circular orbit into an elliptical orbit whose opposite end touches the target orbit. The spacecraft then coasts along half of that ellipse. At the other end, the second impulse changes the elliptical orbit into the final circular orbit. If the target orbit is higher than the starting orbit, the first burn raises apoapsis and the second burn raises periapsis to circularize. If the target orbit is lower, the maneuver is reversed: the first burn lowers periapsis and the second burn circularizes at the lower orbit.

This calculator supports radius mode, altitude mode, phase-angle estimation, bi-elliptic comparison, reverse solving from transfer time, propellant estimation through the rocket equation, scenario presets, and unit conversion. It is built for learning, engineering education, and website visitors who want a clear, interactive explanation of orbital transfers. It is not a full mission design tool. Real missions must include finite burn duration, launch windows, targeting errors, plane changes, perturbations, atmospheric drag, non-spherical gravity, engine performance, margins, and mission operations constraints.

The Hohmann transfer is elegant because it uses a single transfer ellipse tangent to both circular orbits. Under ideal two-body assumptions, it is usually the minimum-delta-v two-impulse transfer between two circular coplanar orbits when the ratio between final and initial orbit radii is moderate. For very large orbit-ratio cases, bi-elliptic transfers can sometimes use less delta-v, though they usually require much longer transfer times.

How to Use This Hohmann Transfer Calculator

Use Hohmann Transfer when you know the orbital radii from the center of the central body. Select the central body, enter initial radius \(r_1\), final radius \(r_2\), choose the unit, and click calculate. Use Altitude Mode when you know orbit heights above a planet or moon surface. The calculator adds the body radius internally to create the orbital radii.

Use Phase Angle when you want an educational estimate of transfer timing. It computes transfer time, angular motion of the target during the coast, synodic period, and a simple phase-angle estimate. Use Bi-Elliptic Compare to compare a standard Hohmann transfer with a three-burn bi-elliptic transfer that uses an intermediate apoapsis. Use Reverse Solver to infer target radius, initial radius, gravitational parameter, or transfer semi-major axis from transfer time.

Use Propellant Estimate to connect transfer delta-v with the Tsiolkovsky rocket equation. Enter specific impulse and final mass after the transfer to estimate required initial mass, propellant mass, mass ratio, and propellant fraction. Use Preset Scenarios for common educational cases such as LEO to GEO or Earth-orbit to Mars-orbit heliocentric transfer. Use Unit Converter for speed and time conversions.

Hohmann Transfer Formulas

The semi-major axis of the transfer ellipse is:

The circular speeds in the starting and final orbits are:

The transfer speed at the first orbit radius is:

The transfer speed at the second orbit radius is:

The two ideal burn magnitudes are:

Total ideal transfer delta-v is:

The Hohmann transfer time is half the period of the transfer ellipse:

The transfer ellipse eccentricity is:

How a Hohmann Transfer Works

A Hohmann transfer works by creating an ellipse that is tangent to both the initial circular orbit and the final circular orbit. The spacecraft begins in a circular orbit. At the correct point, it performs the first burn. This burn changes the spacecraft’s speed so that its new orbit is elliptical. The opposite end of the ellipse touches the destination circular orbit. The spacecraft then coasts without thrust along the transfer ellipse.

When the spacecraft reaches the target orbit radius, it performs the second burn. This burn changes the spacecraft’s speed from transfer-orbit speed to circular-orbit speed at that radius. For an outward transfer, the first burn usually speeds the spacecraft up and the second burn also speeds it up relative to the transfer speed at apoapsis. For an inward transfer, the burns are retrograde in direction, but their magnitudes are still counted as positive delta-v values.

The Hohmann transfer is efficient because it uses the natural shape of a Keplerian ellipse. Instead of thrusting continuously, the spacecraft uses short impulses to change orbital energy and then coasts. In real missions, burns take time and engines are not perfectly impulsive. Still, the impulsive Hohmann model is a foundational approximation used in orbital mechanics education.

Burn 1, Burn 2, and Total Delta-V

The first burn changes the spacecraft from the original circular orbit to the transfer ellipse. The second burn changes it from the transfer ellipse to the target circular orbit. The total delta-v is the sum of the magnitudes of these burns. A calculator must use the circular speed and transfer speed at each radius, not simply subtract orbit radii or compare altitudes.

The direction of the burn depends on whether the transfer is raising or lowering the orbit. Raising an orbit generally requires prograde burns. Lowering an orbit generally requires retrograde burns. The calculator reports magnitudes for the delta-v values because mission budgets normally count the positive velocity-change capability required.

Transfer Time and Phase Angle

A Hohmann transfer time is half of the transfer ellipse period. This is why transfer time can be long for high-altitude or interplanetary transfers. Moving from a low orbit to a very high orbit may require hours. Interplanetary Hohmann-style transfers can require months.

Phase angle matters when the target is moving. During the transfer coast, the target orbiting body or satellite continues to move around the central body. A simple educational phase-angle estimate uses the target’s mean motion multiplied by the transfer time. The departure timing should place the target near the arrival point when the spacecraft reaches the end of the transfer ellipse. Real launch windows require much more precise trajectory analysis.

Hohmann vs Bi-Elliptic Transfers

A bi-elliptic transfer uses three burns. The first burn places the spacecraft on an ellipse with a large intermediate apoapsis. The second burn changes the periapsis of the transfer path at that high point. The third burn circularizes at the final orbit. For some very large radius ratios, a bi-elliptic transfer can use less delta-v than a Hohmann transfer. However, it often takes much longer.

This calculator includes a simplified bi-elliptic comparison. It is useful for seeing when a high intermediate radius starts to reduce delta-v. In practical mission design, the extra time, navigation uncertainty, radiation environment, operational cost, and perturbations may make a theoretically lower-delta-v bi-elliptic transfer unattractive.

Propellant and Rocket Equation Estimate

Delta-v connects directly to propulsion through the Tsiolkovsky rocket equation. If a spacecraft needs a certain Hohmann transfer delta-v and has a specific impulse \(I_{sp}\), the required mass ratio can be estimated with:

The initial mass and propellant mass are then:

This is an ideal estimate. Real propulsion planning must consider engine efficiency, finite burns, residual propellant, margins, attitude control, boiloff, pressure regulation, and mission operations requirements.

Hohmann Transfer Worked Examples

Example 1: Low Earth orbit to geostationary altitude. A common educational example uses an initial radius near low Earth orbit and a final radius near geostationary orbit. The transfer semi-major axis is:

The first burn compares initial circular speed with transfer speed at \(r_1\):

The second burn compares final circular speed with transfer speed at \(r_2\):

Example 2: Transfer time. The spacecraft coasts for half of the transfer ellipse:

Common Hohmann Transfer Mistakes

The first common mistake is using altitude instead of radius. Hohmann equations use distance from the center of the central body. If a satellite is 400 km above Earth, the orbital radius is Earth’s radius plus 400 km. The second mistake is mixing kilometers and meters. Standard gravitational parameters are usually in \(m^3/s^2\), so radii must be converted to meters inside the formula.

The third mistake is forgetting that the transfer must be coplanar and circular-to-circular for the classic formula. If the orbits have different inclination, eccentricity, argument of periapsis, or timing constraints, additional calculations are required. The fourth mistake is treating the transfer time as optional. If the target moves during the coast, phase angle and launch timing matter. The fifth mistake is using ideal delta-v as a final mission budget without including losses, margins, station keeping, navigation corrections, and finite-burn effects.