Hohmann Transfer Calculator - Two-Burn Orbital Transfer

A Hohmann transfer calculator estimates the propellant cost and travel time for a two-burn maneuver between two coplanar circular orbits around the same central body. The Hohmann transfer is the standard textbook baseline for orbit changes when both orbits are circular and in the same plane, and it is the most fuel-efficient two-impulse option for most cases. Use it to size station-keeping burns, compare mission options, or work a geostationary or interplanetary Earth-to-Mars example.

• • LEO to GEO satellite delivery: Estimate the perigee and apogee burns needed to lift a satellite from low Earth orbit to geostationary orbit using a geostationary transfer orbit.
• • Interplanetary mission planning: Compute total delta-v and travel time for an Earth-to-Mars or Earth-to-Venus Hohmann transfer around the Sun.
• • Orbit lowering and disposal: Evaluate the two-burn cost of moving a satellite to a lower operational orbit or a deorbit altitude.
• • Classroom and homework verification: Cross-check worked orbital mechanics problems using the same vis-viva and Kepler formulas.

The Hohmann transfer was described by Walter Hohmann in his 1925 book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies). It assumes two instantaneous engine burns in an ideal two-body central field. The transfer ellipse is tangent to the inner orbit at one end and tangent to the outer orbit at the other, so its semi-major axis is the average of the two orbital radii.

The result panel reports the circular speeds at each orbit, the perigee and apogee speeds on the transfer ellipse, the magnitude of each burn, the total delta-v across both burns, and the half-period travel time. That output is enough to compare a Hohmann maneuver with a bi-elliptic transfer or a direct burn in a homework or preliminary mission study.

For an interplanetary Hohmann transfer, Synodic Period Calculator estimates the alignment cycle that controls how often the launch window opens for a given pair of orbits.

Each circular orbit speed comes from v = sqrt(μ/r), where μ is the gravitational parameter of the central body and r is the distance from its center. The transfer ellipse touches the inner orbit at one end and the outer orbit at the other, so its semi-major axis aH is (r1 + r2)/2. Applying the vis-viva equation at the two ends of that ellipse gives the transfer orbit speeds, and the difference between those speeds and the circular orbit speeds gives the per-burn delta-v.

• r1: Radius of the starting circular orbit, from the central body's center.
• r2: Radius of the target circular orbit, from the central body's center.
• μ: Standard gravitational parameter GM of the central body.
• Δv1: Speed change at the first burn, at the inner end of the transfer ellipse.
• Δv2: Speed change at the second burn, at the outer end of the transfer ellipse.
• tH: Travel time on the transfer ellipse, half its orbital period.

The same equations work in both directions. If r2 is smaller than r1, the first burn at r1 puts the spacecraft on the apogee end of a transfer ellipse whose perigee is r2, and the second burn at r2 circularizes the lower orbit. Delta-v values are reported as positive magnitudes so the same form handles raising and lowering the orbit without switching formulas.

Travel time is half the period of the transfer ellipse. By Kepler's third law, the period is 2π·sqrt(aH³/μ), so a Hohmann transfer takes π·sqrt((r1+r2)³/(8μ)). That relationship explains why an interplanetary transfer takes months while a geostationary transfer from low Earth orbit only takes a few hours.

According to Wikipedia (Hohmann transfer orbit), the geostationary transfer worked example reports burn 1 = 2.42 km/s, burn 2 = 1.46 km/s, and total delta-v = 3.88 km/s, matching the two-burn formula used by this calculator to within rounding.

Four ideas drive the result. Keeping them separate makes a Hohmann maneuver easy to check.

These four concepts combine in one line per burn. The transfer ellipse's semi-major axis fixes the vis-viva speed at each end, and the difference between those speeds and the matching circular orbit speeds is the burn cost.

A common confusion is treating altitude as orbital radius. For Earth, the equatorial radius is about 6,378 km, so a 400 km altitude orbit corresponds to a 6,778 km radius.

The same semi-major axis and μ pair also appears in the Orbital Period Calculator when comparing orbital timing across orbits, so a Hohmann output and an orbital-period output can be sanity-checked against each other.

The calculator keeps the four input quantities visible at the same time. Each step below maps to one field, and the result panel refreshes as soon as a field changes.

1. 1 Choose the central body: Pick Earth, Moon, Mars, or Sun to load a standard gravitational parameter, or select Custom to enter mu directly.
2. 2 Enter r1 (starting orbit radius): Use the distance from the central body's center to the starting orbit, not altitude above the surface.
3. 3 Enter r2 (target orbit radius): Same unit and reference point as r1. An r2 smaller than r1 produces an inward Hohmann maneuver.
4. 4 Pick the direction: Outward when raising the orbit and Inward when lowering it. The label clarifies which burn is the initial burn.
5. 5 Read total delta-v first: Total delta-v is the headline number for a fuel or mission comparison. It varies smoothly with r1 and r2.
6. 6 Inspect the per-burn rows: When Δv1 and Δv2 are very different in size, the larger one usually sets the engine design choice.

The geostationary transfer example is a useful first sanity check. With Earth, r1 = 6,678 km, and r2 = 42,164 km, the panel reports Δv1 ≈ 2.426 km/s, Δv2 ≈ 1.467 km/s, total 3.893 km/s, and a transfer time near 5.27 hours. Those numbers match the textbook and Wikipedia example to within rounding.

When reviewing the circular orbit speeds at each radius, the Circular Motion Calculator provides a quick sanity check on centripetal acceleration and period for the same radius.

A Hohmann transfer calculator is useful whenever a small set of numbers must be turned into a quick fuel and time estimate. The benefits below are the situations where the tool pays for itself.

• • Two-burn fuel budgets: Produces the per-burn delta-v and total delta-v used for propellant sizing and engine selection.
• • Mission timing baseline: Reports the half-period transfer time, which is the earliest reasonable travel window for a Hohmann-class maneuver between two coplanar circular orbits.
• • Central-body flexibility: Switches between Earth, Moon, Mars, and Sun presets without changing the formula, so the same workflow applies to satellite and interplanetary cases.
• • Direction-aware output: Reports burns as positive magnitudes whether the maneuver raises or lowers the orbit, which avoids double-counting signs when planning fuel budgets.
• • Worked-example cross-check: Matches Wikipedia's geostationary transfer and Earth-Mars transfer examples to within rounding, which makes it a quick homework and design sanity check.

The Hohmann transfer is the natural baseline to compare against. A bi-elliptic transfer is more fuel-efficient only when the orbit ratio exceeds about 11.94, and direct burns or low-thrust spirals trade time for fuel differently.

When the burn cost depends on the inertial reaction of a spinning stage or a spinning payload, the Centrifugal Force Calculator explains the apparent force that the maneuver must overcome during the burn.

The Hohmann result depends on a small set of assumptions. Knowing which numbers control the answer helps avoid misreading it.

• • Inclination differences between r1 and r2 are not modeled. A real plane-change maneuver adds its own delta-v.
• • Atmospheric drag, gravity losses, third-body perturbations, and non-spherical gravity are ignored. They matter for low-altitude LEO operations and for inner-planet transfers.
• • Hohmann is not always minimum-fuel. When r2/r1 exceeds about 11.94 and an intermediate apoapsis can be selected, a bi-elliptic transfer can use less total delta-v at the cost of longer travel time.

The worst-case Hohmann delta-v is not at an infinite target radius. It peaks when r2/r1 is about 15.58, where total delta-v is about 53 percent of the inner circular orbit speed. Beyond that ratio, the second burn shrinks faster than the first grows, so total delta-v gradually approaches the escape delta-v of (sqrt(2) − 1) times the circular orbit speed.

According to NASA JPL Solar System Dynamics, Earth's standard gravitational parameter is 398600.435507 km^3/s^2, and the Sun, Moon, and Mars parameters are used as additional presets so the central-body math aligns with mission planning tools.

According to NASA Science, the square of an orbital period is proportional to the cube of the semi-major axis, which is the basis for the Hohmann transfer time formula used here.

Once total delta-v is known, the Ideal Rocket Equation converts it into a propellant mass fraction using the engine's exhaust velocity.