Orbital Transfer Calculator
Calculate Hohmann transfer orbit parameters including delta-V requirements and transfer time between two circular orbits.
About this calculator
A Hohmann transfer is the most fuel-efficient way to move a spacecraft between two circular orbits using only two engine burns. The maneuver places the spacecraft onto an elliptical "transfer orbit" whose closest point (periapsis) touches the starting circular orbit and whose farthest point (apoapsis) touches the target circular orbit -- the transfer orbit's semi-major axis is simply the average of the two orbit radii. The first burn (Delta-V1) happens at the starting orbit and speeds the spacecraft up (or slows it down, for a transfer to a lower orbit) just enough to stretch its orbit into that ellipse; the second burn (Delta-V2), applied at the far end of the ellipse, circularizes the orbit at the new altitude.
Both burns are computed from the vis-viva relationship between orbital velocity, orbit radius, and the central body's gravitational parameter (mu) -- which is why a larger mu (a more massive central body) demands more velocity change for the same altitude change, while transfer time (half the elliptical orbit's period, from Kepler's Third Law) gets SHORTER as mu increases, since a stronger gravitational pull moves the spacecraft through its elliptical path faster. This calculator defaults to Earth's gravitational parameter and radius but works for a transfer around any body by entering its own mu and radius together -- altitude inputs are only meaningful once both of those match the body you're modeling. Real missions add plane-change burns, finite burn losses, and gravity-assist trajectories the idealized two-burn Hohmann transfer does not model.
Inputs
Results
First Burn ΔV₁
2,399.35 m/s
Total ΔV
3,856.58 m/s
How to Use This Calculator
- Enter the initial orbit altitude (km) and desired final orbit altitude (km) above the central body.
- Set the gravitational parameter (µ) in m³/s² and the Central Body Radius in meters — both default to Earth (3.986×10¹⁴ m³/s² and 6,371,000 m) and must be changed together for another body.
- Review the two required delta-V burns (ΔV₁ and ΔV₂ in m/s) and the total ΔV.
- Use transfer time (in minutes) and semi-major axis (in km) to plan mission scheduling and propellant loading.
How the result changes with Central Body Radius
| Central Body Radius | First Burn ΔV₁ | Total ΔV |
|---|---|---|
| 3,185,500 | 3,725.39 m/s | 5,610.71 m/s |
| 4,778,250 | 2,910.75 m/s | 4,553.88 m/s |
| 9,556,500 | 1,775.35 m/s | 2,961.08 m/s |
| 15,927,500 | 1,150.8 m/s | 2,003.76 m/s |
What each input means
- Initial Orbit Altitude
- Altitude of the starting circular orbit above Earth's surface in kilometers.
- Final Orbit Altitude
- Altitude of the target circular orbit above Earth's surface in kilometers.
- Gravitational Parameter (μ)
- Standard gravitational parameter of the central body. Default is Earth (3.986×10¹⁴ m³/s²).
- Central Body Radius
- Radius of the central body in meters, measured to its surface. Default is Earth's radius (6,371,000 m) -- change this together with the gravitational parameter (μ) when modeling another body.
How this is calculated
Worked example, using the default values
- Identify Input ParametersInitial Orbit Altitude = 400, Final Orbit Altitude = 35786, Gravitational Parameter (μ) = 398600000000000, Central Body Radius = 6371000 = 4 input(s) provided
- Calculate First Burn ΔV₁First Burn ΔV₁ = Math2399.35 = 2399.35
- Calculate Total ΔVTotal ΔV3856.58 = 3856.58
- Calculate Second Burn ΔV₂Second Burn ΔV₂ = Math1457.23 = 1457.23
- Calculate Transfer TimeTransfer Time317.34 = 317.34
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does a Hohmann transfer need exactly two burns?
The first burn raises (or lowers) the spacecraft's orbit from a circle into an ellipse that just touches the target altitude on its far side. Without a second burn, the spacecraft would swing back down along that same ellipse rather than staying in the new orbit -- the second burn circularizes it at the target altitude by matching the local circular orbital velocity there.
How does the gravitational parameter (mu) of the central body change the transfer?
A larger mu means stronger gravity, which both requires MORE delta-V to change orbital velocity by a given amount and produces a SHORTER transfer time, since the spacecraft moves faster through a stronger gravitational field. Earth's mu (3.986x10^14 m^3/s^2) and radius (6,371,000 m) are the defaults, but entering the Moon's, Mars', or the Sun's mu AND radius together recalculates the same maneuver for that body -- the radius input has to change alongside mu, since altitude is measured above the surface of whichever body you pick.
Why is the transfer semi-major axis just the average of the two orbit radii?
The Hohmann transfer ellipse is defined so its closest point sits at the starting orbit's radius and its farthest point sits at the target orbit's radius -- for an ellipse, the semi-major axis is always the average of periapsis and apoapsis distances, so it falls out directly from those two endpoints.
What does this calculator NOT account for that a real mission would need?
It models an idealized, instantaneous two-burn maneuver between two coplanar circular orbits. Real missions also budget for plane-change burns if the orbits are inclined differently, finite (non-instantaneous) burn losses, and navigation margins -- all of which add delta-V beyond the theoretical minimum this calculator reports.
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