Plane Change Delta-v Calculator
The delta-v needed to change an orbit’s inclination by a given angle at a given orbital speed — the reason launch sites are placed near the equator and plane changes are done where the spacecraft is slowest.
Rotating a velocity vector by an angle θ without changing its size takes a change of 2 v sin(θ ÷ 2) — the base of an isosceles triangle.
How the plane change delta-v calculator works
Rotating a velocity vector by an angle θ without changing its size takes a change of 2 v sin(θ ÷ 2) — the base of an isosceles triangle. At orbital speeds that is brutal: a 30° change at 7.7 km/s costs 4 km/s, half of what it took to reach orbit. The cost scales with speed, so plane changes are made at apoapsis, or combined with the burn that raises or lowers the orbit.
Formula: Δv = 2 v sin(θ ÷ 2)
Worked examples
| Inputs | Delta-v | Note |
|---|---|---|
| 28.5° at 7.67 km/s | 3.776 km/s | 3.78 km/s; 0.79 at apogee |
| A 1° correction | 0.134 km/s | 0.134 km/s |
| 90° at 3 km/s | 4.243 km/s | 4.24 km/s — √2 times the speed |
FAQFrequently asked questions
Why do launch sites sit near the equator?
A rocket launched due east enters an orbit inclined at the latitude of the site; reaching the equatorial plane for a geostationary satellite then costs a plane change of that many degrees. From 28.5° that is over 2 km/s at low-orbit speed — hence launches from Kourou at 5° and sea launches on the equator.
Why is it cheaper at apoapsis?
Because the spacecraft is moving slowest there and the cost scales with speed. Geostationary transfer orbits carry the inclination change to the apogee burn, where speed is 1.6 km/s instead of 7.7.
Can it be combined with another burn?
Yes — a combined burn changing both speed and direction costs less than the two separately (the vector sum, not the scalar sum). Mission designers always combine where they can.
What about changing the ascending node?
Rotating the orbit about the pole is also a plane change, done at the equator crossing; the same formula applies with the angle between the two planes.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- Royal Observatory Greenwich — the historic home of the prime meridian
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).