By Zencalcy Editorial TeamLast reviewed About us
The rocket equation relates the velocity change a rocket can achieve to how much of its mass is propellant. Because the fuel must be carried, the delta-v grows only with the logarithm of the mass ratio — the reason orbital rockets are mostly tank by weight.
Delta-v, mass ratio and propellant mass for a rocket burn.
Δv = v_e ln(m₀ / m_f) m₀ / m_f = e^(Δv / v_e)
The equation assumes a single stage, constant exhaust velocity and no gravity or drag losses. Real launches add 1.5–2 km/s of losses on the way to low Earth orbit.
| Symbol | Meaning |
|---|---|
| Δv | Velocity change the rocket can produce, in m/s. |
| v_e | Effective exhaust velocity, in m/s. |
| m₀ | Initial (wet) mass, in kilograms. |
| m_f | Final (dry) mass after the burn, in kilograms. |
A mass ratio of 5 with an exhaust velocity of 3,000 m/s gives Δv = 3,000 × ln 5 = 4,828 m/s. Four fifths of the rocket's mass was propellant.
Continue with the Tension Calculator, Rocket Thrust Calculator, or the Weight Calculator — or browse more dynamics tools and all physics calculators.
Each increment of velocity requires burning fuel, and that fuel itself had to be accelerated. The required mass grows exponentially with delta-v, so the velocity grows logarithmically with mass ratio.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026