Rocket Equation Calculator

How this is worked out

The ideal rocket equation (Tsiolkovsky) relates the change in velocity a rocket stage can achieve to its specific impulse and the ratio of its initial (fuelled) mass to its final (empty) mass: Δv = I_sp × g₀ × ln(m₀/m_f), where g₀ = 9.80665 m/s² is the internationally defined standard acceleration of gravity (used here purely as the conversion factor between specific impulse in seconds and effective exhaust velocity in m/s, not as a claim about the local gravity anywhere). This is an idealised, single-stage result: it ignores gravity losses, aerodynamic drag and steering losses during an actual launch, so a real rocket needs more delta-v capability than its mission's "ideal" requirement.

Frequently asked questions

Why does so much of a rocket have to be propellant?

Because the relationship is exponential (through the natural logarithm, inverted): each extra increment of delta-v costs proportionally more propellant than the last. NASA's own worked example (I_sp = 350 s reaching roughly the 25,000 ft/s needed for low Earth orbit) comes out to a mass ratio of about 10 — around 90% of the rocket's liftoff mass is propellant.

What counts as "final mass"?

Everything left once the propellant for that stage is spent: structure, engines, and (if you're sizing a whole vehicle rather than just one stage) the payload and any further stages riding on top.

Related tools: Orbital & Escape Velocity Calculator, Kepler's Third Law Calculator, Hohmann Transfer Delta-v Calculator.

Source / Last verified: NASA Glenn Research Center, "Beginner's Guide to Aeronautics — Ideal Rocket Equation" (grc.nasa.gov), and NIST, "CODATA Value: standard acceleration of gravity" (physics.nist.gov, 9.806 65 m/s², exact), both read 1 October 2026. This tool's result for the NASA page's own worked example (I_sp = 350 s, mass ratio 10) reproduces its "roughly 25,000 ft/s" figure (calculates to about 25,900 ft/s, matching the source's own rounding).