Ideal Rocket Equation Calculator — Tsiolkovsky Δv

Formula

How this is calculated

The Tsiolkovsky rocket equation is the governing relation of propulsive spaceflight: Δv = ve × ln(m0/mf), where ve = Isp × g0 is the effective exhaust velocity in m/s, m0 is the initial (wet) mass including all propellant, mf is the final (dry) mass after burning all propellant, and the mass ratio m0/mf measures how much of the vehicle is fuel. The natural logarithm is the critical insight: doubling the mass ratio only adds one exhaust-velocity increment, not double the Δv — each kilogram of extra propellant must first be accelerated along with all the other propellant, yielding sharply diminishing returns.

Specific impulse Isp (in seconds) is the universal measure of propellant efficiency: the thrust per unit weight flow of propellant. Multiplied by g0 = 9.80665 m/s², it converts to exhaust velocity. Typical values: solid rocket motors 230–280 s; kerosene/LOX engines (Falcon 9 Merlin vacuum) ~311 s; liquid hydrogen/LOX (RS-25 Space Shuttle) ~453 s; ion thrusters 1 000–10 000 s (high efficiency, very low thrust). The default values (m0 = 100 000 kg, mf = 20 000 kg, Isp = 311 s) model a kerosene-fuelled upper stage and yield ≈ 4 900 m/s.

This is an ideal limit: it assumes constant Isp, all propellant burned instantaneously (or in vacuum with no gravity or drag), and no structural inefficiency. Real mission Δv budgets must add gravity losses (≈ 100–1 500 m/s for launches), drag losses (≈ 50–150 m/s), and steering losses. Multi-stage rockets subdivide the problem into smaller mass ratios, each operating the equation fresh, to reach orbital Δv (≈ 9 400 m/s for low Earth orbit) that would require impractical mass ratios from a single stage.