Rocket Equation Calculator (Tsiolkovsky Delta-v)

The Tsiolkovsky rocket equation, Δv = v_e·ln(m₀/m₁), gives the total velocity change a rocket can achieve from burning all its propellant, where m₀ is the rocket's initial mass (including propellant) and m₁ is its final mass after that propellant is spent. It comes directly from conservation of momentum: each small parcel of exhaust ejected backward at the effective exhaust velocity v_e gives the ever-lighter rocket a forward momentum kick, and integrating that effect from m₀ down to m₁ produces the logarithm.

Engine performance is conventionally rated as specific impulse, Isp, in seconds — a unit-system-independent figure — rather than a raw exhaust velocity, so this calculator converts it with v_e = Isp·g₀, where g₀ = 9.80665 m/s² is standard gravity, a fixed international constant used purely as a conversion factor here, not a claim about gravity at any particular place. Because mass only ever appears in the equation as the ratio m₀/m₁, that ratio — and the propellant mass fraction (m₀−m₁)/m₀ derived from it — comes out identical whether both masses are entered in kilograms or in pounds.

The logarithm is why delta-v gets dramatically harder to add as a mission's requirements grow: reaching one more increment of Δv equal to v_e multiplies the required mass ratio by e (≈2.72) rather than just adding to it, which is the mathematical root of the rocketry maxim that most of a rocket's mass has to be propellant.