Rocket Equation (Delta-v) Calculator – Tsiolkovsky, Isp, Mass Ratio & Stages

How much delta-v does a rocket have?

The Tsiolkovsky rocket equation links how much a rocket can change its speed, called delta-v, to how fast its exhaust leaves and how much of its mass is fuel: Δv = Isp × g₀ × ln(m₀ ÷ m_f). This rocket equation calculator works in both directions. Enter the dry mass, propellant mass and Isp of up to three stages plus a payload and it adds up the delta-v of every stage. Or enter a target delta-v and an engine Isp to find the mass ratio and, with a final mass, the propellant you must carry.

The working is shown line by line so it can be checked against a textbook or a spreadsheet. All of it is calculated in your browser.

How to use the Rocket Equation Calculator

1. Enter the payload mass, then the dry mass, propellant mass and Isp of stage 1. Stage 1 fires first.
2. Add stage 2 and stage 3 if the rocket has them, or leave their rows empty.
3. Read the total delta-v, the liftoff mass, and the table with the mass ratio and delta-v of each stage.
4. In the second block, enter a target delta-v and an Isp to get the mass ratio, the propellant share and, with a final mass, the propellant in kilograms.

Rocket Equation Calculator features

The equation and a worked example

With specific impulse Isp in seconds, the exhaust velocity is v_e = Isp × g₀, where g₀ = 9.80665 m/s² is standard gravity. The delta-v is Δv = ve × ln(m0 ÷ mf), where m₀ is the mass before the burn and m_f the mass after all the propellant is used. Turned round, the mass ratio for a given delta-v is m0 ÷ mf = eΔv ÷ ve.

Example: a stage with 400,000 kg of propellant, 25,000 kg of dry mass and 109,000 kg above it burns from 534,000 kg to 134,000 kg. With Isp 300 s the delta-v is 300 × 9.80665 × ln(534,000 ÷ 134,000) ≈ 4,067 m/s. For a target of 9,400 m/s with an engine of Isp 350 s the mass ratio is e^{9,400 ÷ 3,432} ≈ 15.5, so about 94 per cent of the starting mass must be propellant, which is why staging is used.

Why staging helps

Because the equation is logarithmic, doubling the delta-v squares the mass ratio. Dropping an empty tank and engine part-way means the next burn no longer has to push that dead mass, so two or three stages reach speeds one stage cannot. To see what speed an orbit or an escape needs, use the orbital period calculator or the escape velocity calculator.

Limits of this calculator

• It is the ideal equation: gravity losses, atmospheric drag and steering losses are not modelled. Add them to the target delta-v yourself; the table gives typical budgets.
• One Isp is used per stage. Real engines have a different Isp at sea level and in vacuum, so use the value that matches where most of the burn happens.
• Boil-off, residual propellant, side boosters and payload shrouds dropped during flight are not modelled; model them as extra stages if needed.