Rocket Equation Calculator
Work out a rocket's delta-v from its specific impulse and mass ratio using the Tsiolkovsky equation — and see why spacecraft are mostly fuel.
Como usar esta calculadora
- 1Enter your engine's specific impulse in seconds, or its exhaust velocity in m/s.
- 2Enter the wet mass (fully fuelled) and the dry mass (empty) in kilograms.
- 3Read the delta-v, then check the table to see which manoeuvres it can achieve.
Como funciona
The Tsiolkovsky rocket equation
Δv = vₑ × ln(m₀ ÷ m_f) vₑ = exhaust velocity = Isp × g₀ m₀ = wet mass (with fuel), m_f = dry mass (empty) g₀ = 9.80665 m/s² the mass ratio sits inside a natural logarithm
A rocket accelerates by throwing propellant out the back, so its delta-v depends on how fast it throws (exhaust velocity) and how much of its mass is throwable (the mass ratio). Derived by Konstantin Tsiolkovsky in 1903, the equation contains a natural logarithm, and that logarithm is the tyranny of the problem: doubling your delta-v does not need double the fuel, it needs the mass ratio squared. This is why rockets are almost entirely fuel and why reaching orbit is so hard.
Exemplo resolvido
A stage with a 450-second specific impulse (exhaust velocity 4,413 m/s), a wet mass of 500 tonnes and a dry mass of 100 tonnes has a mass ratio of 5. Its delta-v is 4,413 × ln(5) ≈ 7,103 m/s — about 7.1 km/s, not quite enough on its own to reach low Earth orbit, which is why real launchers use multiple stages.
Rocket Equation Calculator: o guia completo
Delta-v is the currency of spaceflight
In space there is no road and no distance that matters in the everyday sense — what matters is delta-v, the total change in velocity a spacecraft can produce. Every manoeuvre has a delta-v price: reaching orbit costs about 9.4 km/s, a trip to Mars a few more, landing on the Moon and returning several more still. A mission is planned by adding up these costs into a delta-v budget, and the rocket must be able to pay it.
This is why the rocket equation is the first thing any mission designer computes. It converts an engine's efficiency and a vehicle's fuel fraction into the one number that determines whether the mission is even possible.
The tyranny of the rocket equation
The cruelty of the equation is the logarithm. Because delta-v depends on the natural log of the mass ratio, gains get exponentially harder. To double your delta-v with the same engine, you do not carry twice the fuel — you must square the mass ratio, carrying far, far more. Reaching a mass ratio of 20 means 95% of the rocket is propellant, leaving almost nothing for structure, engines, and payload.
This is the fundamental reason spaceflight is so unforgiving. A launch vehicle sitting on the pad is typically 85–95% fuel by mass. The tiny remainder is everything else, which is why aerospace engineers fight for every kilogram and why the payload delivered to orbit is a small fraction of the towering rocket that lifts it.
Two ways to win: better engines or staging
The equation offers only two levers. Raise the exhaust velocity — a better, higher-Isp engine throws propellant faster, so hydrogen engines (Isp ≈ 450 s) beat kerosene (≈ 300 s), and ion thrusters (≈ 3,000 s) beat both, though they push very gently. Or raise the mass ratio by carrying more fuel, which the logarithm punishes.
Staging is the clever workaround for the second lever. By discarding empty tanks and engines partway up, a rocket sheds dead weight and effectively resets its mass ratio for the next stage. This is why every orbital rocket in history has been multi-stage: no single stage can achieve orbit efficiently, but a stack of them can, each one lighter and faster than the last.
Perguntas frequentes
What is delta-v?
Delta-v is the total change in velocity a rocket can achieve by burning all its propellant. It is the fundamental measure of a spacecraft's capability — every manoeuvre in space has a delta-v cost, and the mission works only if the rocket's delta-v exceeds the sum of those costs.
What is specific impulse?
Specific impulse (Isp) measures engine efficiency — roughly, how much thrust you get per unit of propellant burned per second, expressed in seconds. Multiply it by g₀ (9.80665) to get the exhaust velocity. Higher is better: hydrogen engines reach about 450 s, ion drives about 3,000 s.
Why are rockets almost entirely fuel?
Because the rocket equation contains a logarithm. Achieving high delta-v requires a large mass ratio, and since the relationship is logarithmic, even modest delta-v gains demand disproportionately more propellant. Orbital rockets end up 85–95% fuel by mass, leaving little room for anything else.
Why do rockets have multiple stages?
Staging beats the tyranny of the mass ratio. By dropping empty tanks and spent engines during ascent, a rocket sheds dead weight and effectively restarts its mass ratio for the remaining fuel. This delivers far more delta-v than a single stage of the same size ever could.