Rocket Equation Calculator
Enter an exhaust velocity and the wet and dry mass to get the change in velocity (Δv) a rocket can achieve — and see why carrying more propellant pays off only logarithmically.
Delta-v from the mass ratio
Enter the effective exhaust velocity and the initial (wet) and final (dry) mass and the rocket equation calculator returns the change in velocity (Δv) in metres per second.
Use SI units
Exhaust velocity in metres per second and both masses in kilograms give Δv in metres per second — the dry mass must be smaller than the wet mass.
What is the rocket equation?
Δv from exhaust speed and mass ratio
The rocket equation calculator applies the Tsiolkovsky rocket equation, the single most important relation in spaceflight. It tells you the change in velocity — the "delta-v" or Δv — a rocket can gain by burning its propellant, given how fast that propellant leaves the nozzle and how much of the rocket's mass is fuel. The two ingredients are the effective exhaust velocity (in metres per second) and the mass ratio: the initial wet mass with full tanks divided by the final dry mass once the propellant is spent. Δv is the currency of orbital mechanics: every manoeuvre, from reaching orbit to landing on the Moon, has a delta-v price tag a mission must afford.
Enter an exhaust velocity in metres per second and the wet and dry mass in kilograms to get the change in velocity (Δv) instantly.
The change in velocity is the effective exhaust velocity multiplied by the natural logarithm of the mass ratio — the wet mass divided by the dry mass.
Δv = ve × ln(m0 / mf)The natural logarithm is what makes rockets hard. Because Δv depends on the logarithm of the mass ratio, doubling your propellant does not double your delta-v — it adds only a fixed increment. Raising the exhaust velocity, by contrast, scales Δv directly. Use metres per second for the exhaust velocity and kilograms for both masses and the Δv comes back in metres per second.
Suppose a rocket stage has an effective exhaust velocity of 3000 m/s, a wet mass of 50,000 kg, and a dry mass of 10,000 kg.
Form the mass ratio
50,000 / 10,000 = 5 — the wet mass is five times the dry mass.
Take the natural log
ln(5) ≈ 1.6094 — the logarithm that the exhaust velocity is multiplied by.
Multiply by the exhaust velocity
3000 × 1.6094 ≈ 4,828.31 m/s — the change in velocity the stage can deliver.
The Δv your stage produces (about 4,828 m/s in the example) is a budget you spend on manoeuvres. Reaching low Earth orbit costs roughly 9,400 m/s of Δv once gravity and drag are included, so a single stage with a 5:1 mass ratio falls well short — which is exactly why rockets are staged. Staging lets you shed empty tank and structure mass partway up, so the later stages start with a smaller dry mass and a more favourable mass ratio, and each contributes its own Δv on top of what came before. The logarithm is the catch: because Δv grows with the natural log of the mass ratio, the cost of carrying more propellant is exponential. To double your Δv at a fixed exhaust velocity you must square the mass ratio — a stage needing twice the Δv of a 5:1 vehicle would need a 25:1 ratio, almost all of it fuel. That punishing relationship is why a higher exhaust velocity, not simply bigger tanks, is the lever engineers reach for first.
The equation is exact for an idealised rocket, but real launches lose Δv to forces it ignores.
Ideal Δv only — gravity and drag losses are not included
This calculator gives the ideal change in velocity in free space. It assumes a constant effective exhaust velocity throughout the burn and ignores gravity losses, atmospheric drag, and steering losses, which together can subtract well over a thousand metres per second on a launch from the ground. Keep your units consistent — metres per second for the exhaust velocity and kilograms for both masses — and make sure the dry mass is smaller than the wet mass, since a mass ratio below one has no physical meaning here.