Delta-V Budget Calculator

The Tsiolkovsky rocket equation (1903) is the fundamental equation of rocketry. It relates the change in velocity a rocket can achieve (delta-v) to the mass of propellant burned and the efficiency of the engine.

The Rocket Equation: Δv = ve × ln(m0 / mf)

Where:

• Δv (delta-v) = total velocity change achievable (km/s)
• ve = exhaust velocity of the engine (km/s), how fast the exhaust exits the nozzle
• m0 = total initial mass (wet mass: ship + fuel)
• mf = final dry mass (ship + payload, with no fuel)
• ln = natural logarithm

Solving for Mass Ratio: m0 / mf = e^(Δv / ve)

This ratio tells you how much heavier the full rocket is compared to its empty weight. A mass ratio of 5 means 80% of the launch mass is fuel, and only 20% is ship.

Fuel Mass: Fuel = mf × (e^(Δv/ve) − 1)

Total Launch Mass: m0 = mf × e^(Δv/ve)

Delta-V Requirements for Common Missions:

A word on that last row, because it is the one most often quoted wrongly. You will see 42.1 km/s attached to “solar system escape” all over the place. That number is the escape velocity from the Sun’s gravity at Earth’s orbit, and it is not a delta-v budget, because Earth is already carrying you at 29.8 km/s around the Sun for free. You only need to make up the difference of about 12.3 km/s, and thanks to the Oberth effect you buy that far more cheaply by burning deep in Earth’s gravity well: about 8.8 km/s starting from low Earth orbit, so roughly 18.3 km/s all in from the launch pad. The departure burn itself, that 8.8 km/s, needs a mass ratio of 7.3 on a chemical engine. Feed the same engine the mistaken 42.1 km/s and it asks for 14,300. One of those is a hard mission and the other cannot be built out of any material.

Common Engine Types and Exhaust Velocities:

Why the Mass Ratio Matters: Every kg of dry mass requires exponentially more fuel as delta-v increases. Going to LEO at 9.4 km/s with a chemical engine (ve = 4.4) requires a mass ratio of 8.47. That means 88.2% of launch mass is propellant, which is why rockets are mostly fuel tank.

Push the budget to a Mars round trip, call it 30 km/s on the same chemical engine, and the ratio jumps to 914. Every tonne of ship needs 913 tonnes of propellant, which no structure can hold. Nothing about the physics changes; the exponential simply runs away. That is the whole argument for ion drives, nuclear thermal engines and refueling in orbit: they either raise ve or reset the dry mass partway through the trip.

One thing this calculator deliberately does not model: staging. The rocket equation assumes a single vehicle with one dry mass. Real launchers throw away empty tanks, which is why a Falcon 9 reaches orbit on a mass ratio far below what a single-stage version would need. Run each stage through the calculator separately, using that stage’s own dry mass and the payload it still has to carry, then add the delta-v figures together.