Delta-V Budget Calculator
Calculate fuel mass and mass ratio for rocket missions using the Tsiolkovsky equation.
Enter delta-v, exhaust velocity, and dry mass for total fuel required.
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:
| Mission | Delta-v Needed |
|---|---|
| Low Earth Orbit (LEO) | ~9.4 km/s |
| Lunar orbit and back | ~15.93 km/s |
| Mars (one-way, landing) | ~16.0 km/s |
| Jupiter (Hohmann transfer) | ~30.0 km/s |
| Solar system escape | ~42.1 km/s |
Common Engine Types and Exhaust Velocities:
| Engine | Exhaust Velocity | Example |
|---|---|---|
| Chemical (liquid) | ~4.4 km/s | Space Shuttle Main Engine |
| Nuclear Thermal | ~8.0 km/s | NERVA (tested in 1960s) |
| Ion Thruster | ~30 km/s | Dawn spacecraft |
| VASIMR | ~50 km/s | Proposed plasma engine |
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 ~8.4. That means 87.5% of launch mass is fuel — which is why rockets are mostly fuel tank.
Getting to Mars with a chemical engine and returning requires mass ratios above 100 — making it impractical without refueling in space or using more efficient propulsion. This is exactly why ion drives and nuclear propulsion are so important for deep-space missions.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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