Delta-V Budget Calculator
Calculate fuel mass and mass ratio for any rocket mission using the Tsiolkovsky rocket equation.
Enter delta-v, exhaust velocity, and dry mass to find 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.