Free Tsiolkovsky Equation Calculator
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
m/s
m/s
Required Mass Ratio (m0/mf)
22.9504
Fuel Mass Fraction0.956428
Fuel Fraction (%)95.64 %
Required Mass Ratio (m0/mf) vs Required Delta-V
Tsiolkovsky Equation: Mass Ratio Form
Given a target delta-v and an engine's exhaust velocity, this tells you how massive the rocket must be at launch relative to its dry mass.
Formula
m0/mf = exp(dv / ve)
The fuel fraction is 1 - 1/(m0/mf). For orbital velocity (9.4 km/s) with a 3 km/s exhaust, over 95% of the rocket must be propellant.
Example Calculation
Reach LEO (dv = 9400 m/s) with ve = 3000 m/s.
- 01m0/mf = exp(dv / ve)
- 02m0/mf = exp(9400 / 3000)
- 03m0/mf = exp(3.133) = 22.94
- 04Fuel fraction = 1 - 1/22.94 = 0.9564 = 95.64%