Tsiolkovsky Equation Calculator Formula

Understand the math behind the tsiolkovsky equation calculator. Each variable explained with a worked example.

Use the Tsiolkovsky Equation Calculator

Formulas Used

Required Mass Ratio (m0/mf)

mass_ratio = exp(delta_v / exhaust_velocity)

Fuel Mass Fraction

fuel_fraction = 1 - 1 / exp(delta_v / exhaust_velocity)

Fuel Fraction (%)

fuel_fraction_pct = (1 - 1 / exp(delta_v / exhaust_velocity)) * 100

Variables

VariableDescriptionDefault
delta_vRequired Delta-V(m/s)9400
exhaust_velocityExhaust Velocity(m/s)3000

How It Works

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.

Worked Example

Reach LEO (dv = 9400 m/s) with ve = 3000 m/s.

delta_v = 9400exhaust_velocity = 3000
  1. 01m0/mf = exp(dv / ve)
  2. 02m0/mf = exp(9400 / 3000)
  3. 03m0/mf = exp(3.133) = 22.94
  4. 04Fuel fraction = 1 - 1/22.94 = 0.9564 = 95.64%

Ready to run the numbers?

Open Tsiolkovsky Equation Calculator