Rocket Equation Calculator (Tsiolkovsky Delta-v)
Enter the engine’s specific impulse and the stage masses.
Your numbers
Your results
Rocket Equation Calculator (Tsiolkovsky Delta-v) by TheCalcTools
How the Rocket Equation Calculator (Tsiolkovsky Delta-v) works
The Tsiolkovsky equation gives the change in velocity a rocket can achieve: Δv = Isp × g₀ × ln(m₀ ÷ m_f), with g₀ = 9.80665 m/s². Delta-v depends on exhaust speed and how much of the rocket is propellant.
Reaching low Earth orbit takes about 9.3 to 10 km/s including gravity and drag losses, which is why rockets use stages to drop empty mass.
The formula
Worked example
Using the default values shown in the calculator:
| Specific impulse (s) | 311 |
|---|---|
| Initial (wet) mass (t) | 550 |
| Final (dry) mass after the burn (t) | 140 |
| Target delta-v (m/s, optional) | 9400 |
- Isp 311 s, 550 t down to 140 t: Δv = 4,173 m/s.
- A single stage would need a mass ratio of 21.80 to reach 9,400 m/s.
Result:
| Delta-v (m/s) | 4,173 |
|---|---|
| Effective exhaust velocity (m/s) | 3,050 |
| Mass ratio | 3.929 |
| Propellant fraction | 74.5% |
| Mass ratio needed for the target (single stage) | 21.80 |
Frequently asked questions
Why not one big stage?
The needed mass ratio grows exponentially with delta-v. Dropping empty tanks part-way resets the dry mass and makes orbit practical.
Sources and further reading
- Wikipedia: Tsiolkovsky rocket equation
- Wikipedia: Specific impulse
- NASA Glenn Research Center: Ideal rocket equation
Related calculators
More in Physics · All calculators
This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.