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Rocket Equation

The equation that governs all of spaceflight. Your delta-v budget depends only on exhaust velocity and the ratio of full-to-empty mass — and it's punishingly logarithmic.

Rocket Equation (Tsiolkovsky)Live

Delta-v budget

5524 m/s

LEO (Earth orbit)
59%
Moon transfer
44%
Mars transfer
42%
Escape Earth
49%

Controls

The equation that rules spaceflight. Your Δv budget depends only on exhaust velocity and the ratio of full-to-empty mass — and it's brutally logarithmic.

Presets

▶ Run in Python

Data Inspector

Δv5524 m/s
Mass ratio5.00
Propellant400 t
Exhaust vel.3432 m/s

Governing equation

Reading this result: At 5524 m/s this stage cannot reach orbit; since Δv grows only with the log of mass ratio, big gains need a much emptier tank or higher Isp.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

The Tsiolkovsky rocket equation, Δv = g·Isp·ln(m₀/m_f), sets how much velocity change a rocket can achieve. This calculator shows your Δv against real mission targets — low Earth orbit, lunar and Mars transfers, Earth escape — so you can feel why staging matters.

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Frequently asked questions

Is this rocket equation calculator tool really free?
Yes. Rocket Equation runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.