How much velocity can a rocket gain? The answer grows only with the logarithm of its mass ratio — the brutal math that forces every orbital rocket to shed stages.
Rocket Equation (Tsiolkovsky)Live
the tyranny of the rocket equation
Controls
Presets
Δv = Isp·g·ln(m₀/mf). Because Δv grows only with the log of the mass ratio, reaching orbit (~9.4 km/s) demands enormous propellant fractions — which is exactly why rockets stage.
Reading this result: Short of orbit by 4.7 km/s. Because Δv scales only with ln(mass ratio), raise Isp, lift the mass ratio, or add a stage rather than just adding propellant.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
The Tsiolkovsky rocket equation gives Δv = Isp·g·ln(m₀/mf). Because the mass ratio enters logarithmically, single-stage vehicles struggle to reach the ~9.4 km/s needed for low Earth orbit. Staging discards empty tanks so later stages push less dead mass. Educational tool.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this tsiolkovsky rocket equation calculator tool really free?▾
Yes. Rocket Equation (Tsiolkovsky) 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.