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
Δv = g·Isp·ln(m₀/m_f)
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.
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.
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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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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.