Rocket Delta-v Calculator (Tsiolkovsky)
Find a rocket’s change in velocity from its specific impulse and wet-to-dry mass ratio using the Tsiolkovsky equation.
How it works
Δv = Isp·g₀·ln(m₀ ÷ m_f) · g₀ = 9.80665 m/s²
The Tsiolkovsky rocket equation gives the total velocity change a rocket can achieve from its exhaust velocity (Isp·g₀) and the natural log of its wet-to-dry mass ratio. Because the mass ratio enters as a logarithm, gains get expensive fast — each extra unit of delta-v needs exponentially more propellant, which is why staging and high-Isp engines matter so much.
Worked example
A stage with Isp = 350 s, wet mass 50,000 kg and dry mass 20,000 kg: exhaust velocity = 350 × 9.80665 = 3,432 m/s, mass ratio = 2.5, so Δv = 3,432 × ln(2.5) ≈ 3,432 × 0.9163 ≈ 3,145 m/s.
Frequently asked questions
What is delta-v used for?
Delta-v is the "budget" of velocity change a rocket carries. Every manoeuvre — launch, orbit changes, landing — costs a known amount of delta-v, and a mission works only if the vehicle’s total delta-v exceeds the sum of those costs.
What is specific impulse (Isp)?
Isp measures how efficiently an engine uses propellant, expressed in seconds. Multiplying it by g₀ (9.80665 m/s²) gives the effective exhaust velocity used in the rocket equation. Higher Isp means more delta-v per kilogram of fuel.
Why does adding more fuel give diminishing returns?
Because delta-v depends on the logarithm of the mass ratio, the rocket must also accelerate the extra fuel it carries. Doubling the mass ratio does not double delta-v, so beyond a point, staging beats simply adding propellant.
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This calculator is for educational purposes. Double-check important results before acting on them.