Rocket Equation Calculator
Delta-v from mass ratio and exhaust velocity — Tsiolkovsky's equation, and why rockets are mostly fuel.
The rocket equation is Δv = ve × ln(m₀/m₁): the velocity change you can achieve depends on exhaust velocity and the natural logarithm of your mass ratio.
How the rocket equation calculator works
The rocket equation is Δv = ve × ln(m₀/m₁): the velocity change you can achieve depends on exhaust velocity and the natural logarithm of your mass ratio.
The logarithm is the tyranny. Doubling the fuel does not double the delta-v — it adds only ve × ln(2). Getting twice the velocity change needs the mass ratio squared, which is why launch vehicles are around 90% propellant by mass and why staging exists at all: dropping empty tanks is the only way to keep the ratio favourable.
Specific impulse is exhaust velocity divided by standard gravity, quoted in seconds. It is the single figure of merit for an engine: around 300 s for kerosene and oxygen at sea level, 450 s for hydrogen and oxygen in vacuum, and several thousand for ion engines that produce almost no thrust.
Formula: Δv = ve × ln(m₀ / m₁); ve = Isp × g₀
Worked examples
| Inputs | Delta-v | Note |
|---|---|---|
| A Falcon 9 first stage | 4,234 m/s (4.234 km/s) | about 4.2 km/s |
| A hydrogen upper stage | 9,684 m/s (9.684 km/s) | far more delta-v |
| An ion thruster | 11,929 m/s (11.929 km/s) | high Isp, tiny thrust |
FAQFrequently asked questions
What is the rocket equation?
Δv = ve × ln(m₀/m₁) — the velocity change available from a given mass ratio and exhaust velocity.
Why are rockets almost entirely fuel?
Because delta-v grows only with the logarithm of mass ratio. Getting to orbit needs about 9.4 km/s, which forces a mass ratio around 20.
What is specific impulse?
Exhaust velocity divided by standard gravity, in seconds. It is the efficiency figure for an engine: about 300 s for kerolox, 450 s for hydrolox.
Why do rockets have stages?
Because carrying empty tanks wastes delta-v. Dropping them mid-flight resets the mass ratio in your favour.
Why do ion engines have such high Isp?
They expel a small amount of propellant extremely fast. Efficient, but the thrust is measured in millinewtons, so they need months of burn time.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- Royal Observatory Greenwich — the historic home of the prime meridian
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).