About the Rocket Equation Calculator
This rocket equation calculator applies the Tsiolkovsky equation, Δv = vₑ · ln(m₀/m_f), to work out how much change in velocity (delta-v) a rocket stage can deliver. Enter the engine’s specific impulse (or exhaust velocity) together with the fully fuelled and empty masses, and it returns delta-v, mass ratio, propellant mass and propellant fraction. Switch the mode to work backwards: give a target delta-v and the dry mass, and it tells you how much propellant you need.
It is useful for physics and aerospace students, Kerbal Space Program and other game players planning stages, model-rocket hobbyists, and anyone curious why reaching orbit needs such enormous rockets. The chart shows the brutal logarithm at the heart of spaceflight: each extra km/s of delta-v needs exponentially more propellant.
The ideal rocket equation ignores gravity losses, air drag and steering losses, so a real launch to low Earth orbit needs about 9.3–10 km/s even though orbital speed is only about 7.8 km/s. For multi-stage rockets, calculate each stage separately and add the delta-v values.
With the default inputs, the delta-v is 7,022.6 m/s. Change any value above to recalculate instantly.
How to use the rocket equation calculator
- 1Choose whether to find delta-v or the propellant needed for a target delta-v.
- 2Enter the engine’s specific impulse in seconds (or its exhaust velocity in m/s).
- 3Enter the dry mass — structure, engines and payload without propellant.
- 4Enter the wet mass, or the target delta-v in the propellant mode.
- 5Read delta-v, mass ratio and propellant mass; repeat per stage and add the delta-v values.
Formula and method
Konstantin Tsiolkovsky’s 1903 rocket equation follows from conservation of momentum: as a rocket throws mass backwards at exhaust velocity vₑ, its speed rises by vₑ times the natural log of the ratio between its starting mass m₀ and final mass m_f. Specific impulse in seconds is converted to exhaust velocity by multiplying by standard gravity g₀ = 9.80665 m/s².
Rearranging gives the initial mass needed for a target delta-v: m₀ = m_f · e^(Δv/vₑ), so propellant mass is m₀ − m_f. Because the relationship is exponential, doubling delta-v squares the mass ratio. The equation is ideal: it ignores gravity and drag losses and assumes constant exhaust velocity, and any unit of mass works as long as both masses use the same one.
- Δv
- Change in velocity the stage can deliver (m/s)
- vₑ
- Effective exhaust velocity (m/s)
- Isp
- Specific impulse (s)
- g₀
- Standard gravity, 9.80665 m/s²
- m₀
- Initial (wet) mass, with propellant
- m_f
- Final (dry) mass, after burning propellant
Worked examples
Kerosene stage, 100 t wet, 10 t dry, Isp 311 s
vₑ = 311 × 9.80665 = 3,049.9 m/s. The mass ratio is 100 ÷ 10 = 10, and ln 10 = 2.3026, so Δv = 3,049.9 × 2.3026 ≈ 7,023 m/s — not quite enough to reach orbit on its own.
Hydrogen upper stage, Isp 450 s, 20 t → 5 t
vₑ = 450 × 9.80665 = 4,413 m/s. With a mass ratio of 4, Δv = 4,413 × ln 4 = 4,413 × 1.3863 ≈ 6,118 m/s from a stage that is only 75% propellant.
Propellant needed for 9.4 km/s with 10 t dry mass
m₀ = 10 × e^(9,400 ÷ 3,049.87) = 10 × e^3.0821 ≈ 218 t, so about 208 t of propellant is needed — a 95.4% propellant fraction, which is why orbital rockets are staged.
Frequently asked questions
What is delta-v?+
Delta-v (Δv) is the total change in velocity a spacecraft can achieve by burning its propellant. Mission planners budget delta-v for each manoeuvre — about 9.4 km/s to reach low Earth orbit and roughly 3.1–3.2 km/s more for a trans-lunar injection burn from LEO.
What is specific impulse?+
Specific impulse (Isp) measures engine efficiency: the number of seconds a given weight of propellant (at standard Earth gravity) can produce a thrust equal to that weight. Multiply by 9.80665 to get exhaust velocity in m/s. Higher Isp means more delta-v from the same propellant.
Why do rockets use multiple stages?+
Because delta-v grows only with the logarithm of the mass ratio. Dropping empty tanks and engines lets later stages start with a much better mass ratio, so the total delta-v (the sum of each stage) is far higher than a single stage could achieve.
Does the rocket equation include gravity and drag?+
No. The ideal Tsiolkovsky equation gives delta-v in empty space. Launch vehicles lose roughly 1.5–2 km/s to gravity, drag and steering during ascent, which is why 9.3–10 km/s is budgeted for an orbit that needs about 7.8 km/s.
What mass units should I use?+
Any unit works — tonnes, kilograms or pounds — because only the ratio of wet to dry mass enters the equation. Just use the same unit for both masses. Propellant mass is reported in the same unit.