Rocket Equation Calculator (Delta-v)
Delta-v from specific impulse and the wet and dry masses of a stage, with mass ratio and propellant load.
Results
What this tool does
Tsiolkovsky wrote this in 1903 and nothing since has softened it: the velocity change a rocket can achieve depends only on how fast it throws mass out the back and on the logarithm of how much of itself it is willing to throw. Reaching low Earth orbit takes roughly 9.4 km/s of delta-v once gravity and drag losses are included, which is why a launch vehicle is almost entirely propellant by mass.
Formula
Δv = Isp g₀ ln(m₀ ÷ mf) (Tsiolkovsky equation)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
is | Specific impulse | s |
m0 | Wet mass | t |
mf | Dry mass | t |
DV | Delta-v | m/s |
DK | Delta-v | km/s |
VE | Effective exhaust velocity | m/s |
MR | Mass ratio | — |
PM | Propellant burned | t |
Worked example
- Specific impulse450 s
- Wet mass500 t
- Dry mass100 t
- Delta-v7102.4 m/s
- Delta-v7.1024 km/s
- Effective exhaust velocity4413.0 m/s
- Mass ratio5.0000
- Propellant burned400.000 t
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
Why is the rocket equation so unforgiving?
Because the mass ratio sits inside a logarithm. Doubling the delta-v does not double the propellant: it squares the mass ratio. A stage that needs a ratio of 5 to reach orbit would need 25 to do it twice over, which is why rockets are staged and why a few seconds of extra specific impulse from a better engine is worth so much.