Case 1
- Exhaust velocity
- 3000m/s
- Wet mass m₀
- 50000kg
- Dry mass m_f
- 10000kg
4,828.313737m/s
Open with these valuesRocket Equation Calculator
4,828.313737m/s
Result: 4,828.313737 m/sDelta-v is the exhaust velocity times the natural logarithm of the wet-to-dry mass ratio. That logarithm is why rockets have stages: doubling the delta-v means squaring the mass ratio. Enter the exhaust velocity, not the specific impulse — the two differ by a factor of 9.80665.
Worked examples
Case 2
- Exhaust velocity
- 2500m/s
- Wet mass m₀
- 20000kg
- Dry mass m_f
- 5000kg
3,465.735903m/s
Open with these valuesCase 3
- Exhaust velocity
- 4400m/s
- Wet mass m₀
- 549054kg
- Dry mass m_f
- 137000kg
6,108.149835m/s
Open with these valuesHow it's calculated
Δv = v_e × ln(m₀ ÷ m_f)
- StepEnter the effective exhaust velocity in m/s, not the specific impulse.
- StepEnter the wet mass — the whole rocket with full tanks.
- StepEnter the dry mass — structure and payload once the tanks are empty.
- ResultRead the delta-v the stage can produce, in metres per second.
Reference table
| v_e, m₀, m_f | What that is | Delta-v (m/s) |
|---|---|---|
| 3000, 10000, 10000 | nothing burned at all | 0 |
| 2500, 20000, 5000 | mass ratio 4 to 1 | 3465.735903 |
| 3000, 50000, 10000 | mass ratio 5 to 1 | 4828.313737 |
| 4400, 549054, 137000 | Saturn V first stage | 6108.149835 |
| 3000, 90000, 10000 | mass ratio 9 to 1 | 6591.673732 |
| 4500, 120000, 20000 | a cryogenic upper stage | 8062.917612 |
Questions
How do I calculate delta-v with the rocket equation?
Multiply the effective exhaust velocity by the natural logarithm of the mass ratio: Δv = v_e × ln(m₀ / m_f). With 3000 m/s of exhaust velocity, a 50000 kg wet mass and a 10000 kg dry mass, that is 3000 × ln(5), about 4828 m/s.
I only have the specific impulse. What do I enter?
Multiply the specific impulse in seconds by 9.80665 to get the effective exhaust velocity in metres per second. An engine with an Isp of 306 s therefore has a v_e of about 3000 m/s. Entering the Isp directly would understate the delta-v by a factor of nearly ten.
What is delta-v?
Delta-v is the total change in velocity a stage can produce by burning its propellant, measured in metres per second. Every mission is budgeted in it, and reaching low Earth orbit costs roughly 9400 m/s once gravity and drag losses are counted.
Why does staging increase a rocket's total delta-v?
Because the mass ratio sits inside a logarithm, which gives diminishing returns. Dropping empty tanks partway up lets each later stage start with a smaller dry mass and a better ratio, and every stage adds its own delta-v on top of the previous one.
What units should I use?
Metres per second for the exhaust velocity, and any consistent mass unit for the two masses. The mass ratio is dimensionless, so the delta-v comes out in the same unit as the exhaust velocity. The dry mass must be smaller than the wet mass, otherwise the result turns negative.
Sources and last check
Information, not professional advice.