What this calculator does
The rocket equation says the velocity change a rocket can achieve depends on the logarithm of its mass ratio, multiplied by the exhaust velocity. The logarithm is what makes spaceflight so difficult: each additional increment of delta-v costs exponentially more propellant.
Doubling the propellant does not double the performance. To keep gaining delta-v at a steady rate, the mass of propellant has to rise geometrically, which is why launch vehicles are almost entirely fuel by mass and why staging exists at all.
The formula
Multiply the effective exhaust velocity by the natural logarithm of the wet mass divided by the dry mass. Exhaust velocity comes from specific impulse multiplied by standard gravity.
| Term | Meaning |
|---|---|
| Delta-v (Δv) | The total velocity change a vehicle can produce, which is the currency of orbital mechanics. |
| Mass ratio | Wet mass divided by dry mass. The whole performance depends on this ratio, not on the absolute masses. |
| Specific impulse (Isp) | Thrust per unit propellant weight flow, in seconds. A measure of engine efficiency. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial mass (wet, with propellant) (kg) | The initial mass including propellant, in kilograms. |
| Final mass (dry, propellant spent) (kg) | The final mass after the propellant is spent, in kilograms. |
| Specific impulse (s) | Specific impulse in seconds. Chemical rockets range from around 250 to 450; ion drives are in the thousands. |
When to use it
Assessing whether a mission is feasible
Every destination has a delta-v requirement, and this determines whether a given vehicle can meet it.
Understanding why staging helps
Discarding empty tanks reduces the dry mass, improving the mass ratio for the remaining journey.
Comparing engine types
A higher specific impulse multiplies the whole result, which is why ion drives achieve so much with so little propellant.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much delta-v does the mass ratio buy?
The same vehicle with different amounts of propellant burned.
| Final mass | Delta-v (Δv) | Propellant mass burned |
|---|---|---|
| 12,000 kg | 4,352.5 m/s | 38,000.0 kg |
| 20,000 kg | 2,794.6 m/s | 30,000.0 kg |
| 30,000 kg | 1,558.0 m/s | 20,000.0 kg |
Questions
Why is there a logarithm?
Because as propellant burns, the rocket gets lighter, so each remaining kilogram of fuel accelerates less mass. Integrating that changing relationship over the burn produces a natural logarithm.
Why does staging help so much?
Because empty tanks and spent engines are dead weight in the dry mass. Dropping them improves the mass ratio for the rest of the flight, and since the relationship is logarithmic that improvement is worth a great deal.
What is a typical delta-v requirement?
Reaching low Earth orbit takes roughly 9.4 km/s once gravity and drag losses are included, which is why launch vehicles are overwhelmingly propellant by mass.
Does this account for gravity and drag?
No. It gives the ideal delta-v in the absence of external forces. Real launches lose a substantial amount to gravity and atmospheric drag, so the vehicle must carry more than the bare orbital figure suggests.
For the engine efficiency term, see the specific impulse calculator. For the speed needed to escape a body, see the escape velocity calculator.