Rocket Equation Calculator (Tsiolkovsky Delta-V)
Use the Tsiolkovsky rocket equation to find the delta-v your rocket can achieve, or work backwards to plan the propellant needed for a target mission. Choose from seven propellant presets, switch between metric and imperial units, and check your result against standard mission delta-v budgets for low Earth orbit, geostationary transfer orbit, and trans-lunar injection.
Formula
Worked example
A second-stage rocket has a wet mass of 100,000 kg, a dry mass of 10,000 kg, and burns LOX/LH2 at Isp = 450 s. Exhaust velocity ve = 450 x 9.80665 = 4,413 m/s. Mass ratio R = 100,000 / 10,000 = 10. Delta-v = 4,413 x ln(10) = 4,413 x 2.3026 = 10,163 m/s, or about 10.2 km/s. Propellant consumed = 90,000 kg (90% of initial mass).
What is the Tsiolkovsky rocket equation?
The Tsiolkovsky rocket equation, derived by the Russian mathematician Konstantin Tsiolkovsky in 1903, is the fundamental equation of rocket propulsion. It describes how a rocket's velocity changes as it burns propellant and ejects mass. The equation is: delta-v = ve * ln(m0 / mf), where ve is the effective exhaust velocity, m0 is the initial (wet) mass, and mf is the final (dry) mass after all propellant is consumed. Because velocity change depends on the natural logarithm of the mass ratio, carrying more propellant gives diminishing returns - you have to carry all that extra propellant to orbit too, which is why most real rockets use multiple stages.
Specific impulse (Isp) and exhaust velocity
Specific impulse (Isp, in seconds) measures how efficiently an engine uses propellant: it is the thrust produced per unit weight of propellant consumed per second. Higher Isp means you need less propellant to achieve the same delta-v. Exhaust velocity (ve) is related to Isp by ve = Isp * g0, where g0 is 9.80665 m/s2. The most efficient chemical propellant in common use is liquid hydrogen burned with liquid oxygen (LOX/LH2), with an Isp around 450 s. Ion thrusters achieve 1,500-10,000 s but produce very low thrust, so they are practical only in space where continuous low acceleration is acceptable.
How to use this calculator
Choose which quantity you want to solve for using the "Solve for" selector. The default mode computes delta-v from the initial (wet) mass, final (dry) mass, and engine type. The initial-mass mode answers the mission-planning question: given a target delta-v and a payload mass, how heavy does the fully fuelled rocket need to be? The final-mass mode finds the dry mass (and therefore propellant load) required for a given initial mass and target velocity. The Isp-solver mode tells you what engine efficiency you need to achieve a target delta-v with the masses you have. Select a propellant preset to fill in Isp automatically, or choose Custom and enter any value.
Delta-v budgets for common space missions
Every space mission has a "delta-v budget" - the total velocity change needed from Earth's surface to the destination. Reaching low Earth orbit (LEO) from the ground requires about 9,200 m/s once gravity losses (roughly 1,500 m/s) and aerodynamic drag are included, even though the orbital velocity itself is only about 7,800 m/s. A geostationary transfer orbit (GTO) adds another 1,500-2,000 m/s, and a trans-lunar injection trajectory (TLI) requires around 12,300 m/s from the ground. This calculator reports the ideal delta-v (no gravity or drag losses), so add about 1,500 m/s to a launch-to-LEO figure for a realistic estimate.
Common propellants and their typical Isp values
| Propellant / engine | Isp (s) | Exhaust vel. ve (m/s) | Typical application |
|---|---|---|---|
| LOX / LH2 (liquid hydrogen) | 450 | 4413 | Upper stages, Shuttle Main Engine, J-2 |
| LOX / Methane (methalox) | 363 | 3560 | SpaceX Raptor, reusable launch |
| LOX / RP-1 (kerosene) | 311 | 3050 | Falcon 9 Merlin, Saturn V F-1 |
| NTO / MMH (hypergolic) | 340 | 3334 | Spacecraft thrusters, Orbital Maneuvering System |
| Solid propellant | 280 | 2746 | Solid rocket boosters, small launch vehicles |
| Monoprop hydrazine | 220 | 2157 | Attitude control, small satellites |
| Ion / Hall thruster | 3000 | 29420 | Deep-space probes, station keeping |
Sea-level Isp values vary with engine design and chamber pressure. Vacuum Isp is higher (typically +10-15%). Ion thruster values represent current state of the art.
Frequently asked questions
What is the rocket equation used for?
The Tsiolkovsky rocket equation is used to calculate how much a rocket's velocity can change (delta-v) given its propellant and engine efficiency. It is the starting point for mission design: engineers compute the delta-v needed to reach a target orbit or destination, then work backwards to find the propellant mass and staging required to achieve it. Every space mission from the simplest cubesat thruster burn to an interplanetary trajectory uses this equation.
What is delta-v and why does it matter?
Delta-v (symbol dv) is the change in velocity a spacecraft can produce by burning its propellant. It is the universal "currency" of space travel: each manoeuvre - launch to orbit, orbit raise, plane change, landing - has a delta-v cost, and the total must not exceed the spacecraft's budget. Unlike fuel quantity (which depends on mass), delta-v is independent of vehicle size, making it easy to compare missions and designs.
Why does staging improve performance?
Once a rocket stage has burned its propellant, the empty tank and engine are dead weight that reduces efficiency for the rest of the flight. By dropping the empty stage, the remaining stack can achieve a higher mass ratio for subsequent burns, dramatically increasing total delta-v. The Saturn V, for example, used three stages: the first stage accelerated the stack to about 2,300 m/s, the second to roughly 6,800 m/s, and the third provided the trans-lunar injection burn. A single-stage-to-orbit rocket is theoretically possible but extremely difficult because the structural mass fraction (tank and engine weight as a fraction of total mass) must be very low.
What is mass ratio and why is it important?
Mass ratio (R = m0 / mf) is the initial (wet) mass divided by the final (dry) mass. Because delta-v = ve * ln(R), the logarithm relationship means you need an exponentially larger mass ratio for each additional unit of delta-v. A mass ratio of 10 with an Isp of 450 s gives about 10,370 m/s of delta-v. To double that would require R = 100, meaning 99% of the vehicle would be propellant. This is why chemical rockets struggle to reach much beyond low Earth orbit without staging.
What propellant fraction is realistic for a single stage?
In practice, structural mass (tank walls, engine, plumbing) accounts for roughly 5-10% of a rocket's dry mass, which means the propellant fraction (mass of propellant / initial mass) is limited to about 85-95% for a single stage. The Falcon 9 first stage has a propellant fraction around 94%, which is close to the upper limit. Propellant fractions above 95% shown by this calculator indicate that the mission almost certainly requires staging or a more efficient engine to be buildable.
Does the rocket equation account for gravity and air resistance?
No. The Tsiolkovsky rocket equation is the ideal case, assuming no gravity, no atmospheric drag, and instantaneous burns. For a real launch vehicle, you must add gravity losses (typically 1,500 m/s for a vertical ascent to LEO) and aerodynamic drag losses (roughly 50-100 m/s at low altitude) to the orbital velocity to get the actual delta-v needed from the engines. For manoeuvres performed in space (orbital transfers, deep-space burns), the ideal equation is an excellent approximation.
How does ion propulsion compare to chemical rockets?
Ion thrusters have a specific impulse of 1,500-10,000 s versus 220-450 s for chemical engines, so a given mass of propellant produces far more delta-v. However, electric thrusters produce very low thrust (millinewtons to a few newtons) and cannot accelerate a spacecraft quickly enough to launch from Earth or make rapid manoeuvres. They are ideal for long-duration deep-space missions where time is not critical and solar power is available, such as the Dawn, Hayabusa, and BepiColombo spacecraft.