Delta-V Calculator (Tsiolkovsky Rocket Equation)
Enter your rocket's specific impulse (or exhaust velocity), initial wet mass, and dry mass to calculate delta-v using the Tsiolkovsky rocket equation. You can also solve in reverse: find the required propellant mass for a target delta-v, or determine what exhaust velocity your engine needs. Choose a propellant type preset to auto-fill specific impulse, and see a mass breakdown alongside a mission delta-v reference table.
Formula
Worked example
A Falcon 9 first stage uses kerosene/LOX (RP-1) engines with Isp of 311 s in vacuum, giving ve = 311 x 9.807 = 3050 m/s. With an initial mass of 549,000 kg and dry mass of around 29,000 kg, the mass ratio is 549,000 / 29,000 = 18.9. Delta-V = 3050 x ln(18.9) = 3050 x 2.94 = 8,967 m/s. This confirms the first stage can provide most of the 9,400 m/s needed to reach LEO.
What is delta-V and why does it matter?
Delta-V (dV, written with the Greek letter delta and the letter V for velocity) is the total change in velocity a rocket can achieve by burning its propellant. It is the single most important number in mission planning because it is independent of the rocket's mass - only the mass ratio and exhaust velocity matter. Every maneuver in space costs a delta-V budget: reaching low Earth orbit from the ground costs about 9.4 km/s, transferring to the Moon costs another 3.9 km/s from LEO, and a Mars transfer orbit costs roughly 3.6 km/s. A rocket's total delta-V must exceed the sum of all the maneuvers along its route.
The Tsiolkovsky rocket equation explained
The delta-V formula comes from the conservation of momentum and was derived by Konstantin Tsiolkovsky in 1903: dV = ve x ln(m0 / mf), where ve is the effective exhaust velocity of the engine (in m/s), m0 is the initial (wet) mass including propellant, mf is the final (dry) mass after the propellant is burned, and ln is the natural logarithm. The ratio m0/mf is called the mass ratio. Because the logarithm grows slowly, doubling the mass ratio does not double the delta-V - it only adds another ve x ln(2) approximately 0.69 x ve. This is the "tyranny of the rocket equation": achieving very high delta-V requires exponentially more propellant. In imperial units, the same equation applies with consistent units (ft/s throughout). Specific impulse Isp (seconds) is converted to exhaust velocity by multiplying by standard gravity g0 = 9.80665 m/s^2.
How to use this calculator
Use the "Solve for" dropdown to choose which quantity you want to find. To find delta-V, enter your engine's specific impulse (or pick a propellant preset), your rocket's initial wet mass, and its final dry mass after the burn. To find how much propellant you need for a target mission, select "Final dry mass" and enter the desired delta-V along with the initial mass and Isp. To find what initial mass is required for a given payload and delta-V, select "Initial wet mass" and enter the dry mass, target delta-V, and Isp. To back-calculate the exhaust velocity or Isp your engine must produce, select "Exhaust velocity / Isp" and enter the masses and required delta-V. The propellant preset buttons auto-fill Isp for common engine types from solid motors (Isp about 265 s) through liquid hydrogen engines (Isp about 450 s) up to electric ion thrusters (Isp 1,600 to 3,000 s or more).
Specific impulse, exhaust velocity, and engine efficiency
Specific impulse (Isp) measures how efficiently an engine uses propellant: higher Isp means more delta-V per kilogram of propellant burned. Isp is measured in seconds and is the same in metric or imperial units, making it the universal engine efficiency metric. The exhaust velocity ve equals Isp times g0 (9.80665 m/s^2). A solid rocket motor has Isp around 265 s (ve about 2,600 m/s), kerosene-oxygen engines like the Falcon 9 Merlin reach about 311 s vacuum (ve about 3,050 m/s), and liquid hydrogen-oxygen engines like the Space Shuttle main engine reach 453 s (ve about 4,440 m/s). Ion thrusters achieve Isp of 1,600 to 10,000 s but produce very low thrust, making them practical only in the vacuum of space for long, slow missions.
Common mission delta-V budgets
| Maneuver | Delta-V (km/s) | Notes |
|---|---|---|
| Surface to LEO (300 km) | 9.4 | Includes gravity and drag losses |
| LEO to GEO (direct) | 4.2 | Hohmann transfer + circularisation |
| LEO to GEO (bi-elliptic) | 3.9 | Slower, more fuel-efficient transfer |
| LEO to Lunar orbit | 3.9 | Trans-lunar injection + LOI |
| LEO to Moon surface | 5.9 | Includes powered descent |
| LEO to Mars transfer | 3.6 | Hohmann-like interplanetary transfer |
| LEO to Venus transfer | 3.5 | Venus comes closer to Earth than Mars |
| LEO to Jupiter (direct) | 6.3 | Without gravity assists |
| GEO station-keeping (year) | 0.05 | North-south + east-west combined |
| ISS reboost (typical) | 0.002 | Atmospheric drag compensation |
Approximate delta-V requirements for common space mission maneuvers from Earth. Values assume chemical propulsion and typical trajectories.
Frequently asked questions
What is delta-V in simple terms?
Delta-V is the total speed change a rocket can produce by burning all its propellant. Think of it as a fuel budget expressed in velocity: every maneuver costs a fixed amount of delta-V regardless of the rocket's size. A LEO orbit costs about 9.4 km/s from the ground, a lunar transfer costs another 3.9 km/s from LEO, and so on. If your rocket's delta-V budget exceeds the sum of the maneuvers needed, the mission is feasible.
Why does the rocket equation use a logarithm?
As a rocket burns fuel, it becomes lighter, so each kilogram of propellant burned accelerates the remaining lighter rocket more than it would have at the start. The cumulative result of this continuously changing mass is a logarithm: dV = ve x ln(m0/mf). The logarithm grows slowly, which is why carrying more fuel gives diminishing returns - doubling your mass ratio only adds about 69% of ve in extra delta-V, not twice as much.
What is specific impulse (Isp) and why does it matter?
Specific impulse is the standard measure of rocket engine efficiency, in seconds. It tells you how many seconds one kilogram (or one pound) of propellant produces one kilogram-force (or one pound-force) of thrust. Higher Isp means more delta-V per kilogram of propellant. Chemical rockets top out around 450 s (hydrogen-oxygen), while ion thrusters can reach several thousand seconds. The trade-off is that ion thrusters produce very low thrust and can only operate efficiently in space.
How do I use this calculator to plan a multi-stage rocket?
The Tsiolkovsky equation applies to each stage independently. For a two-stage rocket, first calculate the delta-V of the upper stage (using its own Isp, wet mass, and dry mass). Then calculate the first stage, treating the entire upper stage assembly as part of its payload (dry mass). Add the two delta-V values together. Each stage discards its empty tank and engines, which is why staging is so powerful: it eliminates dead mass before the next stage fires.
What mass ratio do I need to reach LEO?
Reaching low Earth orbit requires about 9,400 m/s of delta-V (accounting for gravity and drag losses). With a kerosene-oxygen engine (Isp about 311 s, ve about 3,050 m/s), the required mass ratio is e^(9400/3050) = e^3.08 = approximately 21.7. That means about 95.4% of the launch mass must be propellant, leaving only 4.6% for the rocket structure and payload. This is why reaching orbit is so difficult: most of a rocket's mass is fuel.
Can I use this calculator for electric (ion) thrusters?
Yes. Ion thrusters follow the same Tsiolkovsky equation. Enter the Isp (typically 1,600 to 10,000 s for ion engines), your initial mass, and final dry mass. The delta-V will be very large for a given mass ratio because of the high Isp. The practical constraint is that ion thrusters produce very low thrust (millinewtons), so they are only used for missions that can tolerate months of continuous thrusting, such as interplanetary probes or satellite station-keeping.