Compute the ideal velocity change (Δv) a rocket stage can deliver from its specific impulse and its wet and dry masses, using the Tsiolkovsky rocket equation. The calculator also reports the mass ratio, the propellant mass, and the propellant mass fraction — the numbers that decide whether a mission is reachable.
Konstantin Tsiolkovsky's rocket equation is the single most important relation in astronautics. Derived from conservation of momentum, it links the velocity change a rocket can achieve to just two things: how efficiently it throws mass out the back (specific impulse) and how much of its mass is propellant (the mass ratio). Every launch vehicle, upper stage, and spacecraft maneuver is sized against it.
Δv = I_sp · g₀ · ln(m₀ / m_f).
Here Δv is the ideal velocity change (m/s), I_sp the specific impulse (s), g₀ = 9.80665 m/s² the standard gravity used to convert I_sp to an effective exhaust velocity (v_e = I_sp·g₀), m₀ the initial (wet) mass, and m_f the final (dry) mass after the burn. The logarithm is the crux: Δv grows only with the logarithm of the mass ratio, so squeezing out more performance demands exponentially more propellant.
Orbits and trajectories are defined by velocity changes, not distances. Reaching low Earth orbit takes roughly 9.4 km/s of Δv (including gravity and drag losses); a trans-lunar injection adds about 3.1 km/s, and landing on the Moon and returning adds more. Mission planners build a Δv budget by summing every maneuver, then size the vehicle so its rocket-equation Δv meets or exceeds that budget with margin. Δv is, quite literally, the fuel gauge of spaceflight.
Specific impulse measures propulsive efficiency — the thrust produced per unit weight-flow of propellant, expressed in seconds. Higher I_sp means more Δv from the same propellant. Solid motors deliver roughly 250 s, storable and kerosene/LOX liquids 300–340 s, hydrogen/LOX upper stages around 450 s, and electric (ion/Hall) thrusters thousands of seconds — though at tiny thrust. Because Δv scales linearly with I_sp, propulsion choice has an outsized effect on what a vehicle can do.
Because Δv depends on the logarithm of the mass ratio, the propellant needed climbs exponentially with required Δv. Demanding a mass ratio of e ≈ 2.72 buys one exhaust velocity of Δv; a mass ratio of 20 is needed for about 3 times that — and structure, tanks, and engines impose a floor on dry mass. The escape from this "tyranny" is staging: discarding empty tanks and engines mid-flight so later stages no longer carry dead weight, multiplying the achievable Δv.
Wet mass (m₀) is the total mass at the start of the burn, including all usable propellant. Dry mass (m_f) is what remains after the propellant is consumed — structure, engines, tanks, payload, and any residuals. Their ratio m₀/m_f is the mass ratio, and the propellant burned is simply m₀ − m_f.
It falls out of integrating Newton's second law as the rocket continuously expels mass: each increment of velocity costs a fixed fraction of the remaining mass, which integrates to a logarithm. The practical consequence is diminishing returns — doubling your propellant does not double your Δv, it only adds one more v_e times ln(2) ≈ 0.69.
It is the harsh exponential relationship between required Δv and required propellant. Because Δv grows only logarithmically with mass ratio, achieving high Δv with a single stage demands an impractically large fraction of the vehicle to be propellant, leaving almost nothing for structure or payload. Staging and high-I_sp propulsion are the main ways engineers fight back against it.
A staged vehicle drops spent tanks and engines once their propellant is gone, so the next stage does not have to accelerate that dead mass. The total Δv becomes the sum of each stage's individual rocket-equation Δv. This lets multi-stage rockets reach orbit and beyond, where no single stage with realistic structural mass fractions could.
No — it gives the ideal (theoretical) Δv with no external forces. Real launches lose velocity to gravity (thrusting against weight) and atmospheric drag, typically 1.5–2 km/s combined to reach orbit. Engineers therefore size vehicles for a Δv budget that adds these losses on top of the orbital velocity the mission requires.