Delta-V Calculator

The Tsiolkovsky rocket equation, also called the ideal rocket equation, is Δv = Isp × g₀ × ln(m₀/mf). It states that the maximum delta-V a rocket can achieve equals the effective exhaust velocity (Isp × g₀) multiplied by the natural logarithm of the ratio of initial (wet) mass to final (dry) mass. The equation shows that increasing delta-V requires exponentially more propellant — a rocket doubling its delta-V budget needs far more than twice as much fuel, which is why reaching orbit is so challenging.

Specific impulse (Isp) measures the efficiency of a rocket propellant — it is the thrust produced per unit weight of propellant per second, expressed in seconds. Higher Isp means more efficient propellant use: a LOX/LH₂ engine at 450 s Isp requires far less propellant mass than a solid rocket at 260 s Isp to achieve the same delta-V. Ion thrusters reach 3,000+ s Isp, allowing tiny amounts of xenon propellant to generate large delta-V over time — though at very low thrust.

Delta-V (Δv) represents the total change in velocity a spacecraft must achieve to complete a maneuver or mission. It is used because it is independent of spacecraft mass — the same delta-V budget applies whether the spacecraft weighs 100 kg or 1,000 kg (though the required propellant mass scales with the spacecraft mass). Mission designers plan around delta-V budgets: low Earth orbit requires about 9,400 m/s from the ground, a lunar transfer adds ~3,200 m/s, and a Mars transfer adds ~4,300 m/s.

Wet mass (m₀) is the total mass of the spacecraft including all propellant loaded for the mission. Dry mass (mf) is the mass after all propellant has been expended — the structure, engines, payload, and any residual propellant. The ratio m₀/mf (mass ratio) directly determines how much delta-V the rocket can generate. A mass ratio of 4 (75% of the initial mass is propellant) with a hydrazine thruster (Isp = 230 s) yields roughly 3,100 m/s of delta-V.

Ion thrusters (and Hall thrusters) accelerate propellant ions to very high exhaust velocities using electric fields powered by solar panels or nuclear reactors, rather than chemical combustion. Xenon ion thrusters achieve 2,500–10,000 s Isp by accelerating ions to 30–80 km/s exhaust velocity, compared to 4–4.5 km/s for LOX/LH₂ chemical rockets. The tradeoff is extremely low thrust (millinewtons), requiring months or years of continuous firing to accumulate useful delta-V, making them suitable for deep space missions but not launch vehicles.

Approximate delta-V budgets for common missions from Earth's surface: Low Earth Orbit (LEO) ≈ 9,400 m/s; Geostationary Transfer Orbit (GTO) ≈ 10,400 m/s; Lunar orbit ≈ 12,600 m/s; Mars orbit insertion ≈ 13,700 m/s; Jupiter flyby ≈ 14,200 m/s. Orbital maneuvers from LEO: ISS orbit raise ≈ 100 m/s; deorbit burn ≈ 100 m/s; GEO from GTO ≈ 1,800 m/s. These figures guide the propellant fraction required and the choice of propulsion system.

Propellant mass fraction (also called mass ratio efficiency) is the fraction of the wet mass that is propellant: (m₀ − mf) / m₀. A fraction of 0.9 means 90% of the launch mass is propellant. For launch vehicles reaching LEO, propellant fractions of 0.85–0.95 are typical due to the enormous delta-V requirement. Upper stages and spacecraft have lower fractions (0.4–0.7) because they start from orbit. Electric propulsion spacecraft may have fractions below 0.3 due to their high Isp.

This calculator handles a single stage. For a multi-stage rocket, calculate the delta-V for each stage separately and sum them. Each stage's dry mass becomes the wet mass of the payload for the previous stage. The Tsiolkovsky equation shows why staging is efficient: discarding empty propellant tanks reduces the mass that subsequent stages must accelerate, dramatically improving overall delta-V performance compared to a single-stage vehicle with the same total mass.