The Tsiolkovsky equation
In the absence of gravity and drag, a rocket’s change in velocity depends only on its effective exhaust velocity ve and the ratio of the mass at ignition to the mass at burnout:
Δv = ve ln(m0 / mf) = Isp g0 ln(m0 / mf)
Specific impulse Isp is defined so that ve = Isp g0, with the standard gravity g0 = 9.80665 m/s² — even when the engine is firing in vacuum. A mass ratio of e ≈ 2.718 at any Isp produces a delta-v equal to the exhaust velocity. An Isp of 300 s and a mass ratio of 5 produces Δv = 300 × 9.80665 × ln 5 ≈ 4,735 m/s.
Stages
A multi-stage vehicle’s ideal delta-v is the sum of each stage’s ideal delta-v, evaluated with that stage’s Isp and its own m0/mf (the “final” mass of a lower stage includes everything still stacked above it). Staging throws away empty tankage, which raises the effective mass ratio of the remaining vehicle.
Sources
Tsiolkovsky (1903); Sutton and Biblarz, Rocket Propulsion Elements; NASA Glenn Beginner’s Guide to Propulsion (specific impulse, rocket equation). For the orbital delta-v a Hohmann transfer needs, see the Hohmann transfer calculator.
Frequently asked questions
Why is g0 used in space?
Isp is defined by ve = Isp × 9.80665 m/s² regardless of the local gravity. The product Isp g0 is simply a convenient way to quote exhaust velocity in seconds. The equation itself does not assume the vehicle is sitting on Earth.
What masses go into m0 and mf?
m0 is the mass at the start of the burn (vehicle plus remaining propellant plus payload). mf is the mass at cutoff — everything that is not expended in that burn, including residual propellant if you want a conservative figure.
Does this include gravity and drag losses?
No. Those depend on the trajectory. A launch to orbit can lose on the order of 1.5 km/s or more to gravity and drag relative to the ideal burn; a high-thrust vacuum burn loses much less. Add losses separately.