Specific Impulse Calculator

Specific impulse (Isp) is the most important measure of rocket engine efficiency. It is defined as the thrust produced per unit weight flow rate of propellant: Isp = F / (m_dot x g0), in seconds. A higher Isp means more thrust per kilogram of propellant consumed. Isp in seconds is the same for all units systems, which is why it is universally used in rocketry.

Cold gas thrusters (nitrogen): 50-80 s. Solid rocket boosters (e.g. Space Shuttle SRBs): 250-270 s. Liquid bipropellant (kerosene/LOX, e.g. Falcon 9 Merlin): 282 s (sea level), 311 s (vacuum). Liquid hydrogen/LOX (e.g. Space Shuttle main engines): 366 s (sea level), 453 s (vacuum). Ion thrusters: 1,000-10,000 s but very low thrust.

Effective exhaust velocity ve = Isp x g0, where g0 = 9.80665 m/s2 is the standard gravitational acceleration. For a Merlin engine with Isp = 311 s, ve = 311 x 9.80665 = 3,050 m/s. The Tsiolkovsky rocket equation uses ve directly: delta-V = ve x ln(m0/mf), where m0 is initial mass and mf is final mass (after propellant burn).

The Tsiolkovsky (or ideal rocket) equation is: delta-V = ve x ln(m0 / mf) = Isp x g0 x ln(m0 / mf). It gives the maximum velocity change a rocket can achieve for given Isp and mass ratio. m0 is wet mass (full), mf is dry mass (empty of propellant). This equation was derived by Konstantin Tsiolkovsky in 1903 and is the cornerstone of astronautics.

Mass ratio is m0/mf, the ratio of initial (wet) to final (dry) mass. For a single-stage rocket to reach low Earth orbit (delta-V approximately 9.4 km/s) with Isp = 311 s, mass ratio = exp(9400/3050) = exp(3.08) = approximately 21.7. This means 95.4% of the liftoff mass must be propellant. This extreme requirement is why orbital rockets use staging.