Specific Impulse Calculator

Specific impulse measures how efficiently a rocket engine turns propellant into thrust. In the seconds convention used everywhere in rocketry, Isp = F / (mdot x g0), where F is thrust, mdot is propellant mass flow rate and g0 = 9.80665 m/s2 is standard gravity. Example: an engine producing 4,413,000 N of thrust while burning 1,000 kg/s of propellant has Isp = 4,413,000 / (1,000 x 9.80665) = 450.0 s.

Use Isp = F / (mdot x g0) with g0 = 9.80665 m/s2. Thrust must be in newtons and mass flow in kg/s; the result is in seconds. Worked example: F = 4,413,000 N and mdot = 1,000 kg/s gives Isp = 4,413,000 / 9,806.65 = 450.0 s. The calculator above also solves the equation in reverse: given thrust and Isp it finds the mass flow rate, and given Isp and mass flow it finds the thrust.

Effective exhaust velocity is ve = Isp x g0, and inversely Isp = ve / g0. It is the velocity the exhaust would need if it carried all of the engine's momentum. Example: 450.0 s x 9.80665 = 4,413.0 m/s. In SI units, N.s/kg is dimensionally the same as m/s, so Isp in seconds is simply exhaust velocity in m/s divided by 9.80665.

Seconds is a convention: Isp in seconds is the number of seconds one unit weight of propellant can produce one unit of thrust. Equivalently, it is thrust divided by propellant weight flow rate (instead of mass flow rate). The seconds figure is the exhaust velocity divided by g0 = 9.80665 m/s2, which is why the unit works out to time.

No. The g0 = 9.80665 m/s2 in Isp = F / (mdot x g0) is always the standard value by definition: it is a conversion factor between thrust-per-mass-flow (m/s) and the seconds convention, not the gravity of the planet where the engine fires. A calculator offering a Moon or Mars g0 for Isp only rescales the same exhaust velocity into different numbers; the engine itself is unchanged.

Total impulse is the total momentum an engine delivers: Itot = F x tb = Isp x g0 x mprop, where tb is burn time and mprop is the propellant mass burned. Example: 4,413,000 N of thrust for 100 s gives Itot = 441,300,000 N.s (441.3 MN.s). The same result follows from 450 s x 9.80665 m/s2 x 100,000 kg = 441,299,250 N.s, because 1,000 kg/s x 100 s = 100,000 kg of propellant.

Approximate vacuum values: cold gas thrusters ~70 s, hydrazine monopropellant 180-285 s, APCP solid motors ~242 s (sea level), NTO/MMH hypergolics ~316 s (AJ10-190, Shuttle OMS), LOX/RP-1 ~348 s (Merlin 1D Vacuum) to 282 s at sea level, LOX/LH2 ~452 s (RS-25/SSME vacuum), SPT-100 Hall thruster ~1,600 s and gridded ion thrusters 500-3,000 s. Electric propulsion wins on Isp but produces millinewtons of thrust, while chemical engines produce meganewtons.

Density impulse is bulk propellant density times Isp (rho x Isp), in s.kg/m3, or rho x Isp x g0 in N.s/m3. It measures how much total impulse fits in a given tank volume. Hydrogen engines have the best Isp (~452 s) but hydrogen is so light that LOX/LH2 bulk density is only about 361.14 kg/m3, giving 163,237 s.kg/m3 = 1,600,810 N.s/m3. Kerosene and hypergolic combinations score far better on density impulse, which is why first stages use them.

This calculator computes Isp itself (the engine's efficiency figure) from thrust, mass flow, exhaust velocity and propellant data. The ideal rocket equation calculator uses Isp as an input to plan missions: dv = Isp x g0 x ln(m0/mf). Use this tool to find or compare engine performance; use that tool to turn a chosen Isp into mission delta-v.

Chemical engines are limited by the energy of chemical bonds: exhaust velocity tops out around 4,400-4,500 m/s (about 452-460 s of Isp for LOX/LH2). Electric thrusters accelerate ions with electric and magnetic fields, reaching exhaust velocities of 15-80 km/s (roughly 1,500-8,000 s). The trade-off is power: pushing propellant that fast takes enormous electrical energy, so thrust is measured in millinewtons and burns last for months.