Specific Impulse Calculator

Specific impulse (Isp) is a measure of how efficiently a rocket or jet engine uses propellant to produce thrust. It is defined as the thrust produced per unit weight flow rate of propellant, and is expressed in seconds. A higher Isp means the engine extracts more thrust per kilogram of fuel consumed.

The most common formula is Isp = ve / g₀, where ve is the effective exhaust velocity in m/s and g₀ is standard gravitational acceleration (9.80665 m/s²). You can also compute it as Isp = F / (ṁ × g₀), where F is thrust in Newtons and ṁ is the mass flow rate in kg/s.

Specific impulse is measured in seconds (s). This unit is convenient because it is the same regardless of whether SI or imperial units are used for thrust and mass flow rate, making it a universal metric for comparing engine efficiency across different designs.

Exhaust velocity (ve) is the actual speed at which propellant gases exit the nozzle, measured in m/s. Specific impulse is simply the exhaust velocity divided by standard gravity (g₀ ≈ 9.807 m/s²). They convey the same physical information but in different units. Effective exhaust velocity (c) accounts for both gas momentum and pressure thrust from the nozzle.

Thrust-specific fuel consumption (TSFC) is the reciprocal of specific impulse when expressed in consistent units. It measures how much fuel an engine burns per unit of thrust per unit of time. Lower TSFC means a more fuel-efficient engine. It is commonly used for air-breathing jet engines, while Isp is standard in rocket propulsion.

Jet engines use atmospheric oxygen to combust fuel, so they carry only the fuel and benefit from a free oxidizer source, yielding much higher Isp (typically 3,000–6,000 s). Rocket engines must carry both fuel and oxidizer, limiting their Isp to roughly 250–450 s for chemical rockets. Ion thrusters can achieve Isp values above 10,000 s but produce very low thrust.

Effective exhaust velocity (c) combines the kinetic contribution of the exhaust gases (ve) with the pressure difference between the nozzle exit and the ambient environment: c = ve + (Pe − Pa) × Ae / ṁ. It represents the total momentum-equivalent velocity per unit mass flow and is used in the ideal rocket equation for mission planning.

The Tsiolkovsky rocket equation is Δv = Isp × g₀ × ln(m₀ / m_dry), where m₀ is the initial (wet) mass and m_dry is the dry mass. This equation shows that higher Isp directly reduces the propellant mass fraction needed to achieve a given Δv, which is why engine efficiency is so critical for interplanetary missions.