Specific Impulse Calculator

Estimate how efficiently an engine generates thrust using the specific impulse calculator.

Specific impulse282.072 sF/(ṁg₀) from the thrust and mass flow entered — compare the 282 s used for the delta-v above

Delta-v3,839.08 m/s3.8391 km/s — Tsiolkovsky's equation, v_e ln(m₀/m_f)

Effective exhaust velocity2,765.48 m/sI_sp × g₀. The seconds are a convention, not a physical time — g₀ appears in the definition even for a rocket that will never be near Earth

Mass ratio4.00769:1propellant is 75.05% of the launch mass

Propellant mass412,054 kg

Delta-v is LOGARITHMIC in mass ratiothe tyranny of the rocket equationdoubling the propellant does not double the delta-v; a mass ratio of 4.008 gives 1.3882 exhaust velocities, and each further one costs e times as much propellant

Mass ratio for twice this delta-v16.0616:1the SQUARE — which is why staging exists

Delta-v at 10% better I_sp4,222.98 m/sexhaust velocity multiplies delta-v directly, so it is worth far more than carrying more propellant

Thrust7,607 kNas entered

Thrust-to-weight at liftoff1.4128above 1, so it can lift off — the excess over 1 is what accelerates it

Thrust-to-weight when empty5.662rises through the burn as propellant leaves, which is why acceleration climbs steeply near the end

Initial acceleration4.048 m/s²net of gravity, straight up

Burn time2.497 minat 2,750 kg/s

Total impulse1.1398 GN·s

Against the budget for low Earth orbit-5,561 m/sshort by 5,561 m/s — needs staging or a boost

Against the budget for the Moon's surface-12,061 m/sshort by 12,061 m/s — needs staging or a boost

Against the budget for Mars transfer injection-9,261 m/sshort by 9,261 m/s — needs staging or a boost

Against the budget for escaping the solar system-12,761 m/sshort by 12,761 m/s — needs staging or a boost

The formula

Δv = I_sp g₀ ln(m₀/m_f); F = ṁ v_e

The tyranny of the rocket equation

Tsiolkovsky's equation says delta-v is the exhaust velocity times the natural log of the mass ratio. The logarithm is the whole problem: each additional exhaust velocity of delta-v costs e times as much propellant as the last. Getting twice the delta-v needs the mass ratio SQUARED, not doubled.

That is why staging exists. Throwing away empty tanks resets the mass ratio partway up, so the vehicle is not carrying dead structure through the expensive part of the climb. It is also why improving exhaust velocity is worth so much more than carrying more fuel — exhaust velocity multiplies delta-v directly, while propellant only enters through a logarithm.

Specific impulse in seconds

Quoting specific impulse in seconds means dividing the exhaust velocity by standard gravity. It is a unit convention, not a physical duration, and g₀ appears in the definition even for an engine that will never be near Earth. Multiplying seconds of I_sp by 9.80665 recovers the exhaust velocity in m/s, which is the quantity that actually does the work.

Thrust-to-weight below one is not a broken design. It only prevents a vertical liftoff — as an upper stage, with no weight left to fight, a low-thrust high-efficiency engine is exactly what you want.