Understand the relationship
The reasoning behind the result
Specific impulse is thrust per weight-flow convention
Isp=F/(ṁg0); veffective=F/ṁ
Dividing thrust F in newtons by total expelled mass flow ṁ in kg/s gives a velocity unit, m/s. This effective exhaust velocity describes thrust per unit propellant flow. Dividing it by standard gravity g0=9.80665 m/s² gives specific impulse in seconds.
The second is a performance unit here, not an engine burn duration. Using lunar or local gravity in this conversion would change the convention incorrectly. Local gravity belongs in vehicle weight and force-balance calculations, not in the Isp conversion.
Exit momentum and pressure contribute separately
Fmomentum=ṁuexit; Fpressure=(pexit−pambient)Aexit
The simplified steady axial nozzle equation includes momentum carried out by gas and a pressure term at the exit plane. The pressure contribution can be positive, zero or negative, depending on exit pressure relative to ambient. Absolute pressures are entered in kPa and converted to Pa so their difference times area gives newtons.
Consequently effective exhaust velocity can differ from the gas exit speed. Equal exit and ambient pressures remove this pressure term. The equation alone does not describe shocks, separation, losses or off-design nozzle operation; a nonpositive net-thrust scenario falls outside this positive-performance calculator.
Compare like operating conditions
A thrust measurement and flow measurement must refer to the same operating condition and time basis. A vacuum specification cannot be combined indiscriminately with sea-level thrust. The outputs do not account for a changing mixture ratio, pulsed transients or another fluid stream omitted from the entered total flow.
This workflow establishes a performance ratio. To relate flow to available propellant and elapsed burn time, use the separate mass-flow and burn ledger; to relate vehicle masses to ideal delta-v, use the rocket-equation tools.
Follow the numbers
A pressure term changes effective exhaust velocity
- At 10 kg/s and an axial gas exit speed of 3,000 m/s, momentum thrust is 30,000 N.
- Exit pressure 100 kPa minus ambient pressure 20 kPa gives 80,000 Pa. Across 0.05 m², pressure thrust is 4,000 N, so net thrust is 34,000 N.
- Effective exhaust velocity is 34,000/10=3,400 m/s. Specific impulse is 3,400/9.80665≈346.703512 s.
The gas leaves at the entered 3,000 m/s, while the pressure-inclusive effective exhaust velocity is 3,400 m/s.
Quick guide
How to use this calculator
- Choose the performance information actually known; a gas exit speed is not automatically an effective exhaust velocity.
- Use total expelled propellant mass flow, including all propellants represented by the thrust measurement.
- For the nozzle equation, enter absolute pressures and the effective axial exit quantities for the stated simplified model.
- Read momentum and pressure thrust separately, then check the resulting positive net thrust and Isp.
Calculation method
Calculation and interpretation
Keep measured thrust, propellant flow, physical exit speed and effective exhaust velocity distinct.
veffective=Isp·g0=F/ṁ; F=ṁuexit+(pexit−pambient)Aexit; Isp=F/(ṁg0).
Worked example
A pressure term changes effective exhaust velocity
The gas leaves at the entered 3,000 m/s, while the pressure-inclusive effective exhaust velocity is 3,400 m/s.
veffective=Isp·g0=F/ṁ; F=ṁuexit+(pexit−pambient)Aexit; Isp=F/(ṁg0).
Supported inputs
Precision and limits
An entered engine model
These calculations do not establish combustion stability, nozzle operability, thermal margins, structural capacity, vehicle guidance or launch capability. Use consistent measured or specified performance at the same operating condition.
Effective exhaust and standard gravity
Effective exhaust velocity includes the thrust contribution represented by the entered performance. Converting Isp in seconds uses the fixed standard gravity 9.80665 m/s², even away from Earth; local gravity is a different quantity.
Continue calculating
Related calculators
