Exit Velocity Calculator

Exit velocity is how fast exhaust gases leave the nozzle of a jet engine or gas turbine. It's what produces thrust: the gas shoots out the back, and the engine (with the aircraft attached to it) gets pushed forward. The faster the exhaust, the more thrust you get. But thrust isn't free, and how exit velocity compares to flight speed is what separates an efficient airliner engine from a fighter jet in afterburner.

How to use this calculator

You'll need five inputs:

Specific heat (Cp) of the exhaust gas at constant pressure. Around 1,150 J/(kg·K) for hot combustion products.
Total inlet temperature in Kelvin. Modern turbines run between 800 and 1,500 K.
Inlet pressure and ambient pressure. The ratio between them is what drives the expansion.
Gamma ratio (γ), about 1.33 for hot exhaust gases.
Nozzle efficiency, typically 90 to 98% for modern designs.

Understanding the formula

The exit velocity comes from the energy balance for isentropic expansion through a nozzle:

V_e = \sqrt{2 \cdot \eta_n \cdot C_p \cdot T_{in} \left[ 1 - \left( \frac{P_{amb}}{P_{in}} \right)^{\frac{\gamma-1}{\gamma}} \right]}

Here's a concrete example. A small gas turbine with gas entering the nozzle at 1,000 K, exiting to ambient at 101.325 kPa. Inlet pressure is 200 kPa, specific heat is 1,150 J/(kg·K), gamma is 1.33, and the nozzle is 95% efficient.

First, the pressure ratio term:

\left( \frac{101{,}325}{200{,}000} \right)^{\frac{1.33-1}{1.33}} = (0.5066)^{0.2481} \approx 0.8317

Then plug into the main formula:

V_e = \sqrt{2 \times 0.95 \times 1{,}150 \times 1{,}000 \times (1 - 0.8317)}

V_e = \sqrt{2{,}185{,}000 \times 0.1683} = \sqrt{367{,}735.5} \approx 606.4 \text{ m/s}

About 606 m/s, which is typical for a small turbine at moderate pressure ratios.

Where this gets used

Commercial airliners cruise around Mach 0.85, and their high-bypass turbofans keep exit velocity in the 300 to 400 m/s range. That's the sweet spot for fuel efficiency: a big slug of air moving at moderate speed, well matched to flight speed, with little waste in the jet wash.

Military jets in afterburner do the opposite. Exit velocities past 1,000 m/s get them supersonic, but propulsive efficiency tanks because the exhaust is moving so much faster than the aircraft.

For engineers, the math shows up in two places. Nozzle designers use it to balance thrust against efficiency when sketching geometry. Performance engineers use it to predict how thrust shifts across the flight envelope as altitude, throttle, and ambient conditions change.

Tips for accurate calculations

Keep temperature in Kelvin and use the same pressure units on both sides (both Pa, or both bar). Mixed units silently break the math.
For gamma, use 1.4 for air, 1.33 for hot combustion products, or 1.67 for monatomic gases like helium and argon.
Modern convergent-divergent nozzles hit 95 to 98% efficiency. Simpler converging-only designs run lower, around 85 to 95%.
Ambient pressure has to be below inlet pressure. Otherwise there's nothing for the gas to expand into, and the formula returns nonsense.

Frequently asked questions

What happens if exit velocity is much higher than flight speed?

Thrust goes up, but fuel efficiency falls off a cliff. The extra kinetic energy in the exhaust is wasted: you spent fuel to accelerate the gas and got nothing useful back. That's why rockets, with their huge exit velocities, are terrible for atmospheric flight compared to a high-bypass turbofan moving a lot of air at moderate speed.

How does altitude affect exit velocity?

Higher altitude means lower ambient pressure, which makes the pressure ratio larger and pushes exit velocity up. That's why an engine produces more specific thrust at altitude than at sea level.

Why do commercial jets use lower exit velocities than fighter jets?

Propulsive efficiency. Accelerating a big mass of air a little is more efficient than accelerating a small mass of air a lot. Airlines care about fuel burn per seat-mile; fighter jets care about going fast even if the fuel bill is painful.

What's the difference between static and total temperature and pressure?

Total (or stagnation) values include both the static value and the kinetic energy of the moving gas. For nozzle calculations, use the total values at the inlet, since the formula converts that thermal and pressure energy into kinetic energy at the outlet.

Does this calculator account for supersonic flow?

The formula assumes ideal isentropic expansion and works for both subsonic and supersonic exit conditions, but it doesn't capture choked flow limits or shock waves in a converging-only nozzle. For actual supersonic exit you need a convergent-divergent geometry, and you'll want to check separately whether the design pressure ratio is being met.