Calculate signed axial thrust from mass flow, velocity, pressure, and exit area, with reverse sizing, a flow-normalized thrust ratio, optional TWR, and total impulse.

Use axial velocities in the same engine frame and equal inlet/exit mass flow. For a rocket, enter 0 for inlet velocity; do not subtract flight speed.

Enter 0 for a rocket. Signed velocities use one consistent axial convention.

Vehicle mass and burn time

Blank omits TWR. Zero mass makes TWR undefined.

Blank omits impulse. Enter 0 for zero duration; thrust is assumed constant.

Thrust Formula

The following formula applies to a rocket using actual nozzle exit velocity relative to the rocket and zero inlet velocity. The calculator also supports the equal-inlet/exit-mass-flow approximation F = ṁ(Vₑ − Vᵢ) + (Pₑ − Pₐ)Aₑ, with axial velocities in one engine/control-volume frame. Do not subtract rocket flight speed as inlet velocity. F/(ṁg₀) is rocket specific impulse only when ṁ is total propellant flow and the rocket-frame inlet term is zero; it is not fuel-based Isp for an air-breathing engine.

T = ṁ Ve + (Pe − Pa) Ae

  • ṁ – propellant mass-flow rate (kg/s)
  • Ve – actual nozzle exit velocity relative to the rocket (m/s), not pressure-adjusted effective exhaust velocity
  • Pe – static pressure at the nozzle exit (Pa)
  • Pa – ambient (back-) pressure (Pa)
  • Ae – exit area of the nozzle (m²)

Thrust Definition

Thrust is the force produced by an engine (such as a rocket or jet) when it expels mass as exhaust. For a rocket nozzle, thrust includes both the exhaust momentum term (ṁVe) and the nozzle pressure-difference term (Pe − Pa)Ae.

Thrust Example

How to calculate thrust?

  1. First, determine the exhaust velocity.

    Use the actual nozzle exit velocity Vₑ relative to the rocket, and enter 0 for inlet velocity.

  2. Next, determine the propellant mass flow.

    Measure the propellant mass used (Δm) over a burn time (Δt), then compute ṁ = Δm/Δt.

  3. Next, determine the pressure/area terms.

    Find the nozzle exit pressure Pₑ, ambient pressure Pₐ, and nozzle exit area Aₑ (or set Pₑ = Pₐ to neglect the pressure-thrust term).

  4. Finally, calculate the thrust.

    Compute T = ṁVₑ + (Pₑ − Pₐ)Aₑ.

FAQ

What is thrust?

Thrust is the force produced by an engine when it expels mass (exhaust). For rocket nozzles, it includes both the exhaust momentum term and (when applicable) a nozzle pressure-difference term.