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Formula of Thrust

Force and laws of motion formulasVectorClass 9Updated 1 Nov 2026

F=vrΔmΔtF = v_r \frac{\Delta m}{\Delta t}
SI unit
newton (N)
Dimensions
[M¹ L¹ T⁻²]
where
  • F thrust force N
  • v_r exhaust speed relative to the rocket or engine m/s
  • Δm/Δt mass of gas or fluid ejected per second kg/s

The formula of thrust for a rocket or jet is F=vrΔmΔtF = v_r \frac{\Delta m}{\Delta t}: the push equals the exhaust speed relative to the engine multiplied by the mass of gas thrown out each second. A rocket that ejects 50 kg of gas per second at 2500 m/s gets a thrust of 125 000 N.

The word thrust has a second, simpler meaning in Class 9 physics in India: the total force acting perpendicular to a surface, so that pressure is thrust per unit area. Both meanings are forces measured in newtons, and both are covered here. The rocket version is Newton's second and third laws applied to a stream of gas, which places it in the laws of motion section.

Quick facts

  • Rocket thrust

    F=vrΔmΔtF = v_r \frac{\Delta m}{\Delta t}

  • Class 9 thrust

    Force normal to a surface, P=thrustAP = \frac{\text{thrust}}{A}

  • SI unit

    newton (N)

  • Dimensional formula

    [M¹ L¹ T⁻²]

  • Type

    Vector, opposite to the exhaust direction

  • Mass flow rate unit

    kg/s

Where the thrust force formula comes from

In a short time Δt the engine pushes out a mass Δm of gas at speed vrv_r backward. The gas gains momentum Δm vr\Delta m \, v_r. By the second law, the force on the gas is Δm vrΔt\frac{\Delta m \, v_r}{\Delta t}. By the third law the gas pushes the rocket forward with an equal force. That forward push is the thrust.

So a rocket does not push against the air or the ground. It works in empty space better than in air. The idea is the continuous version of the recoil velocity of a gun, and it rests on conservation of momentum.

Worked examples using the formula of thrust

Example 1: thrust and launch acceleration

A 5000 kg rocket ejects gas at 2500 m/s relative to itself at 50 kg/s. Find the thrust and the initial upward acceleration (g = 9.8 m/s²).

F=2500×50=1.25×105 NF = 2500 \times 50 = 1.25 \times 10^5\ \text{N}

Weight: 5000 × 9.8 = 49 000 N. Net force upward: 125 000 − 49 000 = 76 000 N.

a=76 0005000=15.2 m/s2a = \frac{76\,000}{5000} = 15.2\ \text{m/s}^2

As fuel burns, the mass falls and the acceleration rises even if the thrust stays the same.

Example 2: a water jet

A hose sprays 0.50 kg of water per second at 10 m/s. Find the reaction force on the nozzle.

F=10×0.50=5.0 NF = 10 \times 0.50 = 5.0\ \text{N}

This is why a fire hose at full pressure needs firm hands.

Example 3: Class 9 thrust and pressure, with cm

A 2.0 kg block rests on a table on a face measuring 10 cm by 20 cm. Find the thrust on the table and the pressure.

Thrust = weight = 2.0 × 9.8 = 19.6 N. Area = 0.10 m × 0.20 m = 0.020 m².

P=19.60.020=980 PaP = \frac{19.6}{0.020} = 980\ \text{Pa}

Thrust in Class 9: force on a surface

In this sense thrust is the force pressing perpendicular to a surface. A block sitting on a table exerts a thrust equal to its weight. Pressure tells you how concentrated that thrust is: P=FAP = \frac{F}{A}. The same thrust over a smaller area gives more pressure, which is why a sharp knife cuts and why wide tyres stop a tractor sinking into mud. See the pressure formula for more.

Liquids exert thrust too. The upward thrust of a liquid on an immersed object is the buoyant force.

The full rocket thrust equation

Engineers write the thrust of a rocket engine as F=m˙ve+(pe−pa)AeF = \dot{m}v_e + (p_e - p_a)A_e. The first term is the momentum term used on this page. The second adds the effect of the exhaust pressure pep_e differing from the outside pressure pap_a across the nozzle exit area AeA_e. For school problems the pressure term is ignored, which leaves the simple formula.

For a rocket's speed after burning fuel, combine the thrust with the changing mass to get v=u+vrln⁡m0mv = u + v_r \ln\frac{m_0}{m}, ignoring gravity. Here m0m_0 is the starting mass and m the mass left.

Mistakes with thrust

  • Leaving the mass flow rate in kg per minute.
  • Forgetting the rocket's weight when finding the launch acceleration.
  • Thinking a rocket needs air to push against.
  • Confusing thrust in the Class 9 sense with pressure. Thrust is in N; pressure is in Pa.
A rocket lifts off only when thrust exceeds weight. If the thrust is smaller, it sits on the pad with the engine running.

Thrust is one of many named forces; the force formula page lists the others.

Frequently asked questions

What is the formula of thrust?

For a rocket or jet, thrust F = v_r × (Δm/Δt), the exhaust speed times the mass ejected per second. In Class 9, thrust is the force acting perpendicular to a surface, and pressure is thrust divided by area.

Which SI unit applies to thrust?

The newton, N, since thrust is just a particular force.

What is the difference between thrust and pressure?

Thrust is the total perpendicular force on a surface, in newtons. Pressure is that force per unit area, in pascals.

Can a rocket produce thrust in space?

Yes. The thrust comes from pushing exhaust gas backward, not from pushing on the air. With no air around, it works at least as well.