Rocket Thrust Calculator
An engine expelling 250 kg/s at 3000 m/s produces 724.94 kN at sea level, slightly less than its momentum thrust because the nozzle is over-expanded.
724.94 kN
Full answer, then cut to fewer decimals (not rounded):
- 724.94 kN
- 724.9 kN
- Momentum thrust ṁvₑ
- 750 kN
- Pressure thrust (pₑ − pₐ)Aₑ
- -25.06 kN
- Specific impulse I_sp = F/(ṁg₀)
- 295.6932286 s
- Effective exhaust velocity c = F/ṁ
- 2899.76 m/s
- Thrust in vacuum (pₐ = 0)
- 806 kN
- Nozzle
- over-expanded
Step-by-step solution
- F = ṁvₑ + (pₑ − pₐ)Aₑ = 250 × 3000 + (70000 − 101325) × 0.8
- F = 750000 + -25060 = 724940 N
- I_sp = F ÷ (ṁ g₀) = 295.6932286 s
Rocket Thrust Formula
F = ṁvₑ + (pₑ − pₐ)Aₑ
I_sp = F/(ṁg₀); effective exhaust velocity c = F/ṁ
Worked Example
250 kg/s at 3000 m/s, exit pressure 70 kPa, 0.8 m² exit at sea level:
- F = ṁvₑ + (pₑ − pₐ)Aₑ = 250 × 3000 + (70000 − 101325) × 0.8
- F = 750000 + -25060 = 724940 N
- I_sp = F ÷ (ṁ g₀) = 295.6932286 s
Pressure thrust (pₑ − pₐ)Aₑ: -25.06 kN · Specific impulse I_sp = F/(ṁg₀): 295.6932286 s · Effective exhaust velocity c = F/ṁ: 2899.76 m/s · Thrust in vacuum (pₐ = 0): 806 kN · Nozzle: over-expanded
GATE tip
Thrust coefficient C_F = F/(p₀A*) separates nozzle performance from combustion. Optimum expansion (pₑ = pₐ) maximises C_F at that altitude.
More Propulsion Calculators
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Rocket Equation Calculator
Δv = I_sp g₀ ln(m₀ / m_f)
m₀ initial (wet) mass, m_f final (dry) mass, g₀ = 9.80665 m/s², vₑ = I_sp g₀
Example: A stage with I_sp = 350 s burning from 100 t to 10 t: Delta-v Δv = 7903.23 m/s.
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Jet Engine Thrust Calculator
F = ṁₐ[(1 + f)vₑ − V₀] + Bṁₐ(v_f − V₀)
TSFC = ṁ_f/F; η_p = FV₀/ΔKE; η_th = ΔKE/(ṁ_f Q_R)
Example: A turbojet with 50 kg/s of air, f = 0.02, flying at 250 m/s with a 600 m/s jet: Thrust F = 18.1 kN.
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Axial Compressor Stage Calculator
w = U(C_θ2 − C_θ1), ΔT₀ = w/c_p
π = (1 + ηΔT₀/T₀₁)^(γ/(γ−1)); R = 1 − (C_θ1 + C_θ2)/(2U)
Example: A stage with U = 300 m/s turning the whirl from 100 to 200 m/s at 288 K inlet and 88 % efficiency: Stage pressure ratio = 1.35711.
Frequently asked questions
Why does thrust rise with altitude?
Ambient pressure falls, so the pressure term (pₑ − pₐ)Aₑ grows. Vacuum thrust is typically 10–20 % higher than sea-level thrust.
What is specific impulse?
Thrust per unit weight flow of propellant, in seconds: a measure of propellant efficiency. Kerosene-oxygen engines reach about 300–350 s, hydrogen-oxygen 450 s in vacuum.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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Scientific Converters. (2026, October 15). Rocket Thrust Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/rocket-thrust-calculator/
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Scientific Converters, "Rocket Thrust Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/rocket-thrust-calculator/