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Formula & Calculator

Total Impulse

Integral of thrust over the engine's burn time, quantifying total momentum delivered by a rocket motor.

Written by the Vorzep Team

PropulsionRocketryFundamental

Total Impulse Calculator

It = ∫ F dt ≈ Favg · tb
Solve for It, Favg, or tb
It⟷Favg, tb
N·s
N
s
Solve for:
Result —
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Total Impulse vs. Average Thrust It(Favg) = Favg · tb
It(Favg) for fixed tb Computed point
All values positive • It = Favg · tb
I_t = ∫ F dt ≈ F_avg * t_b
Total Impulse

Variables

SymbolQuantityUnit
I_tTotal impulseN*s
F_avgAverage thrustN
t_bBurn times

What it means

Total impulse is the total thrust integrated over the burn time, representing the change in momentum of the rocket. It is a key performance metric for solid rocket motors and for comparing different propulsion systems. For a constant thrust, it is simply thrust multiplied by burn time. Total impulse is used to size motors and to calculate the total Δv capability. It also appears in the definition of specific impulse: Isp = I_t/(m_prop · g₀). Understanding total impulse is essential for mission design and for selecting propulsion systems for given applications.

Worked example

Total Impulse – Two Examples

Real‑World
Scenario: A rocket motor produces 50,000 N average thrust for 60 s. Find total impulse.
ParameterValue
F_avg50,000 N
t_b60 s
1I_t = F_avg × t_b = 50000 × 60 = 3,000,000 N·s
Result 3.0×10⁶ N·s ✓ Moderate
Scenario: F_avg = 100,000 N, t_b = 120 s. Find total impulse.
ParameterValue
F_avg100,000
t_b120
1I_t = 100000 × 120 = 12,000,000 N·s
Result 1.2×10⁷ N·s ✓ High
Key insight: Total impulse = thrust × burn time – it measures the total change in momentum.

Common mistakes

  • Total impulse I_t: I_t = ∫F dt ≈ F_avg·t_b – in N·s.
  • F_avg: Average thrust over burn time.
  • t_b: Burn time (s).
  • Unit N·s = kg·m/s – same as momentum.
  • Related to propellant mass and I_sp: I_t = ṁ·I_sp·g₀ = m_p·I_sp·g₀.

Applications

Total impulse, I_t = ∫F dt ≈ F_avg·t_b, is the total thrust integrated over the burn time, representing the total momentum imparted to the rocket. It is a fundamental measure of the total energy of a rocket motor. Engineers use total impulse to size motors for applications like missiles, boosters, and small satellite propulsion. It combines thrust and duration, allowing direct comparison of motors of different sizes and burn times. By calculating total impulse, aerospace engineers can select the appropriate motor for a given mission and verify that the required Δv can be achieved.

  • Rocket motor sizing for launch vehicles and missiles
  • Comparison of solid and liquid rocket motors
  • Mission planning and Δv budgeting
  • Propulsion system selection for satellite orbit insertion
  • Performance verification during static tests