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Total Impulse

Total impulse is the total amount of push a rocket motor delivers during its entire burn. It is the integral of thrust over time, or for a roughly constant thrust, simply average thrust times burn time. For example, a booster that produces 100,000 N for 120 seconds delivers 12 million newton-seconds of total impulse. This number tells you how much momentum the motor can give to a spacecraft. It is used to compare solid rocket motors and to plan missions.

Written by the Vorzep Team

Propulsion Rocketry Fundamental
PROPULSION · ROCKET MOTORS · PERFORMANCE TOOLS

Total Impulse Calculator

Solve for total impulse, average thrust or burn time, see it as the area under the thrust curve, find the motor class, and estimate propellant mass and Δv.

It = ∫ F dt ≈ Favg · tb
Solve for
Motor presets (approximate, illustrative)
Thrust profile (shape of the thrust curve)
Force unit

Result

TOTAL IMPULSE
—
— MOTOR CLASS
TOTAL IMPULSE—
AVERAGE THRUST—
BURN TIME—
PEAK THRUST—

Step-by-step

Related metrics

Impulse as area under the thrust curve

Thrust curve F(t)Equal-area rectangle Favg × tb

Motor class (each letter doubles the impulse)

Charts

Total impulse

Total impulse is the thrust of a motor integrated over its whole burn, It = ∫F dt. It is the area under the thrust-time curve and measures how much "push" a motor delivers, in newton-seconds. When thrust is not constant it is convenient to use the average thrust, defined so that Favg · tb equals the true area. Total impulse is also tied to propellant: It = Isp · g₀ · mp.

It = ∫ F(t) dt ≈ Σ Fi · Δt
It = Favg · tb
Favg = It / tb · tb = It / Favg
mp = It / (Isp · g₀) · Δv = Isp · g₀ · ln(m₀ / (m₀ − mp))
SymbolMeaningUnit
ItTotal impulseN·s (kN·s, lbf·s)
FavgAverage thrust over the burnN (kN, lbf)
tbBurn times
IspSpecific impulse (optional)s
m₀Vehicle mass at ignition (optional)kg
mpPropellant mass burnedkg

Worked example

Favg = 133 N, tb = 1.8 s
It = 133 × 1.8 = 239.4 N·s → class H (160.01 to 320 N·s)
At Isp = 200 s: mp = 239.4 / (200 × 9.80665) ≈ 0.122 kg

Hobby motor classes (N·s)

ClassImpulse rangeClassImpulse range
A1.26 to 2.5H160 to 320
C5.01 to 10J640 to 1,280
E20 to 40L2,560 to 5,120
G80 to 160N10,240 to 20,480

FAQ

How do I get total impulse from a measured thrust curve?

Integrate the data numerically: sum thrust times the time step for each sample (or use the trapezoid rule). The result is the area under the curve, and dividing by burn time gives the average thrust.

Is peak thrust or total impulse more important?

They answer different questions. Total impulse sets how much altitude or Δv a rocket can gain, while peak thrust matters for launch acceleration and structural loads. The same impulse can be delivered as a short strong burn or a long gentle one.

Why does each motor class double the impulse?

Hobby classes (NAR and Tripoli) are defined by doubling bands, so an H motor has up to twice the total impulse of a G, and so on. Motors above O are usually treated as professional or research scale.

Variables

Symbol Quantity Unit
I_t Total impulse N*s
F_avg Average thrust N
t_b Burn time s

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

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  • Published July 10, 2026
  • Last updated October 22, 2026