What is the impulse?
Type an average force and how long it acts, or a mass with its velocity before and after an impact. The impulse calculator gives the impulse in newton-seconds and pound-force seconds, and the average force when you give the contact time.
- Impulse (N·s)
- 50
The impulse is 50 N·s (11.2404 lbf·s).
- Impulse (lbf·s)
- 11.2404
- Average force (N)
- 500
- Average force (lbf)
- 112.404
Impulse (N·s): 50. The impulse is 50 N·s (11.2404 lbf·s).
How to calculate
Computes impulse from an average force and the time it acts (J = FΔt), or from a mass and its change in velocity (J = mΔv), with the average force of an impact, in N·s and lbf·s.
Example with the default inputs (Impulse from Force × time, Average force 112.404471549855 lbf, Contact time 100 ms): The impulse is 50 N·s (11.2404 lbf·s).
Method: J = F_avg × Δt; J = Δp = m × (v₂ − v₁); F_avg = J ÷ Δt.
- Motion along one line: a positive velocity or force points one way, a negative one the other way.
- The mass stays the same during the impact. Exact unit sizes: 1 lbf = 4.4482216152605 N; 1 lb = 0.45359237 kg; 1 mph = 0.44704 m/s; 1 km/h = 1/3.6 m/s; 1 ft/s = 0.3048 m/s.
Worked examples
Each example is checked against the calculator on every build.
- Impulse from Force × time, Average force 112.4 lbf, Contact time 100 ms gives Impulse (N·s) 50, Average force (N) 500.Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions
- Impulse from Change in momentum, Mass 0.3197 lb, Initial velocity -131.2 ft/s, Final velocity 164 ft/s, Contact time 1 ms gives Impulse (N·s) 13.05, Change in velocity (m/s) 90, Average force (N) 13,050.Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions
- Impulse from Change in momentum, Mass 2,205 lb, Initial velocity 65.62 ft/s, Final velocity 0 ft/s gives Impulse (N·s) -20,000, Change in velocity (m/s) -20.Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions
- Impulse from Force × time, Average force 1 lbf, Contact time 1,000 ms gives Impulse (lbf·s) 1, Impulse (N·s) 4.448222.Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; NIST SP 811 (1 lbf = 4.4482216152605 N), https://www.nist.gov/pml/special-publication-811
How it works
Pick how to find the impulse J, in N·s:
- Force × time: J = F × Δt, with the average force F in newtons and the contact time Δt in seconds. The contact time is needed in this mode.
- Change in momentum: J = m × (v₂ − v₁), with the mass m in kg and the velocities in m/s. The change in velocity v₂ − v₁ is shown too.
When the contact time is given, the average force is F = J ÷ Δt, in newtons and pounds-force. The impulse also shows in lbf·s (N·s ÷ 4.4482216152605).
Signs: velocities and forces along one line; a negative value points the other way. A negative impulse pushes against the direction you chose as positive.
Unit sizes: 1 kN = 1,000 N; 1 lbf = 4.4482216152605 N; 1 ms = 0.001 s; 1 min = 60 s; 1 g = 0.001 kg; 1 lb = 0.45359237 kg; 1 oz = 0.028349523125 kg; 1 km/h = 1/3.6 m/s; 1 mph = 0.44704 m/s; 1 ft/s = 0.3048 m/s.
Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size is exact, so each result is an exact fraction until it is rounded for display.
Output format. Every value shows 6 significant figures; values of 10¹⁵ or more, or below 10⁻⁶, show in scientific form.
When there is no answer.
- Force × time with no contact time.
- An impulse that is not 0 but is below the smallest number a computer can hold (about 5 × 10⁻³²⁴ N·s).
Assumptions
- Motion along one line, and a mass that stays the same during the impact.
- Force −10¹² to 10¹² N; contact time 10⁻¹² to 10⁹ s; mass more than 0 and at most 10⁹ kg; velocities −10⁸ to 10⁸ m/s.
Worked examples by hand
500 N for 0.1 s. J = 500 × 0.1 = 50 N·s; average force 50 ÷ 0.1 = 500 N.
A 0.145 kg baseball, −40 m/s to 50 m/s, in 1 ms. Δv = 50 − (−40) = 90 m/s; J = 0.145 × 90 = 13.05 N·s; F = 13.05 ÷ 0.001 = 13,050 N.
A 1,000 kg car stopping from 20 m/s. Δv = 0 − 20 = −20 m/s; J = 1,000 × (−20) = −20,000 N·s.
1 lbf for 1 s. J = 4.4482216152605 × 1 = 4.4482216152605 N·s = 1 lbf·s.
Other questions people ask
What is the formula for impulse?
Impulse is the average force times the time it acts: J = F × Δt. An average force of 500 N for 0.1 s gives an impulse of 50 N·s.
How is impulse related to momentum?
By the impulse-momentum theorem, the impulse equals the change in momentum: J = Δp = m (v₂ − v₁). A 0.145 kg baseball that goes from 40 m/s toward the bat to 50 m/s away has J = 0.145 × 90 = 13.05 N·s.
How do I find the average force of an impact?
Divide the impulse by the contact time: F = J ÷ Δt. The baseball’s 13.05 N·s delivered in 1 ms is an average force of 13,050 N.
Why does a negative impulse appear?
Impulse has a direction. If the object slows down or turns back, the change in velocity is negative along the direction you chose as positive. A car stopping from 20 m/s takes an impulse of −20,000 N·s per 1,000 kg.
Why do airbags and crumple zones help?
The impulse to stop you is fixed by your mass and speed. Spreading it over a longer time lowers the average force, F = J ÷ Δt.
What are the units of impulse?
Newton-seconds (N·s), which are the same as kg·m/s, the unit of momentum. 1 lbf·s = 4.4482216152605 N·s.