Impulse Calculator
Impulse is force applied over time and equals the change in momentum. Choose what to solve for, enter the other values and the object's mass, and get the impulse, average force, time and velocity change together.
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Formula
J = F × Δt = Δp = m × Δv
- Force:
F = J ÷ Δt - Time:
Δt = J ÷ F - Velocity change:
Δv = J ÷ m
Inputs are converted exactly: 1 lbf = 0.45359237 × 9.80665 = 4.4482216 N, 1 lb = 0.45359237 kg, 1 ms = 0.001 s. Force is the average force over the contact time.
Worked example
A bat applies an average 500 N for 0.02 s (20 ms) to a 0.145 kg baseball.
- Impulse = 500 × 0.02 = 10 N·s
- Velocity change = 10 ÷ 0.145 = 68.97 m/s
- Reversed: 10 N·s over 0.02 s gives F = 500 N, and 10 N·s at 500 N takes 0.02 s.
Frequently asked questions
What is the impulse formula?
J = F × Δt, the average force times the time it acts, in newton-seconds (N·s). A 500 N force acting for 0.02 s delivers J = 500 × 0.02 = 10 N·s.
How are impulse and momentum related?
Impulse equals the change in momentum: J = Δp = m × Δv. The 10 N·s impulse on a 0.145 kg ball changes its velocity by 10 ÷ 0.145 = 68.97 m/s, and 1 N·s is the same as 1 kg·m/s.
How do I find the average force of an impact?
Divide the impulse by the contact time, F = J ÷ Δt. A 10 N·s impulse over 0.02 s (20 ms) means 500 N on average; stretching the same impulse over 0.1 s cuts the force to 100 N, the idea behind padding and crumple zones.
Why is the force called an average?
Real impact forces rise and fall during contact. Impulse is the area under the force-time curve, and dividing it by the contact time gives the constant force that would deliver the same impulse. The peak force is higher.
Can I use pounds-force and milliseconds?
Yes. Inputs are converted exactly (1 lbf = 4.4482216 N, 1 ms = 0.001 s), so 100 lbf for 20 ms gives 100 × 4.4482216 × 0.02 = 8.896 N·s.