How to use this calculator
- Enter or choose calculate from.
- Enter or choose contact time.
- Enter or choose time unit.
- The impulse updates as you type. Use Copy result or Share to keep it.
Method
J = F Δt = m (v₂ − v₁); average F = J ÷ Δt
- J
- impulse in N·s
- F
- average force in N
- Δt
- contact time in s
- m
- mass in kg
- v₁, v₂
- velocities before and after, with sign for direction
Worked example
- Change in velocity: 50 − (−40) = 90 m/s, because the ball reverses direction.
- J = 0.145 × 90 = 13.05 N·s.
- Average force = 13.05 ÷ 0.001 s = 13,050 N.
Reversing a 145 g ball from 40 m/s to 50 m/s in 1 ms takes an impulse of 13.05 N·s, an average force of about 13 kN.
What the result means
For a fixed change in momentum, a longer contact time means a smaller force. Airbags, crumple zones and bending your knees on landing all work by stretching Δt.
Assumptions and limits
- Motion along one line; the force shown is the average over the contact time.
- Peak force in a real impact is usually well above the average.
Questions
Why does the sign of velocity matter?
A ball that bounces back changes momentum by more than one that stops dead. Enter the incoming velocity as negative and the outgoing as positive to capture the full change.
Is impulse the same as momentum?
Impulse is the change in momentum, measured in the same units (N·s = kg·m/s).