Impulse Calculator: J = FΔt and Momentum
This impulse calculator applies the impulse-momentum theorem, J = F × Δt = m × Δv. Find impulse from an average force and contact time, or from a mass and its change in velocity, then solve backward for the average force, the time or the final velocity. Enter values in newtons, pounds-force, kilograms, pounds, m/s or mph, and see the result in N·s and lbf·s with each step. It is handy for physics homework, car crash and sports examples, such as how much force a baseball bat applies.
Impulse Calculator
Find impulse from force and time or from mass and change in velocity, and solve for any missing value.
How to use the Impulse Calculator
- Choose what to solve for.
- Enter the known values and pick their units.
- Read the impulse or missing value.
- Check the steps below the result.
Impulse-momentum theorem
J = F × Δt = m × Δv = p₂ − p₁ · 1 lbf·s = 4.448 N·s
Features
- Solve for impulse, force, time or velocity
- SI and US units
- Momentum before and after
- Step-by-step working
Frequently asked questions
What is impulse in physics?
Impulse is the change in momentum of an object, J = F × Δt. It is measured in newton-seconds (N·s), which equals kg·m/s.
How do you calculate impulse from mass and velocity?
Multiply the mass by the change in velocity: J = m × (v₂ − v₁). A 0.145 kg baseball going from −40 m/s to +45 m/s has an impulse of 0.145 × 85 = 12.3 N·s.
How do you find average force from impulse?
Divide the impulse by the contact time: F = J ÷ Δt. 12.3 N·s over 0.7 ms is about 17,600 N.
Why do airbags reduce injury?
They stretch out the stopping time. The impulse needed to stop you is the same, so a longer Δt means a much smaller average force.
What is the unit of impulse in US units?
Pound-force seconds (lbf·s). 1 lbf·s equals about 4.448 N·s.