The Impulse Calculator finds impulse from average force and the time over which it acts, or from mass and change in velocity through the impulse-momentum theorem. Enter either pair, and the tool returns impulse in newton-seconds along with the equivalent momentum change in kilogram-metres per second.
Impulse describes how much a force changes an object's motion, combining both how hard the force pushes and how long it pushes for. A small force over a long time can deliver the same impulse as a large force over a short time, which is the basic idea behind seatbelts, airbags and padded landing surfaces.
Calculate impulse from force and time
Impulse J equals average force times the duration of that force.
J = F Δt| Symbol | Quantity | SI unit |
|---|---|---|
| J | impulse | newton-seconds (N·s) |
| F | average force | newtons (N) |
| Δt | time interval | seconds (s) |
Worked example: a steady 50 N force acts for 0.2 seconds.
1. Multiply force by time. 50 × 0.2 = 10 N·s.
The same impulse could come from a different force-time combination, such as 100 N over 0.1 s or 20 N over 0.5 s. What matters for the impulse is the product, not the individual values.
Calculate impulse from mass and change in velocity
The impulse-momentum theorem states that impulse equals the change in momentum an object experiences, Δp = mΔv.
J = m Δv = ΔpWorked example: a 2 kg object speeds up from 3 m/s to 8 m/s.
1. Find the change in velocity. 8 − 3 = 5 m/s.
2. Multiply by mass. 2 × 5 = 10 kg·m/s, equivalent to 10 N·s.
Both routes to impulse, force times time or mass times velocity change, describe the same physical event and always agree when applied to the same interaction.
Understand why N·s equals kg·m/s
A newton is defined as the force needed to accelerate one kilogram at one metre per second squared, so 1 N = 1 kg·m/s². Multiplying by seconds cancels one power of time:
1 N·s = 1 (kg·m/s²) × s = 1 kg·m/sThat is why impulse and momentum change share identical units, despite looking like different quantities on the surface. Many exam mark schemes accept either unit label for an impulse answer, since they represent the exact same physical dimension.
Find average force in a collision
Rearranging J = FΔt for force gives F = J / Δt = mΔv / Δt, which shows that for a fixed change in momentum, a shorter contact time produces a much larger average force. Worked example: a 0.15 kg baseball arrives at 40 m/s and is caught, coming to a complete stop.
1. Find the change in velocity. 0 − 40 = −40 m/s.
2. Find the change in momentum. 0.15 × (−40) = −6 kg·m/s.
3. Divide by the contact time (0.02 s). −6 / 0.02 = −300 N.
Stretching the same catch to take 0.2 s instead of 0.02 s, ten times longer, would reduce the average force to −30 N, one-tenth as much, for exactly the same change in momentum. That relationship is the physics behind padded gloves, crumple zones and airbags: extending contact time reduces peak force for the same impulse.
Recognize that force is average, not instantaneous
The force used in J = FΔt is an average over the interval. Real collisions often have a force that rises sharply and falls away, rather than staying constant throughout. The impulse-momentum theorem still holds using that average value; the calculator reports the average force implied by the given impulse and time, not the peak force at any single instant.
Work through a second momentum example
A 0.5 kg ball slows from 12 m/s to 4 m/s. 1. Find the change in velocity. 4 − 12 = −8 m/s. 2. Multiply by mass. 0.5 × (−8) = −4 kg·m/s, equivalent to −4 N·s.
The negative sign shows the impulse acted opposite to the ball's original direction of motion, slowing it down rather than speeding it up, consistent with the impulse-momentum theorem applied to a decrease in velocity.
Frequently asked questions
What is the formula for impulse?
Impulse equals average force times time: J = FΔt. It also equals mass times change in velocity: J = mΔv, since both describe the same change in momentum.
What is the unit of impulse?
Impulse is measured in newton-seconds (N·s), which is dimensionally identical to kilogram-metres per second (kg·m/s), the unit of momentum.
How does contact time affect the force in a collision?
For a fixed impulse (change in momentum), a shorter contact time produces a larger average force, and a longer contact time produces a smaller average force. This is why airbags and padding reduce injury by extending contact time.
Can impulse be negative?
Yes. A negative impulse means the force acted opposite to the chosen positive direction, which typically corresponds to slowing an object down or reversing its motion.
Is impulse the same as force?
No. Force is measured in newtons and describes an instantaneous push or pull. Impulse is measured in newton-seconds and describes the total effect of a force acting over time.
How do you find average force from impulse?
Divide the impulse by the time interval: F = J / Δt. A 10 N·s impulse delivered over 0.2 s corresponds to an average force of 50 N.
Does impulse depend on the object's mass?
Impulse itself, calculated as J = FΔt, does not directly involve mass. But when calculated as J = mΔv, mass is a direct factor, since a larger mass needs a proportionally larger impulse to achieve the same change in velocity.
Summary
Impulse combines force and time (J = FΔt) or mass and velocity change (J = mΔv), both giving the same result for a single event, such as 10 N·s for a 50 N force over 0.2 s or a 2 kg object speeding up by 5 m/s.
Because impulse equals change in momentum, a fixed impulse spread over a longer contact time produces a smaller average force, the principle behind airbags, padding and crumple zones.