Impulse Calculator
Enter a force and the time it acts and get the impulse — the single number that tells you how much an object's momentum changes.
What is impulse?
Force applied over time, equal to the change in momentum
Impulse is what you get when a force acts on an object for a stretch of time. Written J = F × Δt, it is simply the force in newtons multiplied by the time interval in seconds, and the answer comes out in newton-seconds (N·s). The key fact is that impulse equals the change in momentum (Δp), which is why a newton-second is the same as a kilogram-metre per second. A bigger force or a longer contact time both increase the impulse, because the value grows with each. This one idea explains why a quick, hard hit and a slow, gentle push can produce the very same change in motion.
Enter the force in newtons and the time interval in seconds to get the impulse instantly.
One short formula, built from the force F and the time interval Δt.
J = F × ΔtMultiply the force in newtons by the time interval in seconds and the answer comes out in newton-seconds. The only thing to watch is the units: keep the force in newtons and the time in plain seconds, and remember that the same N·s figure is also the change in momentum in kg·m/s.
Suppose a constant 50 N force pushes a cart for 4 seconds.
Note the inputs
Force F = 50 N and time interval Δt = 4 s — both already in base units.
Multiply
50 × 4 = 200 — force times the time it acts.
Read it off
J = 200 N·s — the cart's momentum changes by 200 kg·m/s in the direction of the force.
The impulse is a change in motion, not a force on its own, and the first thing to read from it is that the number you get is exactly the change in momentum (Δp) the object experiences — 200 N·s means 200 kg·m/s of extra momentum in the direction the force points. Because the value is a straight product, it moves in lockstep with the two inputs: double the force or double the contact time and you double the impulse. That symmetry is the practical insight behind safety design. In a collision the change in momentum is fixed, so the impulse is fixed too; the only freedom you have is to spread that impulse over more time, which lowers the peak force for the same result. Crumple zones, airbags, and bending your knees on landing all stretch Δt and so cut the force the body feels. Run the other way and the same logic explains a hard, fast hit: a large force over a tiny time still delivers a big impulse. Reading the result, then, is really about deciding whether you want the change in motion to come from a big push, a long contact, or some balance of both.
The formula J = F × Δt is exact for a constant force, but a few practical points are worth keeping in mind.
Constant force, base units, one direction
This calculator assumes a single constant force acting along one direction. Keep the force in newtons and the time in seconds. Real impacts rarely apply a steady force — the force rises and falls during contact — so for those cases the physical impulse is the area under the force-time curve, and the value here represents the equivalent constant force over the interval. Impulse and force are also directional: if forces act along different lines you must combine them as vectors before applying the formula.