Impulse Calculator
Find impulse and momentum change from force and time.
Results update as you type.
How it works
Impulse measures the total effect of a force applied over a period of time, and this calculator finds it, along with the equal change in momentum it produces. You enter the force and the duration it acts, and it returns the impulse and the resulting momentum change. The impulse-momentum theorem, one of the most useful results in mechanics, states that impulse equals the change in an object's momentum, so a force acting for a longer time changes an object's motion more. This principle explains a huge amount of everyday physics and safety engineering: airbags, crumple zones, and padded surfaces all work by extending the time over which a collision force acts, which reduces the peak force for the same momentum change and protects people. Conversely, following through in sports like golf or baseball keeps the force on the ball for longer, increasing its momentum and speed. Rockets, recoil, and collisions are all analysed with impulse. The concept links force, which is often hard to measure during rapid events, to the more easily measured change in velocity and mass. Force and time here are treated as constant over the interval. Enter the force and time to compute the impulse and momentum change.
J = F · t = Δp
Impulse equals the force applied multiplied by the time over which it acts, and by the impulse-momentum theorem it equals the change in an object's momentum. This is why a small force acting for a long time can produce the same momentum change as a large force acting briefly. Impulse and momentum change share the same units when momentum is measured in kilogram-metres per second.
Source:Classical mechanics (impulse-momentum theorem)
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Worked example
How to use this calculator
- 1
Enter your values
Enter force and time.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Impulse updates instantly as you type — no button to press.
Frequently asked questions
What is impulse?
Impulse is the product of a force and the time over which it acts, measured in newton-seconds. It represents the total push or pull delivered over that interval. By the impulse-momentum theorem, impulse equals the change in an object's momentum, so it directly tells you how much an object's motion will change as a result of the force.
What is the impulse-momentum theorem?
The impulse-momentum theorem states that the impulse applied to an object equals its change in momentum. Since momentum is mass times velocity, this links the force and duration to the resulting change in velocity. It is a restatement of Newton's second law and is especially useful for analysing collisions and impacts where forces vary rapidly.
How do airbags use impulse?
In a crash, an occupant's momentum must be reduced to zero. An airbag extends the time over which this happens, and since impulse equals force times time, spreading the same momentum change over a longer time reduces the peak force on the body. Lower force means less injury, which is why airbags, crumple zones, and padding save lives.
Why does following through matter in sports?
Following through keeps the bat, club, or racket in contact with the ball for a longer time. Because impulse is force times time, applying the force over a longer contact time delivers a greater impulse, changing the ball's momentum more and sending it faster and farther. This is why coaches emphasise a full follow-through in striking sports.
What units does impulse use?
Impulse is measured in newton-seconds, which are equivalent to kilogram-metres per second, the units of momentum. This equivalence reflects the impulse-momentum theorem, since impulse and momentum change are the same quantity. So a result of 20 newton-seconds of impulse is identical to a 20 kilogram-metre-per-second change in momentum.