Calculators
Impulse Calculator
Solve impulse, average force, or time with J = FΔt.
Calculate impulse, average force, or interaction time using J = FΔt. For a constant or average net force, impulse equals the change in momentum.
Impulse
100 Ns
J = FΔt
A negative result represents direction relative to your chosen positive axis. The simple product J = FΔt uses a constant force or the average net force over the interval; a varying force generally requires the area under a force–time curve.
About This Tool
Impulse measures the effect of a force acting over a time interval. For a constant force, or when F represents the average net force, impulse is J = FΔt. The impulse–momentum theorem also states J = Δp, so the same quantity describes the change in an object's momentum.
How To Use It
- Choose whether to solve for impulse, average force, or time.
- Enter the two known values and select their units.
- Use signs consistently if direction matters; choose one axis direction as positive.
- Read the result and interpret impulse as change in momentum when the entered force is the net force over the interval.
Examples
Constant force
A 50 N net force acting for 2 s produces 100 N·s of impulse.
Short impact
A 2 kN average force acting for 50 ms produces 100 N·s of impulse.
Average force
An impulse of 100 N·s delivered over 0.5 s corresponds to an average force of 200 N.
Direction
A −20 N average force acting for 0.5 s gives −10 N·s, indicating impulse in the negative axis direction.
Useful Notes
Impulse formula
For constant force, J = FΔt. If force varies with time, the exact impulse is the integral of force over time; the product formula remains valid when F is the average net force over the interval.
Impulse and momentum
The impulse–momentum theorem is J = Δp = pfinal − pinitial. One newton-second is dimensionally equal to one kilogram-meter per second, so impulse and momentum change use equivalent SI dimensions.
Signs and direction
Impulse is a vector quantity. In a one-dimensional calculation, positive and negative signs indicate direction relative to the axis you choose. Time itself cannot be negative.
Average force during impacts
Collision forces often change rapidly. If only total impulse and impact duration are known, J/Δt gives average net force, not the instantaneous peak force.
Model scope
This calculator solves a one-dimensional force–time relationship. It does not reconstruct a varying force curve, determine peak impact force, or automatically include other forces unless the entered force already represents the net force.
FAQ
Is N·s the same as kg·m/s?
Yes dimensionally. N·s is the standard impulse unit, while kg·m/s is commonly used for momentum; the impulse–momentum theorem connects them directly.
Can impulse be negative?
Yes. A negative sign indicates direction relative to the positive axis you selected; it does not mean the physical quantity is invalid.
Does this calculate peak collision force?
No. Dividing impulse by impact duration gives average net force. Peak force requires information about how force changes during the impact.
What if force changes during the interval?
Use the average net force if it is known. Otherwise exact impulse requires integrating the force–time curve rather than multiplying one instantaneous force value by time.
How is impulse related to velocity?
Impulse gives change in momentum. For constant mass, Δp = m(vfinal − vinitial), but this tool focuses on the force–time form so it does not assume a mass or velocity change.
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