Impulse and Momentum Calculator — J = FΔt = mΔv
The impulse-momentum theorem links force, time, mass and velocity change: J = F × Δt = m × (vf − vi). Select what you want to solve for, enter the known values, and get the missing quantity with a vector breakdown.
Solve for
kg
m/s
m/s
N
s
J = F × Δt = m × (vf − vi) — change in momentum
- 1
Impulse = Force × contact time
10 × 1 = 10
How does this calculator work?
Impulse J = F × Δt = m × (vf − vi). Given any three of force, time, mass and velocities you can solve for the fourth. The impulse equals the change in momentum — both in units of N·s or kg·m/s. Select what to solve for and enter the known values.
Formula
How this is calculated
Impulse (J, in N·s) is the product of the average net force acting on an object and the duration of that force: J = F × Δt. By Newton's second law (F = ma = m·Δv/Δt), this is identical to the change in momentum J = m·(vf − vi). This equality is the impulse-momentum theorem.
The calculator solves the theorem for the selected unknown. In all modes, mass and initial velocity are used to compute initial momentum; initial plus impulse gives final momentum, from which final velocity is derived. Inputs that are not needed for a particular mode are shown but ignored in the computation — you can still fill them in for reference.
All quantities are in SI units. The vector diagram represents one-dimensional motion: the initial momentum vector plus the impulse vector equals the final momentum vector. Real collisions involve rapidly varying forces; the force field therefore represents the average force over the contact interval, not an instantaneous value.
Frequently asked questions
The theorem states that the impulse applied to an object (force × time) equals its change in momentum (mass × change in velocity): J = F·Δt = m·Δv. It is derived directly from Newton's second law integrated over the contact time.
Impulse is measured in N·s (newton-seconds), which are equivalent to kg·m/s — the same units as momentum. This equivalence is the physical content of the theorem: impulse and momentum change are the same thing.
They extend the contact time Δt. Since J = F × Δt and the total impulse (momentum change) is fixed by the crash speed, a longer contact time means a smaller average force on the occupant — reducing injury. A brick wall stops you in milliseconds; a crumple zone spreads that over tenths of a second.
Also known as
TG we-Calculate Editorial Team. (2026). Impulse and Momentum Calculator — J = FΔt = mΔv [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/impulse-and-momentum-calculator
TG we-Calculate Editorial Team. "Impulse and Momentum Calculator — J = FΔt = mΔv." TG we-Calculate. 2026. https://we-calculate.com/calculator/impulse-and-momentum-calculator.
TG we-Calculate Editorial Team, "Impulse and Momentum Calculator — J = FΔt = mΔv," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/impulse-and-momentum-calculator
@misc{wecalculate_impulse_and_momentum_calculator, title = {Impulse and Momentum Calculator — J = FΔt = mΔv}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/impulse-and-momentum-calculator}}, year = {2026}, note = {TG we-Calculate} }
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