Impulse connects force and momentum: it is the push (force × time) that changes how fast something is moving. Engineers, physics students, and anyone curious about crash safety use it to see why a longer collision time means a gentler force.
How the Impulse Calculator works
The calculator implements the impulse-momentum theorem, J = FΔt = Δp = m(v₂ − v₁). In Force × Time mode, it multiplies your force by the contact time you enter. In Momentum Change mode, it multiplies mass by the velocity change and treats that as the impulse. Either way, dividing the impulse by the contact time gives the average force — the constant force that would produce the same effect as the real, often-varying force during a collision.
Inputs and what they mean
Force × Time mode needs the applied force in newtons and the contact time Δt in seconds. Momentum Change mode needs mass in kilograms plus the initial and final velocity in m/s — the calculator subtracts v₁ from v₂ to get the velocity change. Both modes share a single Δt field, since average force always needs a time interval to divide by, even when the impulse itself came from a momentum calculation. Contact time has the biggest leverage on average force: doubling Δt halves F_avg for the same impulse.
Limits and edge cases
The formulas assume a well-defined start and end to the interaction — real collisions often have a force that spikes and fades rather than staying constant, so the average force here is exactly that: an average, not a peak. Contact time (Δt) cannot be zero or negative, since average force is undefined at zero duration; the calculator shows an idle result rather than a divide-by-zero error in that case. For rotational impacts (torque, angular momentum) or multi-body collisions, this single-axis linear model does not apply — those need a full angular-momentum or multi-body treatment.