Impulse Calculator
Impulse from force and time or from mass and velocity change, with peak force as well as average, deceleration in g, and an animated impact beside a force–time curve whose area is the impulse.
Impulse from force and time or from mass and velocity change, with peak force as well as average, deceleration in g, and an animated impact beside a force–time curve whose area is the impulse.
What most real collisions look like — force builds, peaks, and falls away The area under every shape is the same impulse — only the peak differs.
The same impulse, delivered gently
Impulse–momentum theorem
J = F·Δt = m·Δv = Δp
Impulse -70.00 N·s — a velocity change of -14 m/s
J = F·Δt = m·Δv = Δp. The change in momentum is fixed by the collision; the time over which it happens is the only negotiable part, and the force is whatever falls out of that choice.
That is the whole principle behind crumple zones, airbags, helmets and bending your knees on landing — stretch Δt, and the force drops in exact proportion.
Peak force -733.04 N — 1.57× the -466.67 N average
No real impact delivers a constant force. For a half-sine the peak is 1.571 times the average, and the peak is what a structure actually has to survive. Sizing anything from the average alone under-specifies it by 57%.
Design to the peak; reason with the impulse. They answer different questions and mixing them is how components end up under-rated.
Double the contact time and the peak drops to -366.52 N
Force and time trade off exactly, because their product is the impulse and the impulse is fixed. 150.00 ms → 300.00 ms halves every force in the problem and changes the momentum not at all.
When peak force is the problem, extending the contact is almost always easier than reducing the momentum.
That is 9.5 g of deceleration
-14 m/s shed in 150.00 ms. Impact severity is usually quoted in g rather than newtons because it is mass-independent — and this is a mild deceleration, comparable to hard braking or a heavy footfall.
Momentum and energy do not scale the same way
Impulse goes as Δv, kinetic energy as v². Here the energy went from 490.00 J to 0.00 nJ. Halve the speed and you halve the impulse — but you quarter the energy. That is why a small increase in impact speed is so much worse than it sounds, and why stopping distance grows faster than speed does.
What the model leaves out
One dimension, a single clean contact, and a force profile chosen from three idealised shapes — this one is a half-sine (typical impact). A real impact's force curve is measured, not assumed: it depends on the materials, the geometry and how they deform, and it can be wildly asymmetric. Use this to size and to reason, not to certify.
Worked out in your browser — nothing is sent anywhere.
Save this result, change your inputs, and recalculate to compare scenarios side by side.
Find the average force in a collision from the momentum change and duration.
See how extending stopping time reduces peak force for the same impact.
Work between impulse, force, time and momentum change.
Compare total impulse from sustained low thrust against a short high-thrust burn.
The change in momentum is fixed by the blow, but stretching the contact time cuts the peak force. Boxers moving away from an impact, and judo breakfalls, are both applying this deliberately.
Work out how many milliseconds of crumple the packaging must provide to keep the force below what a shell survives — then design the padding to deliver it.
Force multiplied by the time it acts, measured in newton seconds. Impulse equals the change in momentum an object experiences, which is why the two share units. A small force over a long time can produce exactly the same momentum change as a large force applied briefly — and that equivalence is the basis of most impact protection.
In a crash the momentum change is fixed: the occupant must go from travelling to stationary. Impulse says force times time equals that fixed change, so extending the time reduces the peak force. An airbag lengthens the stop from milliseconds to tens of milliseconds, cutting the force by roughly the same factor. Crumple zones do the same by deforming progressively rather than stopping rigidly.
To extend the stopping time. Landing stiff-legged brings you to rest in perhaps 50 milliseconds; bending the knees stretches it to 300 or more, cutting the peak force by a factor of six. The same principle governs catching a cricket ball with hands moving backwards, gymnasts rolling on landing, and the padding under playground equipment.
They are the same quantity viewed differently: impulse is what you apply, momentum change is what results. The impulse-momentum theorem states FΔt = mΔv. Rearranged for force, it shows why the duration of an interaction matters as much as its magnitude — a point that force alone never reveals.
It is the area under the force–time curve — J = ∫F dt. That is what the shaded region in the plot on this page is: not an illustration of the impulse but the impulse itself. The average-force rectangle drawn over it encloses exactly the same area, which is what "average force" means. Change the shape of the curve and the area stays put while the peak moves, which is the whole reason the shape matters.
Yes. Rocket engines are rated by specific impulse — impulse per unit of propellant — because what matters is total momentum imparted, not instantaneous thrust. A low-thrust ion engine firing for months can deliver more total impulse than a chemical rocket burning for minutes, which is why deep-space missions use them despite their feeble push.
Average force is the impulse divided by the contact time — a single number that would produce the same momentum change if it acted steadily. Peak force is the largest force at any instant, and it is what actually breaks things. No real impact delivers a constant force, so the two are never equal: design to the peak, reason with the impulse, and never size a component from the average alone.
It depends entirely on the shape of the force–time curve. A half-sine, which is what most real impacts resemble, peaks at π/2 — about 1.57 — times the average. A triangular pulse from a sharp, hard strike peaks at exactly twice the average. Only the textbook rectangular idealisation has a peak equal to its average, and nothing in the physical world does that. Working from the average alone under-specifies by 57% to 100%.
Impact severity is usually quoted in g rather than newtons because it does not depend on mass. Everyday activity produces a few g; a well-restrained car occupant can survive a brief 30 to 50 g; sustained exposure above roughly 50 g makes serious injury likely. The figure follows directly from Δv and Δt, which is why extending the contact time is the single most effective safety measure available.
Because impulse and energy scale differently. Impulse goes as Δv, so doubling the speed doubles the momentum that has to be absorbed. Kinetic energy goes as v², so doubling the speed quadruples it. The structure has to shed both, and the energy term is what grows fastest — which is also why stopping distance grows faster than speed does.