Car Crash Impulse Calculator

Related Calculators

Impulse: The push over time during the crash. In physics, impulse equals the change in momentum.[3][2]

Momentum: The amount of motion an object has, found from mass times velocity. A heavier or faster car has more momentum.[2]

Signed velocity: Velocity with a plus or minus sign to show direction in 1D motion. Positive and negative do not mean good or bad; they only show direction.

Change in velocity (delta_v): Final velocity minus initial velocity. This signed change is what the calculator uses to find impulse for one car.

Average force: A single force value that would produce the same impulse over the same crash time. It is not the exact force at every instant of the crash.[3]

Perfectly inelastic stick-together crash: A collision model where the two cars move together after impact, so one shared final velocity is found from momentum conservation.[1]

Magnitude: The size of a quantity without its sign. For example, impulse magnitude ignores direction.

Mistake: Entering a negative Car 1 initial speed (m/s) while Direction rule (1D) is set to Positive is the car's initial forward direction .
Fix: Either enter the forward speed as a positive number or switch Direction rule (1D) to I will enter + or - speeds myself .

Mistake: Leaving Car 1 final speed (m/s) blank after choosing Custom final speed in Car 1 final outcome .
Fix: Enter the final signed speed you want the calculator to use, or change Car 1 final outcome back to Stops or Rebounds .

Mistake: Typing a Rebound fraction (0 to 1) greater than 1 or less than 0.
Fix: Keep Rebound fraction (0 to 1) between 0 and 1, where 0 means stop and 1 means the same speed back in the opposite direction.

Mistake: Using 0 or a negative value for Crash time (s) and expecting Average force during crash (from impulse and time) to work.
Fix: Enter a positive Crash time (s) because force is found by dividing impulse by time.

Mistake: Mixing units by entering mph into Car 1 initial speed (m/s) or Car 2 initial speed (m/s) without changing the unit setting.
Fix: In Advanced options , set Speed unit for inputs (selected unit) to mph or km/h before you type those speeds.

Mistake: Thinking Impulse on car 1 (signed) and Impulse on car 1 (magnitude) should always match exactly.
Fix: Use the signed output for direction and the magnitude output for size only. A negative signed impulse is normal when the impulse points in the negative direction.

• This calculator uses straight-line 1D motion only. Real crashes happen in 2D or 3D, with rotation, sliding, and changing contact directions.
• Average force is a simplified value over the crash time. Real crash forces usually rise and fall quickly instead of staying constant.
• Single-car speed mode assumes constant mass and uses the entered initial and final velocities directly.
• The two-car mode assumes a perfectly inelastic collision, meaning the cars stick together after impact and external impulses during the short crash are negligible.
• Direction signs depend on your chosen Direction rule (1D). A negative result means the quantity points in the negative direction, not that the answer is wrong.
• Optional occupant outputs are rough learning estimates only. They do not model airbags, seatbelts, body motion, crush zones, or peak force.
• If you use Optional: stopping distance for occupant (m), the distance-based deceleration estimate assumes constant deceleration and a straight stopping path.
• Unit conversions help with entry and display, but the main physics is still done in SI units, so entering the wrong unit choice will change the result.

Core idea

Impulse is the change in momentum, so the calculator uses the same number for impulse in N*s and momentum change in kg*m/s.[2][2]

J = Delta_p = m*(v_final - v_initial)

For time-based modes, the calculator connects impulse and average force over the crash time.[2][3]

J = F_avg*Delta_t

F_avg = J/Delta_t

How signed velocity is handled

The calculator keeps direction with plus and minus signs. It first converts any entered speed to m/s, then applies your chosen direction rule. In single-car mode, Car 1 change in velocity (delta_v) is final minus initial, so a car that stops from a positive speed gets a negative delta_v.

delta_v = v_final - v_initial

impulse_on_car_1 = m1*delta_v

If you choose Stops, the calculator sets final velocity to 0. If you choose Rebounds, it flips the direction and uses the entered rebound fraction times the initial speed magnitude. If you choose Custom final speed, it uses your entered final signed speed.

Two-car stick-together mode

For the perfectly inelastic two-car mode, the calculator finds one shared final velocity from momentum conservation during the short collision.[3]

v_final = (m1*v1_initial + m2*v2_initial)/(m1 + m2)

Then it computes the impulse on each car from that car's own mass and change in velocity.

J1 = m1*(v_final - v1_initial)

J2 = m2*(v_final - v2_initial)

Average force and equivalent momentum change

When crash time is available, average force is impulse divided by time. The calculator also shows Change in momentum (same number as impulse) because 1 N*s equals 1 kg*m/s by unit definition.

F_avg = J/Delta_t

1 N*s = 1 kg*m/s

Optional occupant estimates

If you enter Optional: occupant mass (kg) and a valid Crash time (s), the calculator estimates average deceleration from the same signed change in velocity over time, then converts its size to g using standard gravity 9.80665 m/s^2.

a_avg = delta_v/Delta_t

g_load = |a_avg|/9.80665

If you also enter Optional: stopping distance for occupant (m), the calculator can estimate deceleration size from stopping distance with a constant-deceleration model.

|a| = v^2/(2*d)

Mini example

Suppose Car 1 mass (kg) is 1500, Car 1 initial speed (m/s) is 20, Car 1 final outcome is stops, and Crash time (s) is 0.10. Then final velocity is 0, so delta_v = 0 - 20 = -20 m/s. Impulse is 1500*(-20) = -30000 N*s, and average force is -30000/0.10 = -300000 N. The negative sign means the impulse and average force point opposite the chosen positive direction.

Error handling and assumptions used

The calculator blocks impossible entries such as nonpositive mass, nonpositive crash time in divide-by-time steps, rebound fraction outside 0 to 1, or a blank custom final speed when that option is selected. It also ignores hidden inputs for modes where they do not apply. Results can differ from real crashes because actual forces vary over time, cars deform, and occupants do not move exactly like rigid objects.[3]