Impulse Calculator: J = F·Δt and J = m·Δv
Solve impulse from force and time, or from a change in momentum, m(v2 − v1). Solve any missing value, with each step shown. Free and private in your browser.
Impulse is a force applied for a time: J = F × Δt. Leave one field empty to solve for it.
Fill in all but one field: the empty field is the one you solve for.
About the Impulse Calculator
The Impulse Calculator works with impulse in two ways, chosen by a mode switch. Force and time solves J = F × Δt, and Momentum change solves J = m(v₂ − v₁). In each mode you fill in all but one field and the empty one appears as you type, together with the formula in standard notation, the solved symbol highlighted and a one-line substitution such as 50 N × 0.2 s = 10 N·s.
Impulse is the effect of a force acting over a period of time, and it is equal to the change in an object's momentum. Hitting a ball with a bat, catching an egg, and a car crumpling in a collision are all about impulse. A small force acting for a long time can deliver the same impulse as a large force acting for a short time, which is why airbags and crumple zones save lives.
How to use the impulse calculator
Steps
- Pick a mode. Force and time has Impulse, Force and Time fields. Momentum change has Impulse, Mass, Initial velocity and Final velocity fields.
- Fill in all fields except the one you want to find.
- Choose units. Impulse offers N·s, kN·s, kg·m/s and lbf·s, force offers N, kN and lbf, time offers s, ms, min and h, mass offers kg, g and lb, and velocity offers m/s, km/h, mph, ft/s and knots.
- Read the answer under the formula.
Time and mass must be greater than zero. Force, velocity and impulse can be negative. Each mode remembers its own values, so you can switch back and forth without retyping.
Formulas
Because 1 N·s equals 1 kg·m/s, the two modes give the same unit and the same number whenever they describe the same event.
Worked examples
Example 1: impulse from force and time
A 50 N force acts for 0.2 s. The impulse is J = 50 × 0.2 = 10 N·s.
Example 2: force from impulse
An impulse of 10 N·s is delivered in 0.5 s. The average force is F = 10 ÷ 0.5 = 20 N.
Example 3: impulse from a velocity change
A 2 kg object speeds up from 3 m/s to 8 m/s. Then J = 2 × (8 − 3) = 10 kg·m/s. Check it against force and time: 20 N for 0.5 s also gives 10 N·s.
Example 4: slowing down
The same 2 kg object slows from 8 m/s to 3 m/s. The impulse is J = 2 × (3 − 8) = −10 kg·m/s. The negative sign means the impulse points against the original motion.
Tips
- A velocity change to zero is common: a 1,000 kg car stopping from 20 m/s has J = −20,000 N·s.
- Spreading the same impulse over a longer time lowers the average force, so stopping over 0.5 s needs one fifth of the force of stopping over 0.1 s.
- If the velocities are equal, the impulse is zero and the mass cannot be found from the impulse, so the calculator reports that.
For the related quantity momentum itself, use the Momentum Calculator, and the Force Calculator when you know mass and acceleration instead.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
The Impulse-Momentum Calculator opens directly on the momentum-change mode, and the Momentum Converter changes between kg·m/s, N·s and other units.
Frequently asked questions
What is impulse?
Impulse is the effect of a force acting over time. It equals force times time, J = F × Δt, and it equals the change in momentum of the object.
What are the two modes?
Force and time solves J = F × Δt. Momentum change solves J = m(v₂ − v₁). Switch between them with the mode buttons, and each mode keeps the values you typed.
How do I calculate impulse?
In Force and time, enter the force and the time and leave impulse empty. A 50 N force for 0.2 s gives 10 N·s. In Momentum change, enter the mass and both velocities.
How do I find the average force of an impact?
Work out the impulse from the change in momentum, then divide by the contact time. A 0.5 kg ball changing velocity by −18 m/s has J = −9 kg·m/s, and over 0.01 s the average force is −900 N.
Is a newton-second the same as kg·m/s?
Yes. 1 N·s equals 1 kg·m/s, so the two modes give the same number for the same event. The impulse unit can be N·s, kN·s, kg·m/s or lbf·s.
Why does the calculator say it cannot divide by zero?
If you solve for mass and the initial and final velocities are equal, the velocity change is zero. Impulse would then be zero for every mass, so the mass cannot be found.
Does this page upload my values?
No. The force, time and impulse you enter are calculated locally in your browser, and nothing is uploaded, stored or shared with a server, so your own figures stay on your device.