Impulse Calculator
Impulse from force and time, or from the momentum change it produces — J = FΔt = Δp.
What is Impulse?
Impulse is force applied over a time, J = FΔt, and the second law says that equals the momentum change it produces, J = Δp. The two forms are the same quantity in units of the same size — one newton-second is one kilogram-metre per second — which is why the page offers both and why the momentum page is its mirror. Impulse is also why airbags work: the same momentum change spread over a longer time needs a smaller force.
How it works
The force-time tab computes J = FΔt and, if you add a mass, divides by it for the velocity change Δv = J ÷ m — the number a crash or kick question actually asks for. The momentum-change tab takes m and Δv and multiplies. Velocities and forces are signed, so a stopping force is negative and the arithmetic keeps the direction. The working shows which definition was used and states the N·s = kg·m/s equivalence underneath the answer.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is the difference between impulse and momentum?
Momentum is a state — what an object has at an instant, p = mv. Impulse is a process — what a force over a time does to that state, J = FΔt = Δp. The impulse page computes the change; the momentum page computes the state and the collisions.
Why does an airbag reduce injury if the momentum change is the same?
Because the change is fixed by the crash, but the force is not: J = FΔt with J fixed means a larger Δt buys a smaller F. The bag stretches the stopping time from milliseconds to a tenth of a second and the peak force falls by the same factor.
Can impulse be negative?
Yes — a negative impulse means the force opposed the motion, taking momentum away rather than adding it. A catcher's mitt delivers a negative impulse to the ball it stops. The signed fields keep the direction in the arithmetic.