Impulse Calculator (J = Ft)
Solve J = Ft for impulse, force, or time. Enter any two values and get the third instantly, with unit-labeled step-by-step working shown below.
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The impulse formula
Impulse measures how much a force changes an object's motion when applied over time:
- J — impulse, in newton-seconds (N·s)
- F — force applied, in newtons (N)
- t — time the force acts, in seconds (s) — always positive
Enter any two values and leave the third blank to solve for it.
Worked example
A 20 N force acts on an object for 3 seconds. What is the impulse?
- Formula: J = Ft
- Substitute: J = 20 × 3
- Result: J = 60 N·s
Solving in reverse
- Force: F = J / t — enter J and t, leave F blank. Example: J = 60 N·s over t = 3 s gives F = 20 N.
- Time: t = J / F — enter J and F, leave t blank. Example: J = 60 N·s with F = 20 N gives t = 3 s.
Tip: Impulse explains why airbags, crumple zones, and padded flooring reduce injury: stretching the collision time (t) over a longer interval lowers the peak force (F) needed to deliver the same impulse.
Common mix-ups
- Confusing impulse with force. Force is instantaneous; impulse accumulates force over a time interval — different units (N vs. N·s) reflect this.
- Forgetting time must be positive. A negative or zero time interval has no physical meaning here.
- Skipping the connection to momentum. Impulse isn't just an abstract product — it equals the change in momentum an object experiences (see the impulse–momentum theorem below).
Where this shows up
Impulse explains collision safety design (airbags, seatbelts, crumple zones), sports (following through on a swing extends contact time and increases impulse transferred to the ball), and rocket thrust calculations. It connects directly to momentum and the impulse–momentum theorem, which restates J = Ft as FΔt = mΔv.
Frequently asked questions
- What is the formula for impulse?
- Impulse is J = Ft, where J is impulse in newton-seconds (N·s), F is the force applied in newtons (N), and t is the time over which it acts, in seconds (s).
- How do I find the time if I know impulse and force?
- Rearrange the formula to t = J / F. Enter impulse and force and leave time blank, and the calculator solves it for you.
- Can impulse be negative?
- Yes. A negative force (pushing in the opposite direction) produces a negative impulse. Time must stay positive, since a negative duration isn't physical.
- What is the difference between impulse and force?
- Force is an instantaneous quantity (newtons); impulse is force accumulated over an interval of time (newton-seconds). The same force applied for longer produces more impulse.
- How does impulse relate to momentum?
- Impulse equals the change in an object's momentum — this is the impulse–momentum theorem, J = Δp. See the impulse–momentum calculator to work with mass and velocity change directly instead of force and time.
- Why do airbags and padded landings reduce injury?
- They stretch out the time over which a collision's impulse is delivered. Since impulse (J = Ft) is fixed by the change in momentum, increasing t lowers the peak force F needed to produce that same impulse, reducing injury.