What is the impulse-momentum theorem?
J = Δp = mΔv. The impulse delivered to an object equals its change in momentum.
Impulse Calculator
J = F Δt
Calculate impulse from force and time interval. J = FΔt = Δp — impulse equals change in momentum.
Calculate
Enter values above to calculate
How it calculates
1
Read force F in N and time Δt in seconds
2
Multiply: J = F × Δt
3
Result in N·s = kg·m/s
Formula
J = F Δt
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| J | Impulse | N·s = kg·m/s |
| F | Average force | N |
| Δt | Duration of force | s |
| Δp | Change in momentum | kg·m/s |
How to Use This Calculator
This impulse calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula J = F Δt is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A 500 N force acts for 0.02 s (a bat hitting a ball). Find impulse.
Step 1: J = F × Δt
Step 2: J = 500 × 0.02
Answer: J = 10 N·s
Common Mistakes
- Impulse = Δp — it equals the change in momentum, not the final momentum
- A small force over a long time gives the same impulse as a large force over a short time
- Units N·s and kg·m/s are identical
Related
Frequently Asked Questions
Why do airbags reduce injury?
Airbags increase Δt, so for the same Δp (stopping the occupant), the average force F = Δp/Δt is much smaller.