Impulse From A Graph
An impulse from a force time graph is the area under the force curve. It shows how much momentum changes during contact, push, pull, impact, or thrust. A tall force over a short time can match a smaller force over a longer time. The calculator accepts ordered data points and estimates the area between each pair.
Why Graph Area Matters
Real force readings are rarely constant. Sensors often show rising edges, peaks, drops, and negative rebound. A single average force hides these details. Segment integration keeps more of the graph shape. The trapezoidal rule is best for sampled lab data, because it joins adjacent points with straight lines. Left and right rules are included for comparison. Absolute area can be useful when total force activity matters, but signed area is better for net momentum change.
Practical Inputs
Enter time and force pairs, one pair per line. Use commas or spaces. Choose the time unit and force unit before calculating. The page converts values to seconds and newtons. A baseline field removes sensor offset. For example, if a force plate reads 2 N while unloaded, enter 2 as the baseline. Optional mass and initial velocity convert impulse into velocity change.
Interpreting Results
Impulse is reported in newton seconds and in your selected output unit. Since one newton second equals one kilogram meter per second, the value is also momentum change. Average force is found by dividing impulse by total time. Peak force is the largest adjusted force magnitude in the data. Segment details show how every interval contributes to the answer.
Use In Physics Work
This calculator helps with collisions, jumps, bat swings, rocket thrust pulses, braking tests, and laboratory force sensors. Better results need more points near sharp peaks. Check that time always increases. Use signed area when direction matters. Use consistent units. Compare the graph with the segment table before reporting a final value.
Reporting Tips
State the integration method, units, baseline, and whether signed or absolute area was used. Include a small data table with the result. Mention sensor sampling limits. Round values only after calculation. For formal reports, download the CSV file for audit details and the PDF summary for a clean attachment.