Compute impulse (change in momentum) and related 1D values from the numbers your problem gives, with clear SI units and a negative-sign means direction, not mistake reminder.
Advanced options
How to use our Impulse and Momentum Calculator
- In "What do you know?", pick the option that matches your problem statement (momenta, mass and velocities, force and time, or a solve-for option).
- In "Positive direction note (text)", choose which direction is positive (example: right = +, left = -), and use that same choice for every input sign.
- Set "Number display" to Auto (recommended). Switch to Plain or Scientific only if your class requires a specific format.
- If you chose a momentum option, enter "Initial momentum (kg*m/s)" and "Final momentum (kg*m/s)". Use a minus sign if the momentum points opposite your positive direction.
- If you chose a mass and velocity option, enter "Mass (kg)" (must be greater than 0), plus "Initial velocity (m/s)" and "Final velocity (m/s)" with signs. The calculator will compute the matching momenta and impulse.
- If you chose a force and time option, enter "Average net force (N)" (sign shows direction) and "Time interval (s)" (must be greater than 0). Add "Mass (kg)" if you also want the velocity change.
- Optional: in Advanced options, change "Impulse unit to display" to show impulse as N*s or as kg*m/s (same size in SI).
- Click "Calculate" and read "Notes / warnings" if it appears.
- Sanity-check: "Impulse J (change in momentum)" and "Change in momentum (p_final - p_initial)" should match in both value and sign because they are the same physical change.
Definitions
Momentum (p): Mass times velocity in 1D: p = m*v. The sign (+ or -) tells direction. [1]
Impulse (J): The net push over a time interval. In 1D, impulse equals the change in momentum. [1]
Change in momentum (delta_p): delta_p = p_final - p_initial. This equals impulse (same physical quantity). [1]
Average net force (F_avg): The overall (net) force averaged across the time interval. Its sign tells direction. [1]
Time interval (delta_t): How long the interaction lasts, in seconds. It must be greater than 0 as a duration.
Sign (positive/negative): In this 1D calculator, negative usually means the quantity points opposite your chosen positive direction, not that the math failed. [2]
Common mistakes and quick fixes
Mistake: Treating negative answers as errors (for example, entering speeds but forgetting direction).
Fix: Check What do you know? and then recalculate. In 1D, the sign is direction. If the motion/force is opposite your chosen positive direction, the value should be negative.
Mistake: Mixing up seconds and milliseconds in "Time interval (s)" (example: typing 250 instead of 0.250 for 250 ms).
Fix: Convert your time to seconds before entering it (ms to s: divide by 1000).
Mistake: Expecting "Velocity change (v_final - v_initial)" to work with "Mass (kg)" left blank or set to 0.
Fix: Enter a mass greater than 0. Without mass, the calculator cannot use delta_v = J/m.
Mistake: Entering a force value that is not an average (like a peak force from a graph) into "Average net force (N)".
Fix: Use the average net force over the same time interval. If you have a force vs. time graph, you need the average over that interval, not the maximum.
Mistake: Getting a negative "Time interval" result and thinking the calculator is wrong.
Fix: A duration cannot be negative. If computed time is negative, your impulse sign and force sign disagree. Re-check your chosen positive direction and your input signs.
Mistake: Thinking "Impulse unit to display" changes the physics or the calculation.
Fix: It only changes the unit label shown for impulse. The number stays the same because 1 N*s equals 1 kg*m/s in SI.
Limitations & Key Assumptions / Boundary Conditions
1D only: direction is handled with a plus or minus sign, not full 2D/3D vectors.
Units are exactly as labeled (kg, m/s, N, s). Convert before entering values if your problem uses g, cm/s, km/h, or ms.
The force-time method uses J = F_avg * delta_t, which assumes a single average net force represents the interval well. If force changes over time, you must use the correct average for that interval (often related to area under a force-time graph).
Any calculation that uses mass requires mass greater than 0 (for p = m*v and delta_v = J/m). If mass is 0 or negative, those results are undefined.
Any calculation that uses time as a duration requires time interval greater than 0 (for J = F_avg * delta_t and F_avg = J/delta_t). Time = 0 causes division by zero or a non-physical interval.
Solving delta_t = J / F_avg can produce a negative number if J and F_avg have opposite signs. The math is consistent, but a negative duration means your sign directions are inconsistent, so fix the input signs.
Results are for average net force and do not model details like changing force during impact, rotation, or energy losses. Real situations can differ even when momentum math is correct.
Methodology
The calculator uses 1D sign (plus/minus) and chooses equations based on "What do you know?" It reads only the inputs needed for that mode.
p = m * v
J = delta_p = p_f - p_i
J = F_avg * delta_t
delta_v = J / m
F_avg = J / delta_t
delta_t = J / F_avg
Core idea: impulse equals change in momentum (impulse-momentum theorem). [1]
Unit note: impulse can be shown as N*s or kg*m/s. They are equivalent in SI (a newton is kg*m/s^2, so N*s becomes kg*m/s). [1]
Sign handling: negative results are allowed. A negative impulse, momentum change, velocity change, or average force means the direction is opposite your chosen positive direction. [2]
Worked mini-example (momenta): Suppose p_initial = 12 kg*m/s and p_final = -3 kg*m/s.
delta_p = p_f - p_i = (-3) - (12) = -15 kg*m/s
J = delta_p = -15 N*s
Interpretation: the net effect (impulse) points in the negative direction you chose.
Error and boundary handling used in the math: the calculator stops and shows an error if a needed mass is not greater than 0, if a needed time interval is not greater than 0, or if a solve would divide by zero (for example, solving time with F_avg = 0).