{"id":707,"date":"2026-08-04T21:53:37","date_gmt":"2026-08-04T21:53:37","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=707"},"modified":"2026-08-24T13:03:52","modified_gmt":"2026-08-24T13:03:52","slug":"impulse-formula","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/impulse-formula\/","title":{"rendered":"Impulse Formula (J = F\u0394t): How to Calculate Impulse"},"content":{"rendered":"\n
Definition<\/div>

\nThe impulse formula is J = F \u0394t: impulse equals the average force acting on an object multiplied by the time interval over which that force acts. Because force is the rate of change of momentum, the same impulse also equals the momentum change, J = \u0394p = mv – mu. Impulse is a vector measured in newton-seconds (N\u00b7s).\n<\/p><\/div>\n\n

Drop your phone on a tiled floor and it shatters. Drop it on a thick rug from the same height and it survives. The phone hits the ground with exactly the same momentum both times \u2014 so the change in momentum, and therefore the impulse, is identical.<\/p>\n\n

What changes is how long the stop takes. The rug stretches that stop over maybe ten times longer, and the force collapses by the same factor. That single trade-off is what the impulse formula lets you put a number on.<\/p>\n\n

What Is the Impulse Formula?<\/h2>\n\n

The impulse formula is J = F \u0394t, where F is the average force in newtons and \u0394t is the contact time in seconds. Multiply the two and you get impulse in newton-seconds.<\/p>\n\n

There is a second version of the same equation, and you will use it just as often. Since a force acting for a time is exactly what changes an object’s momentum, impulse can also be worked out from mass and velocity alone: J = mv – mu.<\/p>\n\n

Which version you reach for depends entirely on what the question hands you. Force and a time? Use F \u0394t.<\/p>\n\n

Mass and two velocities? Use the momentum difference. Both routes give the same number in the same units.<\/p>\n\n

One detail that trips people up in the first line of their working: impulse is a vector<\/strong>. It points in the direction of the force, and in one-dimensional problems that means it carries a sign.<\/p>\n\n

The Impulse Formula and Every Rearrangement You Need<\/h2>\n\n

Here are the two forms of the impulse equation, followed by every rearrangement an exam or a lab report will ask for.<\/p>\n\n

J = F \u0394t<\/div>\n\n
J = \u0394p = mv – mu<\/div>\n\n

Every symbol, with its SI unit:<\/p>\n\n

\n\n\n\n\n\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\nNotes<\/th>\n<\/tr>\n<\/thead>\n
J<\/strong><\/td>\nImpulse<\/td>\nnewton-second (N\u00b7s)<\/td>\nVector. Some textbooks write it as I or \u0394p.<\/td>\n<\/tr>\n
F<\/strong><\/td>\nAverage resultant force<\/td>\nnewton (N)<\/td>\nThe time-average, not the peak value.<\/td>\n<\/tr>\n
\u0394t<\/strong><\/td>\nTime interval<\/td>\nsecond (s)<\/td>\nConvert milliseconds first: 5 ms = 0.005 s.<\/td>\n<\/tr>\n
m<\/strong><\/td>\nMass<\/td>\nkilogram (kg)<\/td>\nAssumed constant during the interaction.<\/td>\n<\/tr>\n
u, v<\/strong><\/td>\nInitial and final velocity<\/td>\nmetre per second (m\/s)<\/td>\nSigned. A rebound flips the sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Rearranging for force or time<\/h3>\n\n