How hard was that pull, in numbers? Enter three of the four quantities of straight-line motion and read the fourth, with the rate in m/s2, ft/s2 and g, and the distance alongside it.
Acceleration Formula Calculator - a = (v - v0) / t
How hard was that pull, in numbers? Enter three of the four quantities of straight-line motion and read the fourth, with the rate in m/s2, ft/s2 and g, and the distance alongside it.
Parameters
Enter data for calculations
💡 Fill in all required fields to unlock the calculate button
A speed change, a clock, and the four numbers that follow
Straight-line motion at a steady rate has exactly four quantities in play: the speed you start at, the speed you end at, how long it takes and how far you travel. Give this calculator any three of them and it returns the fourth, plus the acceleration in m/s², in ft/s² and as a fraction of g. A car going from 0 to 60 mph in 5.4 s comes out at 4.97 m/s², which is 16.30 ft/s² or 0.51 g, and it covers 237.6 ft doing it. Speeds go in as mph, km/h, m/s or ft/s, and the answer leads with whichever unit you chose.
This is the physics definition of acceleration, the rate a speed changes at. If what you actually want is how quickly a specific car gets to 60 from its power and weight, that is a different question with a different tool, linked at the bottom.
Pick the unknown first, then fill the boxes that stay
The form rearranges itself around your choice, so you never see a field the selected mode does not use.
-
1
Choose what you are solving for. Acceleration, final speed, time or distance. This decides which three fields remain below.
-
2
Set the speed unit. Everything you type and everything you read back uses it. US readers usually want mph, a lab report usually wants m/s.
-
3
Enter the starting speed. Pulling away from rest is 0. Braking from a cruise is whatever the speedometer read before you touched the pedal.
-
4
Enter the two remaining knowns. A final speed, a time, or an acceleration with its own unit. A minus sign on the acceleration means slowing down, and the sign has to agree with the direction the speed moves.
-
5
Read the answer and the three tiles under it. Time taken, distance covered and speed gained per second come with every mode, so one calculation fills in the whole picture.
Four modes, and which one your question belongs to
Most questions about motion are one of these four sentences with a different word missing. The right-hand column is the sanity check on your own input before you trust the output.
| Mode | You already know | Typical question | Watch for |
|---|---|---|---|
| Acceleration | both speeds and the time | How hard did that pull actually feel? | a stopwatch that starts late flatters the result |
| Final speed | start speed, acceleration, time | Where do I end up after eight seconds of this? | braking can reach a standstill before the clock runs out |
| Time | both speeds and the acceleration | How many seconds does that merge need? | the sign of the acceleration must match the direction of the change |
| Distance | both speeds and the acceleration | How much road does it eat while that happens? | this is the physics distance, with no reaction time added |
The distance mode is the one people most often mistake for a stopping-distance tool. It answers both directions, so 30 to 60 mph at 2 m/s² gives 443 ft of road used while speeding up, and 56 mph down to a standstill at 8 m/s² gives 128 ft of pure braking. Neither figure includes the second or so you spend reacting before anything happens.
The four relations, written out with real numbers
Everything above comes from two relations and their rearrangements: v = v0 + a × t and v² = v0² + 2 × a × s. Speeds go into both in meters per second, which is why the calculator converts your entry before it does anything else. One mph is 0.44704 m/s exactly, and one km/h is 0.2778 m/s.
Result: 4.97 m/s², 0.51 g, and 237.6 ft of road used.
Result: 4.47 s and 229.4 ft, before any reaction time.
Result: 24 m/s, which is 53.7 mph, after 2,362 ft of track.
Result: -1.01 m/s², a gentle 0.10 g, over 79.2 ft.
Result: 1.8 m/s, 0.12 g of extra push into the floor, over 4.4 ft.
Where this arithmetic usually slips
Reference values, from a train to a launch track
The result places your own figure inside this ladder, so you can see at a glance whether a stopwatch reading is plausible. Everything a road vehicle does, hard braking included, sits in the top five rows.
| Situation | m/s² | ft/s² | g |
|---|---|---|---|
| Train pulling out of a station | 0.75 | 2.46 | 0.08 |
| City bus getting up to speed | 1.20 | 3.94 | 0.12 |
| Family car, relaxed start | 2.00 | 6.56 | 0.20 |
| Sports car, 0 to 60 mph in 5.4 s | 4.97 | 16.30 | 0.51 |
| Hard braking on dry asphalt | 9.00 | 29.53 | 0.92 |
| Free fall at the surface | 9.81 | 32.17 | 1.00 |
| Carrier catapult launch | 35.80 | 117.45 | 3.65 |
| Roller coaster launch, top end | 50.00 | 164.04 | 5.10 |
Loose ends worth naming
Related tools
Temperature Converter
Fahrenheit, Celsius, Kelvin and Rankine at once, for when the conditions around the test matter - See calculator
Density Calculator
What the moving object is made of, from its weight and the room it takes up, with a float or sink verdict - See calculator
Force Calculator
Turns the acceleration you just found into the force behind it, through F = m × a - See calculator
Kinetic Energy Calculator
How much energy that final speed carries, and why twice the speed is four times the trouble - See calculator
Kinetic Friction Calculator
Where the braking figures in this page come from: the grip between the tire and the road - See calculator
Braking Distance Calculator
The road-safety version of the distance mode, with reaction time and surface conditions included - See calculator
0-100 km/h Acceleration Calculator
Predicts a specific car's sprint from its power and weight instead of measuring one that already happened - See calculator
Speed Converter
Moves a single speed between mph, km/h and m/s when that is all you need - See calculator