Velocity calculator, speed, time and acceleration.

The velocity formula is v = d ÷ t: velocity is the distance travelled divided by the time it took. A runner who covers 100 m in 12 s moves at 100 ÷ 12 = 8.33 metres per second. Acceleration is how fast the velocity changes, a = (v − u) ÷ t, where u is the start speed and v the end speed. This calculator solves both, with any units, and shows the formula in your numbers.

How to use the velocity calculator

1. Pick the Problem: "Speed, distance and time", "Constant acceleration (any three of five)", "Free fall" or "Stopping distance".
2. Pick the Speed unit, Distance unit, Time unit and Acceleration unit. They apply to every box, and each answer is also shown in the other speed units.
3. For "Speed, distance and time", fill in two boxes and leave the third empty. The empty one is the answer.
4. For "Constant acceleration", fill in three of Start speed u, End speed v, Acceleration a, Time t and Distance d. The two empty ones are worked out.
5. For "Free fall", pick whether you know the height, the time or the final speed. The start speed is 0 for something dropped.
6. For "Stopping distance", type the starting speed, a deceleration you choose and, if you like, a reaction time.
7. Read the big result, then "The working" for each step. "Clear the boxes" empties the boxes of the current problem.

The formulas

These four apply only when the acceleration is constant. The page picks the right ones for the three boxes you fill in. If you give it numbers that cannot go together, such as a distance the object never reaches, it says so.

Worked examples

• Speed. 100 m in 12 s: 100 ÷ 12 = 8.333 m/s. That is 8.333 × 3.6 = 30 km/h, or 18.64 mph.
• Acceleration. From 0 to 27 m/s in 6 s: (27 − 0) ÷ 6 = 4.5 m/s², which is 0.459 g.
• Distance. Start at rest, accelerate at 2 m/s² for 10 s: d = 0 × 10 + 0.5 × 2 × 10² = 100 m, and the end speed is 0 + 2 × 10 = 20 m/s. These are the numbers the page starts with.
• End speed from distance. From rest at 3 m/s² over 150 m: v² = 0 + 2 × 3 × 150 = 900, so v = 30 m/s.

Units and conversions

The conversions are exact definitions. 1 mph is 0.44704 m/s, 1 ft is 0.3048 m, 1 mile is 1,609.344 m, a nautical mile is 1,852 m, and a knot is one nautical mile an hour, or 0.5144 m/s. So 60 mph is 60 × 0.44704 = 26.82 m/s, which is 96.56 km/h. To change other units, use the unit converter, which has a Speed group.

Free fall

Free fall uses the standard acceleration of gravity, g = 9.80665 m/s², a value fixed by definition (NIST, CODATA value for the standard acceleration of gravity, checked 18 Oct 2026). Real gravity varies a little from place to place, and the page lets you type another g. A drop from 20 m: v = √(2 × 9.80665 × 20) = 19.81 m/s, and t = 19.81 ÷ 9.80665 = 2.02 s. After 3 s the fall is 0.5 × 9.80665 × 3² = 44.13 m, at 29.42 m/s. Air resistance is not included, so this is the idealised case, and the page says so.

Stopping distance as a maths exercise

If something slows at a constant rate a from speed v, the braking distance is v² ÷ 2a and the braking time is v ÷ a. From 20 m/s at 5 m/s², that is 400 ÷ 10 = 40 m in 4 s. A reaction time adds v × time before braking starts: 1 s adds 20 m, so 60 m in all. Double the speed and the braking distance is four times as long: 40 m/s gives 1,600 ÷ 10 = 160 m. The deceleration is a number you choose. The page does not know any road, tyre or driver, so this is not safety advice.

Common problems

• Mixed units. Pick one unit for each kind of box. The page converts to metres and seconds, works, then converts back.
• Too many or too few boxes. Constant acceleration needs exactly three. The page tells you how many to clear.
• A negative time. The numbers describe motion that would have to run backwards. Check the signs of the speeds and the acceleration.

For electrical sums, the watts to amps calculator works the same way, and the percentage calculator finds a percent change in a speed.