Velocity Calculator works out velocity from distance and time, final or initial velocity under acceleration, average velocity across several legs, and the water velocity in a pipe.
Pick the method that matches your known values. The panel below changes the unknown and the unit.
Solve For and Result Units
Step-by-Step Working
- Known values: d = 500 m, t = 3 min
- In SI units: d = 500 m, t = 180 s
- v = d ÷ t = 500 ÷ 180 = 2.77778 m/s
- Result: velocity v = 2.77778 m/s
Velocity–Time Graph
The shaded area under the line is the distance, 500.00 m. The slope of the line is the acceleration.
Five Methods in the Velocity Calculator
Velocity is how fast position changes, together with the direction of that change. The Velocity Calculator finds it in five ways, chosen in the Method menu. Each method matches a different set of known values, so start with what your problem gives you.
| Method | You know | Formula |
|---|---|---|
| Distance Covered | Distance and time | v = d ÷ t |
| Acceleration and Time | Initial velocity, acceleration, time | v = v₀ + at |
| Acceleration and Distance | Initial velocity, acceleration, displacement | v² = v₀² + 2as |
| Average Velocity | Up to four velocities and their times | v̄ = Σ(v × t) ÷ Σt |
| Flow in a Pipe | Flow rate and inside diameter | v = 4Q ÷ (π d²) |
Four of the methods also run in reverse. Open the lower section and change Solve For to get distance, time, initial velocity, acceleration, displacement, flow rate or pipe diameter. The first card repeats each result in three other units, and Result Units adds knots.
Velocity Formula From Distance and Time
The basic velocity formula divides the distance covered by the time taken. It gives the average velocity over that stretch. It equals the velocity at every moment only when the object moves at a steady rate in a straight line.
$$v = \frac{d}{t}$$
The Velocity Calculator opens with 500 m covered in 3 minutes. It first converts the time to 180 seconds, then divides. The result is 500 ÷ 180 = 2.78 m/s, which is 10 km/h, 6.21 mph or 9.11 ft/s.
The second card turns that velocity into pace, the form runners and cyclists use. Here it is 6:00 per kilometer and 9:39 per mile, with 100 m taking 36 seconds. The last card shows how far the same velocity carries in a set time, such as 166.67 m in one minute.
The SI unit of velocity is the meter per second, written m/s. Other units are just different sizes of the same quantity. Multiply m/s by 3.6 to get km/h, and by 2.237 to get mph. A knot is one nautical mile per hour, or 0.5144 m/s.
Final Velocity and Initial Velocity
When the velocity changes at a steady rate, the acceleration methods apply. The first works as a final velocity calculator when you know how long the acceleration lasts. A negative acceleration means the object is slowing down.
$$v = v_0 + a t$$
The method opens with a car starting from rest and accelerating at 6.95 m/s² for 4 seconds. Its final velocity is 0 + 6.95 × 4 = 27.8 m/s, which is 100.08 km/h. The second card adds the displacement, 55.6 m, and the average velocity, 13.9 m/s.
A slowing example comes from OpenStax University Physics. An airplane lands at 70 m/s and slows at 1.5 m/s² for 40 seconds. Enter the acceleration as −1.5 and the final velocity is 70 − 60 = 10 m/s, after 1,600 m of runway.
To find velocity without time, switch to Acceleration and Distance. This method links the velocities to the displacement s and leaves time out. It is the form to use for braking distances and drag races.
$$v^2 = v_0^2 + 2 a s$$
The built-in example is the dragster from the same textbook. Starting from rest at 26 m/s² over 402 m, it reaches √(2 × 26 × 402) = 144.58 m/s, which the book rounds to 145 m/s. That is 520.5 km/h, covered in 5.56 seconds. The Quarter Mile Calculator estimates such runs from weight and power.
Change Solve For to turn either method into an initial velocity calculator. The rearranged forms are v₀ = v − at and v₀ = √(v² − 2as). The same menu solves for acceleration, time or displacement, and the SUVAT Calculator handles any two unknowns at once.
Average Velocity Over Several Legs
A trip made of legs at different velocities needs a weighted average. Each velocity counts in proportion to the time spent at it. Adding the velocities and dividing by their number gives the wrong answer unless every leg lasts equally long.
$$\bar{v} = \frac{v_1 t_1 + v_2 t_2 + \dots}{t_1 + t_2 + \dots}$$
The Average Velocity method starts with 25 mph for 1 hour and 70 mph for 3 hours. The trip covers 25 + 210 = 235 miles in 4 hours, so the average velocity is 58.75 mph. The plain mean of 25 and 70 is 47.5 mph, more than 11 mph too low.
The Velocity Calculator shows both figures side by side, so the size of the mistake is clear. Two more legs can be added in the lower section. Enter a leg in the opposite direction with a minus sign, and the result becomes a true average velocity for the net displacement.
Instantaneous Velocity at a Chosen Time
Instantaneous velocity is the velocity at one moment, where average velocity covers a whole interval. With steady acceleration the two are easy to connect. The formula v = v₀ + at gives the instantaneous velocity at any time t you enter.
For the landing airplane, enter 20 seconds and the Velocity Calculator returns 40 m/s, the velocity at that instant. The Velocity–Time Graph shows this as a point on a straight line. The slope of the line is the acceleration, and the shaded area under it is the displacement.
When acceleration is not steady, instantaneous velocity is the derivative of position with respect to time. That case needs the position formula itself and falls outside the methods here.
Speed and Velocity Are Not the Same
Speed says how fast something moves. Velocity says how fast and in which direction. Speed is a scalar and can never be negative. Velocity is a vector, so along a line it carries a plus or minus sign for direction.
To convert velocity to speed, drop the direction and keep the size. A velocity of −12 m/s is a speed of 12 m/s. When a result is negative, the Velocity Calculator states the speed in its note and explains that the motion runs against the positive direction.
The two differ most on a round trip. A runner who completes a 400 m lap in 80 seconds has an average speed of 5 m/s. The average velocity is zero, because the runner ends at the starting point and the displacement is zero.
Velocities in different directions add as vectors, and the sum is often called the total or resultant velocity. The Resultant Velocity Calculator adds up to five of them. For an aircraft in wind, the Ground Speed Calculator does the same job.
Water Velocity in a Pipe
The Flow in a Pipe method turns the tool into a water velocity calculator. Fluid velocity is the flow rate divided by the inside area of the pipe. Written with the diameter, the formula needs only two inputs.
$$v = \frac{4 Q}{\pi d^2}$$
The method opens with 12 L/s through a pipe 100 mm across. The flow area is 78.54 cm², so the velocity is 0.012 ÷ 0.007854 = 1.53 m/s. The cards add the velocity head, 0.119 m, the pipe volume, 7.85 liters per meter, and the volume delivered, 720 liters in one minute.
US units work the same way. Water at 100 gal/min through a 4 inch pipe moves at 2.55 ft/s, which matches the plumbing shortcut v = 0.4085 × gpm ÷ d². The result is the mean velocity across the pipe, since real flow runs faster at the center than at the wall.
Change Solve For to size a pipe. Carrying the same 12 L/s at a target velocity of 2 m/s takes an inside diameter of 87.4 mm. Halving the diameter of any pipe makes the same flow move four times as fast.
Pigeon Velocity and Other Kinds
How is pigeon velocity calculated?
Pigeon racing uses the distance formula with its own unit, yards per minute. A bird that flies 300 miles in 6 hours 40 minutes covers 528,000 yards in 400 minutes. Enter 300 mi and 400 min in the Velocity Calculator and set Result Units to yd/min. The answer is 1,320 yards per minute, the same as 45 mph.
What are the four types of velocity?
Textbooks usually list uniform, variable, average and instantaneous velocity. Uniform velocity stays constant in size and direction. Variable velocity changes in either one. Average velocity is displacement over time, and instantaneous velocity is the value at a single moment.
What is linear velocity?
Linear velocity is velocity along a path, as opposed to the angular velocity of something turning. For a point on a rotating object the two are linked by v = ω r. A point 0.3 m from the axis of a wheel turning at 10 rad/s moves at 3 m/s.
How fast can velocity get?
Nothing with mass can reach the speed of light, 299,792,458 m/s. The third card gives the Mach number against the speed of sound at sea level, 340.29 m/s, and shows the share of light speed once a result passes 0.1% of it. The dragster above runs at Mach 0.425. Falling objects have their own limit in air, covered by the Terminal Velocity Calculator.