About the Velocity Calculator
Velocity is how fast something is moving and in which direction. In everyday speech it is often used to mean speed, and for motion along a straight line the two have the same size. Velocity sits at the heart of physics: it links distance and time, it changes when an object accelerates, and it determines an object's momentum and kinetic energy.
This velocity calculator works out velocity in three ways. It finds the average velocity from a distance and a time, the final velocity after accelerating for a given time, and the final velocity after accelerating over a given distance. Answers are shown in metres per second, kilometres per hour, miles per hour, feet per second and knots, together with the pace in seconds per kilometre and per mile.
How to Use the Velocity Calculator
Choose From distance and time, After accelerating for a time or After accelerating over a distance.
For average velocity, enter the distance and time and their units.
For final velocity, enter the initial velocity (0 if starting from rest), the acceleration, and either the time in seconds or the distance.
Choose the speed unit for the answer.
The Formulas
average velocity v = d ÷ t
after accelerating for a time v = u + a × t
after accelerating over a distance v = √(u² + 2 × a × s)
u = initial velocity, a = acceleration, t = time, s = distanceStep-by-Step Examples
A 100 m sprint in 9.58 seconds.
v = 100 ÷ 9.58 = 10.438 m/s = 37.58 km/h = 23.35 mphA 2-hour marathon.
v = 42,195 m ÷ 7,200 s = 5.8604 m/s = 21.098 km/hFalling for 3 seconds from rest, ignoring air resistance:
v = 0 + 9.80665 × 3 = 29.42 m/s ≈ 105.9 km/hFalling 20 metres from rest:
v = √(2 × 9.80665 × 20) = 19.806 m/s ≈ 71.3 km/hSpeed and Velocity
Speed is a scalar: it only tells you how fast. Velocity is a vector: it tells you how fast and in what direction. A car driving round a roundabout at a steady 30 km/h has a constant speed, but its velocity is always changing because its direction changes. An athlete who runs one lap of a 400 m track in 50 seconds has an average speed of 8 m/s, but an average velocity of zero, because they finish where they started. For motion in a straight line, speed and the size of the velocity are the same, which is what this calculator assumes.
Average and Instantaneous Velocity
The average velocity from distance and time tells you nothing about how the speed varied along the way. Usain Bolt averaged 10.44 m/s in his 9.58-second world record, but he started from rest and reached a top speed of more than 12 m/s. The instantaneous velocity — the reading on a speedometer — is the velocity at one moment. The acceleration equations give instantaneous velocity at the end of a period of constant acceleration.
The SUVAT Equations
For motion with constant acceleration, five quantities are linked: displacement s, initial velocity u, final velocity v, acceleration a and time t. Knowing any three lets you find the other two. This calculator uses two of the equations: v = u + at and v² = u² + 2as. The others are s = ut + ½at² and s = ½(u + v)t. They are the standard tools for solving problems about falling objects, braking cars and accelerating vehicles.
Falling Objects and Air Resistance
Near the Earth's surface, a falling object gains about 9.81 m/s of speed every second if air resistance is ignored. In reality, drag grows with speed until it balances the weight, and the object stops accelerating at its terminal velocity. A skydiver in a spread position reaches about 55 m/s, roughly 200 km/h, after around 12 seconds; a raindrop falls at only a few metres per second. The calculator's results therefore describe dense objects over short drops well, and overestimate speeds for light objects or long falls.
Relative Velocity
Velocity always depends on the point of view. A passenger walking forward at 1.5 m/s on a train moving at 30 m/s is moving at 31.5 m/s relative to the ground but only 1.5 m/s relative to the train. Two cars approaching each other at 90 km/h each close the gap at 180 km/h, which is why head-on collisions are so severe. Aircraft speeds are measured relative to the air as well as the ground: a plane flying at 800 km/h into a 100 km/h headwind covers the ground at only 700 km/h, and the same plane with a tailwind would reach 900 km/h over the ground. Pilots and navigators combine these velocities as vectors, adding speed and direction together, to plan routes and estimate arrival times. The same idea explains why a ball thrown forward from a moving car travels faster over the ground than one thrown by someone standing still.
Understanding Your Result
The headline is the velocity in your chosen unit.
The in other units line converts it to m/s, km/h, mph, ft/s and knots.
The pace line gives the time to cover a kilometre and a mile at that speed.
When Should You Use This Calculator?
Use it for physics homework on motion.
Use it to work out average speeds for runs, drives and journeys.
Use it to find the speed of a falling or accelerating object.
Common Mistakes
Mixing units. Time in hours and distance in metres give unexpected answers; choose matching units.
Confusing average and top speed. An average hides changes along the way.
Using the acceleration equations when acceleration varies. They assume a constant acceleration.
Ignoring air resistance for long falls. Real objects reach a terminal velocity.