Velocity Calculator

What do you want to calculate?

Choose what you know. The calculator shows the matching fields and solves for whichever one you leave blank.

Average velocity (distance and time)

Constant acceleration (with time)

Constant acceleration (with distance)

Enter the distance travelled and the time taken to get the average velocity, or enter the velocity with one of them to find the other. Leave the field you want blank.

Distance / displacement (d)

Time taken (t)

Average velocity (v)

Add mass for momentum and energy

Add a mass to also work out momentum (p = m v) and kinetic energy (half m v squared).

Please input values into the fields

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This velocity calculator calculates the speed of an object and offers three different calculation methods. You can either enter a distance and time to find average speed or acceleration and time/distance to calculate final speed for an accelerating or decelerating object. If one field is left blank, this tool will calculate its value.

Select a method and enter the known values to get the speed clearly displayed. Corresponding values in km/h, mph and ft/s as well as corresponding distances, times or average speeds are shown next to it.

What is speed?

Velocity is the rate of change of an object's position with time. It is a vector quantity as it states how fast an object moves and in which direction. Speed is the magnitude of velocity without considering its direction, and thus is a scalar quantity.

The direction is important so the velocity can be negative. If we define motion to the right as positive then motion to the left is negative. The speed of a car going backwards is negative but the value shown on the speedometer will always be positive.

The difference between speed and velocity.

These two terms are often confused in everyday speech but have different meanings in physics. Speed is the distance traveled divided by time and can never be negative. Velocity is the displacement divided by time. Displacement is the straight-line change of position, so it has both a sign and direction.

If you go around a circular path once and return to the starting point, the average speed is the length of the path divided by the time taken, while the average velocity is zero because the displacement is zero. This tool calculates the speed. In case of linear motion in one direction both values are identical.

Three speed formulas.

There are three standard methods for calculating speed and this tool supports all of them. Select the method that best matches your available measurement data.

To calculate average speed, divide the distance by the time it took to travel that distance.

v = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}

For uniformly accelerated motion where time is known, you add the change in velocity to the initial velocity.

v = v_0 + a\,t

For uniformly accelerated motion where the distance and not the time is known, formulas are used that do not require a specification of the time.

v^2 = v_0^2 + 2\,a\,s

In these formulas, v0 is the initial velocity, v is the final velocity, a is the constant acceleration, t is time, and s is displacement. The last two formulas are only valid if the acceleration is constant.

Instructions for using the calculator tool:

Select a method and enter the corresponding values in the fields provided. Leave one of the fields blank. The tool will calculate the value for the blank field and display the complete result. Here are some common starting methods:

You choose	You enter	You get
Distance and time	Distance and time	Average velocity
Distance and time	Velocity and time	The distance covered
Acceleration with time	Start velocity, acceleration, time	Final velocity and distance
Acceleration with distance	Start velocity, acceleration, distance	Final velocity and time

Example of calculating average speed:

A car travels a distance of 2 kilometers or 2000 meters in 100 seconds. Divide the distance by time.

v = \frac{2000}{100} = 20 \ \text{m/s}

So the average speed is 20 meters per second, which is 72 kilometers per hour or about 45 miles per hour. If you type in 2000 meters and 100 seconds, they will show up simultaneously.

Example of uniformly accelerated motion where time is known:

An object begins at rest and accelerates at a rate of 5 meters per second squared for 5 seconds. The change in velocity is added to the initial velocity.

v = 0 + 5 \times 5 = 25 \ \text{m/s}

The final velocity is 25 meters per second. In those 5 seconds the object traveled a distance of 62.5 meters and its average speed was 12.5 meters per second. If you select "Acceleration and time" method, the tool will automatically fill these values.

Example of uniformly accelerated motion where distance is known:

An object begins at rest and moves with an acceleration of 8 meters per second squared over a distance of 100 meters. The formula for the relationship between distance is used.

v^2 = 0^2 + 2 \times 8 \times 100 = 1600, \quad v = \sqrt{1600} = 40 \ \text{m/s}

The final velocity is 40 meters per second and the time taken is 5 seconds. This method is useful when you know how far an object has traveled but not the time it took to travel that distance.

Backward calculation

All of the methods can be used to work backwards. In the average velocity method, you input either the velocity and time to find distance or the velocity and distance to find time. In the acceleration method, you leave either the acceleration or the time free and input the velocity to solve for that value. This allows you to determine the force required to decelerate an object or the amount of time it takes to reach a certain speed.

Momentum and Kinetic Energy

Velocity also determines two other physical quantities that describe motion: momentum, which is the product of mass and velocity, and kinetic energy, which is half the product of mass and the square of velocity.

p = m\,v \qquad KE = \tfrac{1}{2} m v^2

If you enable the Momentum and Energy options and enter a mass, this tool will show these two values in addition to speed. The direction of momentum is the same as the velocity direction, while kinetic energy is always positive since it depends on the square of the velocity, increasing rapidly when an object accelerates.

Units and Conversions

In the International System of Units (SI), the unit for speed is meters per second, but in everyday life speeds are usually expressed in kilometers per hour, miles per hour, feet per second or knots. The tool displays results simultaneously in different units and allows you to change the unit of each column. As a practical check: 1 meter per second is exactly equivalent to 3.6 kilometers per hour.

Quantity	Symbol	SI unit
Displacement	d or s	metre (m)
Time	t	second (s)
Velocity	v	metre per second (m/s)
Acceleration	a	metre per second squared (m/s2)

Applications of speed

Speed is essential in all fields that study motion. It determines how long a journey takes, what trajectory a thrown ball will take, and how a car will behave when braking. Engineers use speed to determine the specifications of engines and brakes, meteorologists use wind speeds to predict storms, and sports analysts measure the speed of sprints and throws.

If you know the velocity and acceleration of an object, you can predict its position at any time in the future, as well as where it will be going when it gets there. This is the starting point for all kinematics.

Frequently asked questions

How is speed calculated?

To calculate average speed, divide the distance by the time: v=d/t. If a car travels 2000 meters in 100 seconds, its average speed is 20 meters per second. For uniformly accelerated motion, if the time is known, you can also use the formula v=v0+at. If the distance is known, you can use the formula v²=v₀²+2as.

What is the difference between speed and velocity?

Velocity indicates how fast an object is moving and it is always positive. Speed is a vector quantity as it also takes direction into account. If the object is moving in opposite direction, then speed can be negative. In straight line motion in only one direction, magnitude and velocity are same.

Can speed be negative?

Yes. Velocity is a vector and its sign indicates the direction. If one particular direction is defined as positive, then motion in the opposite direction has a negative velocity. Speed is the magnitude of the velocity and can never be negative.

How to calculate final velocity in uniformly accelerated motion?

If the time is known, use the formula v = v0 + a t. If the distance traveled is known, use the formula v² = v0² + 2 a s and take the square root. With an initial velocity of zero and acceleration of 8 meters per second squared, the final velocity at a distance of 100 meters will be 40 meters per second.

How do you convert meters per second to kilometers per hour?

You multiply by 3.6. So 20 meters per second is equal to 72 kilometers per hour. To convert back the other way you divide by 3.6. This tool also shows speeds in miles per hour and feet per second as well as kilometers per hour.

How are momentum and kinetic energy related to speed?

Momentum is the product of mass and velocity (p = m*v). The direction of momentum corresponds to the direction of velocity. Kinetic energy is half the product of mass and the square of velocity, which means that it increases proportionally with the square of velocity and is always positive. You can check these two quantities if you enable the Momentum and Energy options and enter a mass.

Related calculators

Displacement CalculatorCalculate displacement from velocity and time, from a change in velocity, from a constant acceleration, or without a time (stopping distance). Also finds average velocity, final velocity, and time, in any unit.

Average Velocity CalculatorFind average velocity as displacement over time. Solve for any variable, read it off a position-time graph, use the constant-acceleration midpoint, or add up a multi-leg journey.

Angular Velocity CalculatorCalculate angular velocity (ω) from an angle and time, a linear speed and radius, a period or a frequency, and read it in rad/s, RPM, rev/s and deg/s. Solves every method backwards too.

Acceleration CalculatorCalculate acceleration from a change in velocity over time or from force and mass, with displacement, change in velocity, and g-force.

Momentum CalculatorCalculate momentum from mass and velocity, or solve for mass or velocity. Includes kinetic energy, conservation of momentum in elastic and inelastic collisions, and relativistic momentum.

Alfven Velocity CalculatorFind the Alfven velocity of a magnetohydrodynamic wave with v_A = B/sqrt(mu0 x rho), or solve for the magnetic field or the plasma density. Builds the density from a number density, gives the relativistic speed, and times an Alfven wave across a distance.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Velocity
Definition of velocity as a vector, its relationship to speed, displacement, and acceleration, and the kinematic equations.
The Physics Classroom: Speed and Velocity
Plain-language explanation of the difference between speed and velocity with worked examples.
Khan Academy: Kinematic formulas and projectile motion
The four kinematic equations for constant acceleration and how to apply them.