# Velocity Calculator

Created by Mateusz Mucha and Dominik Czernia, PhD
Reviewed by Jack Bowater
Last updated: Sep 15, 2023

This velocity calculator is a comprehensive tool that enables you to estimate the speed of an object. If you have ever wondered how to find velocity, here you can do it in three different ways.

• The first one relies on the basic velocity definition that uses the well-known velocity equation.
• The second method calculates what is velocity change caused by acceleration over a specific time interval.
• Finally, the third part of the velocity calculator makes use of the average velocity formula, which may be useful if you need to analyze journeys with various velocities over different distances.

We've also prepared a brief but informative article about velocity itself. Keep reading to learn what is velocity formula and what are the most common velocity units. Did you know that there is an essential difference between speed vs velocity? We've written about it from the point of view of a physicist in the text below.

## What is velocity? – velocity definition

Velocity definition states that it is the rate of change of the object's position as a function of time. It is one of the fundamental concepts in classical mechanics that considers the motion of bodies. If you want to put this rule down in the form of a mathematical formula, the velocity equation will be as follows:

velocity = distance / time

Keep in mind that this velocity formula only works when an object has a constant speed in a constant direction or if you want to find the average velocity over a certain distance (as opposed to the instantaneous velocity). You have probably noticed that we use the words speed and velocity interchangeably, but you can't do it every time. To learn more about it, head to the speed vs. velocity section.

Aside from the linear velocity, to which we devoted this calculator, there are also other types of velocity, such as rotational or angular velocity with corresponding physical quantities: rotational kinetic energy, angular acceleration, or mass moment of inertia. When an object has only angular velocity, it doesn't displace linearly, and you can't use the average velocity formula, as it only applies to linear movement.

## The average velocity formula and velocity units

The average velocity formula describes the relationship between the length of your route and the time it takes to travel. For example, if you drive a car for a distance of 70 miles in one hour, your average velocity equals 70 mph. In the previous section, we have introduced the basic velocity equation, but as you probably have already realized, there are more equations in the velocity calculator. Let's list and organize them below:

1. Simple velocity equation:

velocity = distance / time

2. Velocity after a certain time of acceleration:

final velocity = initial velocity + acceleration × time

3. Average velocity formula — the weighted average of velocities:

average velocity = (velocity₁ × time₁ + velocity₂ × time₂ + …) / total time

You should use the average velocity formula if you can divide your route into few segments. For example, you drive a car with a speed of 25 mph for 1 h in the city and then reach 70 mph for 3 h on the highway. What is your average velocity? With the velocity calculator, you can find that it will be about 59 mph.

From the above equations, you can also imagine what are velocity units. British imperial units are feet per second ft/s and miles per hour mph. In the metric SI system, the units are meters per second m/s and kilometers per hour km/h. Remember you can always easily switch between all of them in our tool!

## How to calculate velocity – speed vs. velocity

Before we explain how to calculate velocity, we'd like to note that there is a slight difference between velocity and speed. The former is determined by the difference between the final and initial position and the direction of movement, while the latter requires only the distance covered. In other words, velocity is a vector (with the magnitude and direction), and speed is a scalar (with magnitude only).

It's time to use the average velocity formula in practice. Provided an object traveled 500 meters in 3 minutes, to calculate the average velocity, you should take the following steps:

1. Change minutes into seconds (so that the final result would be in meters per second):

3 minutes = 3 × 60 = 180 seconds

2. Divide the distance by time:

velocity = 500 / 180 = 2.78 m/s

Let's try another example. You want to participate in a race with your brand-new car that can change its speed with an acceleration of about 6.95 m/s². The competition just started. What will be your velocity after 4 seconds?

1. Set initial velocity to zero; you're not moving at the beginning of the race.

2. Multiply the acceleration by time to obtain the velocity change:

velocity change = 6.95 × 4 = 27.8 m/s

3. Since the initial velocity was zero, the final velocity is equal to the change in speed.

4. You can convert units to km/h by multiplying the result by 3.6:

27.8 × 3.6 ≈ 100 km/h

You can, of course, make your calculations much easier by using the average velocity calculator. All you'll need to do is type in distance and time. One of the advantages of using this calculator is that you don't have to convert any units by hand. Our tool will do it all for you!

## Terminal velocity, escape velocity and relativistic velocity

Velocity is present in many aspects of physics, and we have created many calculators about it! The first velocity is the so-called terminal velocity, which is the highest velocity attainable by a free-falling object. Terminal velocity occurs in fluids (e.g., air or water) and depends on the fluid's density.

Do you ever wonder what speed is necessary to leave a planet? This speed is called escape velocity and is defined as the smallest speed required for an object to escape the gravitational pull generated by a celestial body, such as a planet, a moon, or a star. Escape velocity is a concept of fundamental importance in astrophysics and in the context of space travel.

In the high energy region, there is another important velocity — relativistic velocity. It results from the fact that no object with a non-zero mass can reach the speed of light. Why? When it approaches light speed, its kinetic energy becomes unattainable, very large, or even infinite. Moreover, this is a cause of other phenomena like relativistic velocity addition, time dilation, and length contraction. Also, Albert Einstein's famous E = mc² formula is based on the relativistic velocity concept.

We hope we've convinced you that velocity plays an essential role in everyday life and not just science, and we hope that you've enjoyed our velocity calculator.

## FAQ

### What is the airspeed velocity of an unladen swallow?

Well, that depends if you are talking about the European or African variety. For the European sort, it would seem to be roughly 11 m/s, or 24 mph. If it's our African avian acquaintance you’re after, well, I'm afraid you're out of luck; the jury's still out.

### How do you find instantaneous velocity?

1. Find an equation that describes how distance (x) changes with respect to time (t).
2. Differentiate the formula with respect to time.
3. Let dx/dt = instantaneous velocity.
4. Input the desired time into the differentiated formula. The result is the instantaneous speed at time t.

### How long does it take to reach terminal velocity?

It will take the average human approximately 15 seconds to reach 99% of terminal velocity with their belly facing the Earth. Reaching 100% terminal velocity is very difficult, if not impossible, as acceleration drops exponentially as an object approaches its terminal velocity. This time will change if the person changes body position.

### Can velocity be negative?

Yes, velocity can be negative. Velocity is directional speed, so if the object is moving opposite to the direction defined as the positive direction, it will be negative. Two objects with equal but opposite velocities have the same speed, but are just moving in opposite directions.

### How do you find initial velocity?

To find the initial velocity:

1. Work out which of the displacement (s), final velocity (v), acceleration (a), and time (t) you have to solve for initial velocity (u).

2. If you have v, a, and t, use:

u = v − at

3. If you have s, v, and t, use:

u = 2(s/t) — v

4. If you have s, v, and a, use:

u = √(v² − 2as)

5. If you have s, a, and t, use:

u = (s/t) − (at/2)

### How do you find final velocity?

To compute the final velocity:

1. Work out which of the displacement (s), initial velocity (u), acceleration (a), and time (t) you have to solve for the final velocity (v).

2. If you have u, a, and t, use:

v = u + at

3. If you have s, u, and t, use:

v = 2(s/t) − u

4. If you have s, a, and t, use:

v = (s/t) + (at/2)

### What is escape velocity?

Escape velocity is the minimum speed an object needs to escape another object's gravitational pull. The most common example of this is the speed a spacecraft requires to leave Earth for distant planets, which is approximately 11.2 km/s.

### What is the difference between velocity and acceleration?

Velocity is the speed and direction with which an object is moving, while acceleration is how the speed of that object changes with time. The units for velocity are m/s, while for acceleration, they are m/s².

### What causes a change in velocity?

Interactions with other objects cause velocity to change. When a moving object collides with another object in its path, it will slow down (if it collides with something smaller, e.g., an air particle) or stop (if it hits a wall). If an object expels matter behind it, it will speed up like a rocket. An object will also accelerate towards other objects via gravity.

### How do I calculate escape velocity?

To calculate the escape velocity:

1. Find the object's mass in kilograms, m, and its radius in meters, r.

2. Multiply m by the gravitational constant (6.674 × 10−11) and then by 2.

3. Divide the result of step 2 by r.

4. Raise the result of step 3 by 0.5. The result is the escape velocity.

Mateusz Mucha and Dominik Czernia, PhD
How would you like to calculate velocity?
Method
Distance covered
Distance covered
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Time
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Velocity
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