# Velocity Calculator

Created by Dominik Czernia, PhD candidate
Last updated: May 18, 2022

Our velocity calculator offers a complete and thorough way to compute the velocity of an object. It includes three various formulae of velocity which you can use depending on the situation. You can use our tool, for example, as:

1. Initial speed calculator - switch to the "Acceleration" method and input all values except initial velocity.
2. Final velocity calculator - use the same method as for the initial velocity calculator but leave the final velocity empty instead.
3. Average velocity calculator - select the third option in the drop-down list and enter up to 10 different velocities with time (how long a certain velocity was maintained) to get the average velocity equation applied.

## Velocity formula in physics

The velocity equation is a fundamental way to express the rate of change in the position of objects in motion. The formula of velocity is the following:

$\vec{v} = \frac{\Delta\vec{x}}{\Delta t}$

, where:

• $\vec{v}$ - The velocity that we often express in miles or kilometers per hour. Use the speed conversion tool to switch between other velocity units.
• $\Delta\vec{x}$ - The displacement which we described more in details in the displacement calculator.
• $\Delta t$ - Time period corresponding to the displacement. For a more precise result, we use the instantaneous velocity formula which finds the limit $\Delta t \rightarrow 0$, i.e., calculates the derivative.

So, by definition, velocity is a vector as opposed to speed which is a scalar or number. Still, we commonly use both terms interchangeably in everyday life.

## Average velocity formula

Our average velocity calculator (the third available method) might need more explanations. First of all, are we simply calculating the average of a few numbers? No, that's not that easy in general!

The average velocity formula, we use in our tool, uses the weighted average, where time is weight. Thanks to that, you can take into account how long have you traveled at a certain speed. For example, if you drive a car $30 \text{ mph}$ for $2 \text{ h}$ and then $40 \text{ mph}$ for $1 \text{ h}$, your average velocity will be about $33.33 \text{ mph}$, not $35 \text{ mph}$ as you would expect for a simple algebraic average.

You can express it with the average velocity formula below (we use the scalar version):

\footnotesize \begin{align*} \text{average velocity} &= (\text{velocity}_1 \times \text{time}_1 \\ &+ \text{velocity}_2 \times \text{time}_2 \\ &... \\ &+ \text{velocity}_N \times \text{time}_N) \\ & \div \text{total time} \end{align*}

, where $N$ is the total number of velocities, and each velocity has a corresponding time.

## Initial and final velocity calculators

Let's talk about the velocity change, which is directly related to the acceleration of an object. We talked more about it in the acceleration calculator, so be sure to check it if you need to know more about this topic. Now, let's focus on estimating initial speed $v_i$ and final velocity $v_f$ using the acceleration $a$, i.e, how to solve for velocity. To find the former, use the following expression:

$v_i = v_f - a \times t$

, and for the latter:

$v_f = v_i + a \times t$

Both equations are equivalent and result from a simple consideration of kinematics. The final and initial speed calculator that you can find under the second method of this velocity calculator is based on the above formulae. Thanks to it, you can estimate your velocities in no time for any units you want without knowing how to solve for velocity!

Dominik Czernia, PhD candidate
How would you like to calculate velocity?
Method
Distance covered
Distance covered
Distance
ft
Time
sec
Velocity
ft/s
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