Average Velocity Calculator

Average velocity indicates how fast and in what direction an object has moved over a certain time period. As it is a vector quantity, it has a sign. A positive value means the motion was forward, while a negative value means that the final position is behind the starting point.

The key term is displacement. This refers to the linear change in position from a starting point to an ending point. It differs from distance traveled. Average velocity only considers the two end points; therefore it remains zero no matter how far one travels if they return to their starting point.

This calculator offers four different methods to calculate average velocity. They correspond with the procedures learned in physics class. You can either input the displacement and time, two positions on a graph, two velocities for uniformly accelerated motion or a path divided into several segments.

Formula for average speed:

The definition is a single line.

The bar over the "v" represents the average. The displacement is the difference between the final and initial position, and the time interval is the difference between the final and start times. If the motion starts at time zero, then the formula can be simplified by dividing the displacement by the elapsed time.

Change, time and speed are closely related in this regard. So if two of them are known, the third can be calculated. If change and speed are given, you get the time. If time and speed are given, you get the change. Leave blank the size that you do not want to know and enter the other two values.

Examples with positive and negative signs:

The runner's position changed from 60 meters to 40 meters in a time of 4 seconds. The change is the difference between 40 and 60, which is negative 20 meters. Dividing this by 4 seconds gives an average velocity of negative 5 meters per second.

The negative sign here has a real meaning. It indicates that the runner is ultimately 20 meters behind the starting point and moving in a negative direction. The average speed only gives the magnitude of 5 meters per second, without taking into account the direction. For this reason, it's important to distinguish between these two concepts.

Difference between average speed and average rate:

The average rate is never negative since it divides the total distance by the total time. The average velocity can be positive or negative or zero as well since it divides the change in position by the total time.

Imagine a remote-controlled car going from point A to B and then returning back to A. Since the displacement is zero, so is the average velocity even though the car was moving throughout the entire time. Only if the motion is in a straight line without any reversals are these two values equal.

Average speed with constant acceleration

When an object is accelerating or decelerating at a constant rate, the average velocity is the mean of the initial and final velocities.

A ship traveling at 25 kilometers per hour gradually accelerates to 37 kilometers per hour. The average speed during this time is 31 kilometers per hour, which is calculated as (25 + 37) / 2. Multiplying this average speed by the amount of time gives you the distance traveled. For that reason, this simple formula is very useful in many kinematics problems.

Finding average velocity with a position-time graph.

In a position-time graph, each point corresponds to a particular time on the horizontal axis and a corresponding position on the vertical axis. If two arbitrary points are selected, the slope of the line connecting those two points is the average velocity between those two points.

It is assumed that a curve passes through two points: one point with the position 20 meters and the time 2 seconds, and another point with the position 40 meters and the time 4 seconds. Since the increase in position is 20 meters and the elapsed time is 2 seconds, the slope is 10 meters per second. This secant's slope corresponds to the average rate of change of position and is the result of a calculation in two-point mode.

A section with a change of direction.

The properties of average speed are all directionally dependent. If a single section is broken into multiple subsections, each with an assigned sign (+ or −), then the resulting displacement is the sum of the signed values of each subsection, and the total distance traveled is the sum of the absolute values of each subsection.

You go east for 100 meters in 50 seconds and then turn around to come back the same 100 meters in another 50 seconds. The average velocity is zero because the net displacement is zero, but the average rate is 2 meters per second, calculated by dividing 200 meters by 100 seconds. In the multi-segment mode these two values are shown side-by-side so that you can see the difference at a glance.

How to use this calculator:

Select a method from above. For displacement and time, enter two of the three values (displacement, time, average velocity), and the third value will be calculated. For two positions, enter the position of the start and end point as well as their corresponding times. For constant acceleration motion, enter the initial and final velocities. For a section with multiple subsections, specify the number of subsections and then enter each subsection. Use a negative sign for sections where direction is reversed.

Adjust the unit to match your data. The results section will display average speed, associated magnitudes and results converted into other units.

The average velocity summarizes the entire time period, thus changes in individual moments within this time period remain hidden. To determine the speed at a particular moment, one must determine the slope of the position-time curve at that point. This is the instantaneous velocity and another measurement result than the average value over the entire time period which the tool outputs.