How to Use the Average Speed Calculator?
To use this calculator, simply select how many speed and time entries you want to use, or leave the setting on Auto to add more rows as you enter values. Then, enter each speed and the amount of time traveled at that speed, and select the appropriate unit for each field. That’s it! The calculator will update the average speed, total distance traveled, and total time taken automatically.
You can also change the units of the results at any time to view the same values in a different form.
What Is Average Speed?
When an object travels at the same speed throughout a journey, its speed is easy to describe. For example, if a car travels at 60 km/h for the entire trip, we can simply say that its speed is 60 km/h.
In real life, however, objects rarely move at exactly the same speed all the time. A car might travel at 40 km/h in city traffic, 80 km/h on a highway, and then slow down again near its destination.
When the speed changes during a journey, we often use average speed to describe how fast the object traveled overall.
Average Speed Formula
Average speed is found by dividing the total distance traveled by the total time taken.
\[ \text{Average speed}=\frac{\text{Total distance traveled}}{\text{Total time taken}} \]
Or simply:
\[ \text{Average speed} = \frac{\text{Distance}_1+\text{Distance}_2+\cdots} {\text{Time}_1+\text{Time}_2+\cdots} \]
Since each distance can be found by multiplying speed by time:
\[ \text{Distance}=\text{Speed}\times\text{Time} \]
the same idea can be written as:
\[ \text{Average speed} = \frac{v_1t_1+v_2t_2+\cdots} {t_1+t_2+\cdots} \]
Here, \(v_1\), \(v_2\), and so on represent the different speeds, while \(t_1\), \(t_2\), and so on represent the amount of time spent traveling at each speed.
Example 1: Two Different Speeds
Suppose a car travels at 60 km/h for 2 hours and then at 40 km/h for 3 hours. What is its average speed for the entire journey?
First, find the distance traveled during the first part:
\[ \text{Distance}_1=60\times2=120\text{ km} \]
During the second part:
\[ \text{Distance}_2=40\times3=120\text{ km} \]
Therefore, the total distance traveled is:
\[ 120+120=240\text{ km} \]
The total time is:
\[ 2+3=5\text{ hours} \]
Now divide the total distance by the total time:
\[ \text{Average speed}=\frac{240}{5}=48\text{ km/h} \]
Therefore, the car’s average speed for the entire journey is 48 km/h.
Notice that simply averaging 60 km/h and 40 km/h would give 50 km/h, but that would be incorrect. The car spent 3 hours traveling at 40 km/h and only 2 hours traveling at 60 km/h. Because it spent more time at the lower speed, the overall average is pulled closer to 40 km/h.
Example 2: Three Different Speeds
Suppose a bus travels at 30 km/h for 1 hour, 50 km/h for 2 hours, and 60 km/h for 3 hours. Find its average speed.
The distance traveled during the first part is:
\[ 30\times1=30\text{ km} \]
During the second part:
\[ 50\times2=100\text{ km} \]
During the third part:
\[ 60\times3=180\text{ km} \]
The total distance is therefore:
\[ 30+100+180=310\text{ km} \]
The total time is:
\[ 1+2+3=6\text{ hours} \]
So the average speed is:
\[ \text{Average speed}=\frac{310}{6}\approx51.7\text{ km/h} \]
Therefore, the bus travels at an average speed of approximately 51.7 km/h.
Example 3: When Times Given in Minutes
Suppose a cyclist travels at 18 km/h for 20 minutes and then at 24 km/h for 40 minutes. Find the cyclist’s average speed.
First, convert both times to hours:
\[ 20\text{ minutes}=\frac{20}{60}=\frac{1}{3}\text{ hour} \]
\[ 40\text{ minutes}=\frac{40}{60}=\frac{2}{3}\text{ hour} \]
Now calculate the distance traveled during the first part:
\[ 18\times\frac{1}{3}=6\text{ km} \]
For the second part:
\[ 24\times\frac{2}{3}=16\text{ km} \]
The total distance is:
\[ 6+16=22\text{ km} \]
The total time is:
\[ 20+40=60\text{ minutes}=1\text{ hour} \]
Therefore:
\[ \text{Average speed}=\frac{22}{1}=22\text{ km/h} \]
So the cyclist’s average speed is 22 km/h.
Example 4: When the Times Are Equal?
There is one important situation in which simply averaging the speeds does work: when the object travels at each speed for the same amount of time.
Suppose a car travels at 40 km/h for 2 hours and then at 60 km/h for another 2 hours.
The distances are:
\[ 40\times2=80\text{ km} \]
and
\[ 60\times2=120\text{ km} \]
The total distance is therefore 200 km, and the total time is 4 hours.
\[ \text{Average speed}=\frac{200}{4}=50\text{ km/h} \]
In this case, we could also calculate:
\[ \frac{40+60}{2}=50\text{ km/h} \]
Both methods give the same answer because the car spends an equal amount of time at each speed. If the times are not equal, however, simply averaging the speeds will generally give the wrong result.
Example 5: Including Time Spent Stopped
Average speed is based on the entire time taken for the journey, so time spent stopped can also affect the answer if that stopped time is included in the journey.
Suppose a delivery van travels at 50 km/h for 2 hours and then stops for 30 minutes before reaching the end of the measured journey. During the 2 hours of driving, it travels:
\[ 50\times2=100\text{ km} \]
The total time, including the stop, is:
\[ 2+0.5=2.5\text{ hours} \]
Therefore:
\[ \text{Average speed}=\frac{100}{2.5}=40\text{ km/h} \]
So although the van moved at 50 km/h whenever it was driving, its average speed over the entire 2.5-hour period was only 40 km/h. The 30 minutes spent stopped added time to the journey without adding any distance, which lowered the average speed.
