# Calculating Workout Speed In WKO

Speed can be defined as how fast something is moving, or in other words the change in distance divided by change in time. Speed, distance, and time are linked; speed = distance / time. If you run a 10k in one hour, your speed is 10k per hour. Simple enough.

It would be unusual for your instantaneous speed at every point on the course to be exactly 10k per hour, however, because we speed up and slow down over hills, our focus drifts, fatigue sets in, etc. The 10k per hour speed is really your average speed over the entire course. The speed recorded by a device second by second will show peaks and valleys. If speed is recorded at even intervals, your average speed is the sum of all second-by-second speed measurements divided by the total duration. This means that the expression avg(speed) should return the same answer as distance/duration.

With some devices, something strange happens. Look at the report below. This athlete ran 8.505 km in 1 hour. For this workout, distance/duration = 8.505 km/hr, but avg(speed) = 8.429 km/hr. How can that be? If the athlete ran 8.505 km in one hour, the two expressions should be equal! The reason the two aren't equal is easy to see in WKO with the Check My Speed Channel chart included in the WKO Chart Library (click here to learn how to add this chart to a workout dashboard). This chart (pictured below) includes two data series: speed and deltadistance/deltatime. We can see that the speed channel (red) is not equal to deltadistance/deltatime (blue). It shows signs of smoothing, because high frequency spikes are missing and it’s shifted slightly right. This seems like a good idea, because the GPS positioning is a bit jittery and probably not very precise on a second-by-second basis. We can see by the cursor position that deltadistance/deltatime(blue) has a spike that shows over 23 km/h; the speed channel (red) reports a probably more realistic 10 km/hr.

Compare that chart to a bike ride (charted below) that uses a magnetic switch speed sensor for speed and distance instead of GPS. The deltadistance/deltatime line (blue) is nearly indistinguishable from the speed channel. In a couple places we see a small amount of blue underneath the red where it’s different by 0.03 km/hr. We can conclude that when using GPS for distance, your speed channel will no longer equal your distance divided by time. The speed channel is more accurate for second-by-second speed measurements, but over a longer period of time (minutes or hours), the deltadistance/deltatimemethod is more accurate.

What does this mean for WKO? If you want to find your average speed when using GPS speed and distance (as opposed to a magnetic speed or distance sensor), you should use deltadistance/deltatime in your expressions.

Here are a few example scenarios:

For average speed, use
distance/duration
avg(speed)

For average pace, use
60/(distance/duration)