# Cadence as a Training Tool

The first thing many runners do when they sign up for a race where they want to set a PR (personal record) or get on the podium in their age group is to find a training plan to follow. There’s nothing wrong with downloading a free training plan off the Internet or using one that’s built-in to your favorite running app but the training plan should be just one step. Once a runner has a plan, it would be ideal for them to start working with a coach who can help them figure out how to do the workouts on the plan to get the most benefit, as well as tailoring the plan to fit their schedule and fitness level. This blog post outlines how coaches and runners can consider using cadence as a training tool to help get the most out of a well-designed training program.

## The Running Speed Equation

I have a background in math, so I’ve always been interested in using mathematics in my coaching to help runners understand what they can do to improve their running and ultimately run faster as part of their training.

There are direct, mathematical relationships between some variables that affect speed that are under a runner’s control, and understanding the relationship between these variables, as well as being able to *change these variables in favorable ways*, can help runners run faster and meet their race day goals.

The mathematical relationship that interests me the most is between cadence (the number of steps/strides a runner takes in one minute of running) and stride length (the distance a runner travels from one footfall to the next). The fundamental relationship is simple: The product of these two variables equals your running speed.

*cadence x stride length = running speed*

Let’s examine this equation in more detail with a sample scenario.

*Two runners each ran a mile. Their average cadence and stride lengths were recorded below:*

*Runner A: 170 steps per minute and 0.75 m stride length. (~ 30 inches)**Runner B: 175 steps per minute and 0.88 m stride length (~35 inches).*

*The question is, which runner ran faster?”*

Basic logic would tell you that Runner B must have run faster because his **legs were moving faster** for the same distance (one mile), and **each of these quick steps was longer** than Runner A’s. Of course, this is precisely the case. To prove it, the data points in the example scenario above were actually pulled from my Garmin after a recent run (see Figure 1), which shows that the faster pace resulted from the 175/0.88 combination of cadence and stride length.

## Can you calculate your running speed from cadence and stride length?

The short answer is “yes.” But the bigger question is, “How?”. The answer is more complicated than you might think.

First, for whatever reason, Garmin and most other run-tracking systems measure stride length using metric units (meters). Yet, they measure pace and speed using imperial or standard units (minutes per mile or miles per hour, for example). The second thing that makes it complicated is that even the units in the same “system” are different (pace uses *minutes* per mile, speed uses miles per *hour*, and cadence uses steps per *minute*.) And since time isn’t a ten-based system like the metric system, it’s challenging to calculate anything measured in minutes or hours. But I’m digressing off the main point. How can we calculate speed or pace if we know cadence and stride?

Earlier in this blog post, I mentioned that I was a math geek and loved calculating and using my math brain. Years ago, after extensive research on the Internet, I could not find a mathematical formula that would enable me to make these calculations, so through trial and error reasoning, I derived the formula for myself. See Figure 2.

*Note: Cadence must be measured in steps per minute and stride length in meters for this formula to work.*

Let’s give an example. What would the average running pace be if a runner’s average cadence is 180 and her stride length is one meter?

- First, we multiply 180 by one and get 180 (cadence times stride length, the inner parentheses).
- Then we divide 5,280 by 180, and we get 29.33 to complete what’s in the outer parentheses.
- Then we multiply 29.33 by 0.3048, and we get 8.9408. This means that the runner’s pace would be 8.9408 minutes per mile. But pace is usually written in hours/minute format, so we have to convert the decimal 0.9408 to minutes by multiplying it by 60 to get 56.

Therefore, if a runner averages a cadence of 180 and a stride length of one meter, her average pace would be 8:56 (minutes per mile).

Once I had figured out the formula mentioned above, I decided to try to create a calculator tool to do the calculations so I wouldn’t have to do them manually. I started with a spreadsheet version, and it worked well. Click here to access that spreadsheet. Enter your cadence and stride length in cells C7 and E7 to see what your pace will be (cell G7). Give it a try!

After creating the spreadsheet version of my cadence/stride length calculator, I decided to put it up on my website, offtoarunningstart.com, so I could share it with others because it could be used as a helpful training tool (more on that in a minute). I used a free tool called Calconic to create the calculator and put it on the website. Here is a link to the webpage with the calculator tool. *Please note that since Calconic doesn’t offer a way to convert decimal time into minutes, you will have to use the conversion table below the calculator to convert Pace into Min:Sec format.*

Have some fun trying out the calculator and read my next blog post, Using Cadence as a Training Tool, Part 2, when I post it next week.

*Keep running to the beat! And leave a comment to let me know if the calculator was helpful.*

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