Math for Sprinters - Step Frequency and Stride Length
Updated: Nov 23, 2020
In this post, I break down sprinting into Step Frequency and Stride Length in the context of the 100m, 200m, and 400m sprints. I discuss Usain Bolt, Tyson Gay, and some of the best sprinters of all time. I then compare Bolt and Gay to some of the top runners in the NCAA and San Diego high schools. I close by discussing key drills to improve your stride length and step frequency.
To read about 5k running math for distance runners, see also my post on 5K Running Math - Cadence and Stride Length.
1. Basic Sprinting Math
There are two ways to run faster:
Take longer steps (cover more ground with each step), and
Take faster steps (move your arms and legs faster).
Two key terms for every runner are (1) Stride length and (2) Cadence. Stride length (or step length, see footnote ) is the length of each step, and cadence is the number of steps per minute. In the formulas below, Stride Length and Cadence are averages throughout a race.
Formula 1. Finishing Time (minutes) = Race Distance / ( Stride Length * Cadence )
The sprints are timed in seconds rather than minutes, so I find it more useful to think in step frequency (steps per second) rather than cadence. The translation from cadence to step frequency is simple - just divide by 60! A 180 cadence is 3 steps per second, a 240 cadence is 4 steps per second, and a 300 cadence is 5 steps per second. Most sprinters will have a step frequency between 3 and 5 during their races.
Formula 2. Finishing Time (seconds) = Race Distance / ( Stride Length * Step frequency )
Example. If a sprinter's average stride length is exactly 2.0 meters, it will take exactly 50 steps to complete the 100m. To complete 50 steps in 10.0 seconds, the sprinter will have to average 5 steps per second.
2. Usain Bolt's World Record 100M in 9.58 seconds
Usain Bolt ran the 100m in a blazing 9.58 seconds to set the world record in Berlin at the 2009 World Championships.
Check out the photo finish below. Bolt's 9.58 is the fastest time ever! Tyson Gay's 9.71 stands as the 6th best 100m dash time ever recorded, and Asafa Powell isn't too far behind at 9.84.
Where are each of these guys on the (step frequency / stride length ) curve?
When we are considering only the elite times, let's zoom in on the chart, as we only need to consider times under 10.5 seconds.
Here are what the data look like in a table:
In addition, here are the data from the NCAA Division 1 2018 final:
Here are the data in a chart. The blue dots are the 2009 World Championships and the red dots are the NCAA Championships.
The striking pattern that emerges is the red dots are all clustered together with higher step frequency and lower stride length.
From this sample, the super elite sprinters actually have lower step frequencies than their college counterparts. They win with longer stride lengths!
3. How to Measure Stride Length and Step Frequency
Here is how to measure it. You can do this yourself at home:
Film a clear video of the athlete running the race (use the video above)
Watch the video in slow motion (or scroll through by hand slowly) and count steps
Note the number of steps it takes the athlete to cross the finish line. Round to the nearest 0.5 steps.
Calculate Stride length = race distance / steps
Calculate Step frequency = race distance / ( finishing time * stride length )
Data Collection Procedure. I watched each video 16 times, counting each athlete's steps twice (always double-check your work). If you notice any errors or have questions, kindly email me at email@example.com.
4. The Running Mountain (100m)
In this section, we will zoom out to view what it looks like in these races:
The top NCAA Men's Division 1 runners, compared with
Some of the boys high school runners in San Diego, CA
Results of NCAA Division 3 Championships, Men's 100m Final
Full race results here 2018 NCAA Division 1 Championships Men's 100m Final
Bronco Invitational Results, March 9, 2019 (San Diego High School Boys)
Zooming a little further out to the distribution of top 100m dash times, of all time, the 10.09 mark has been beaten 3,160 times as of August 2018.
These data come from the All-time Athletics list of top 100m times ever recorded. The distribution takes the shape of a mountain, as many running time distributions do. It's a long road to the top.
5. How to Improve Stride Length
Here are some good drills to improve step frequency:
Improve your hip flexibility (hurdle drills, yoga, hip stretches)
Improve your calf flexibility (calf stretches, foam rolling, yoga, massage / roll your calfs and feet)
Improve your ankle mobility (foot exercises, ankle exercises)
Improve your foot strength (foot exercises, ankle exercises)
Improve your power (plyometrics, bounding, acceleration drills, weight lifting)
Practice running with big steps (bounding drills)
Practice moving your arms and legs in big movements
Practice moving your arms and legs forward / backward and making sure to limit side-to-side movement
Monitor your stride length in races and workouts
Measure your stride length with a yard stick standing still in a lunge pose. How far can you get while maintaining "good running posture"? Is it the same distance with both legs?
6. How to Improve Step Frequency
Here are some good drills to improve step frequency:
Drills to decrease ground contact time (plyometrics, bounding, box jumps, jump rope)
Fast leg drills to increase leg speed
Strides and running with emphasis on fast quick steps
Stair drills with emphasis on fast, quick steps
 Some sources define a stride as heel-to-heel, meaning the length of 2 steps. Much of the running literature uses "stride length" and "step length" interchangeably. I use stride length in this article to mean the length of one step, following the convention of Garmin products I use to collect data.
The Science of Running, Understanding Stride Rate and Stride Length, https://www.scienceofrunning.com/2010/11/speed-stride-length-x-stride-frequency.html?v=7516fd43adaa (accessed 3/27/2019).
SimpliFaster.com, Stride Length vs. Stride Frequency in Reaching Max Speed, Dr. Hristo Stoyanov, https://simplifaster.com/articles/stride-length-vs-stride-frequency/ (accessed 3/29/2019)