I recently published a critical speed calculator app, which makes it super easy to use the critical speed model to estimate your steady-state max. However, the critical speed model is not the most accurate way to predict race performance at new distances—that honor belongs to power law models (sometimes also called Riegel models, after Pete Riegel who popularized their use in running).
I covered the science behind power law models in this earlier article on power law models versus critical speed models for predicting race times. Thanks to the infrastructure I built for the critical speed model, it was super easy to swap out the statistical model for a power law model: so now I have a brand-new power law calculator too!
⏱️ Try my power law calculator here ⏱️
Power law models are great for extrapolating—for example, predicting your half marathon time from a 5k and a 10k, or predicting your 400m time from an 800m and a 1500m time. They perform much better at this task than the critical speed model, and my power law calculator also includes some useful features for prediction.
First among these is uncertainty intervals. If you enter three or more performances (at any distance, including repeated races over the same distance, e.g. a 5k plus two 10ks), you get a 90% uncertainty range for your race performances at any new distances. Though there are still assumptions that go into this uncertainty range, I’ve found them to be quite accurate so far.
There’s also a handy list of all common race distances, which you can filter by discipline: sprints, track events, road races, and cross-country. Plus, you can input custom distances, which is great if you are doing workouts at, for example, “30k pace.”
You can also get the per-mile, per-km, per-400m, or per-200m pace for your predicted performances at any distance, which makes it easy to figure out your predicted race pace (though I do have a separate race pace calculator if you need it!).
Now, there’s one downside that power law models share with the critical speed model: you need at least two performances over different distances to get good predictions. I am working on assembling a larger database of performances so you can get a range of possible race times at other distances given just one performance; that will be a separate calculator at some point in the future.
If you do only have one race performance to work with, remember that I have a critical-speed-based CV/Threshold/VO2max calculator that requires just one performance to use.
As always, let me know if you find any bugs or would like to see any new features!
⏱️ Use the power law calculator here ⏱️
Learn how to train with precision
If you want to apply a more scientific approach to your own training, I have two books that outline exactly how to do it. The most recent is Marathon Excellence for Everyone, which takes a full-spectrum percentage-based approach to running your best in the marathon.
If you live outside of the United States, Marathon Excellence is also available in a Metric Edition, with all workouts in kilometers!
I also have a shorter book, Modern Training and Physiology for Middle and Long-Distance Runners, that covers a simpler scientific approach to 800m–10k training. Check it out!
If you want to get updated when I have a new app, new book, or new article coming out, the best way to do it is to join my free email list below. I’m also on Instagram at @jdruns but by far the best way to follow my work is my email list!
See more of my apps
New web app: Predicting LT1 pace and Zone 2 pace from 5k time
New app for making power law predictions for race performance
New web app for calculating critical speed
New features in my pace percentage calculator
New calculator for track workouts on windy days
The Marathon Excellence plans are now supported by the Defy Calendar Hack
New web app: a fast and simple race pace calculator for runners
