Tinman Running Calculator

1. Pick the distance of a recent race or time trial and enter your finish time.
2. Keep the fatigue exponent at 1.06, or change it. Optionally add a second race at another distance.
3. Read your race pace, the predicted times for other distances and, with two races, your critical speed pace.

About the Name

"Tinman" refers to a coach's published training-pace system, and runners search for it by that name. We could not find its pace formulas on a public page we could cite, so this calculator does not reproduce them. It uses published general methods instead: the Riegel formula and critical speed. This page is not affiliated with or endorsed by the Tinman coach or his programs.

A race equivalency calculator predicts what you could run at one distance from a result at another. It answers "if I ran 25:00 for 5K, what is my 10K or marathon potential?"

The standard tool is the Riegel formula. Most race predictors are built on it, according to Vickers and Vertosick, who note it came from a study of world-record times across endurance sports. Its key number is the fatigue exponent k.

Critical speed (CS) is a second, related idea from exercise physiology. Research describes it as the speed that separates the heavy and severe intensity domains, linked to the maximal metabolic steady state. For pace basics, see how to calculate your running pace.

The tool scales your race time by distance raised to the power k, then, with two races, fits a straight line of distance against time.

1. Race equivalents. With k = 1.06, doubling the distance multiplies the time by 2^1.06 = 2.085, so the pace slows about 4%.
2. Personal exponent. Two races give your own k. Vickers and Vertosick used k between two races to improve marathon predictions.
3. Critical speed. The linear model d = D prime + CS x t (Monod and Scherrer) is solved with your two races. The slope is CS and the intercept is D prime.
4. Paces. Every time is divided by its distance and shown per mile (1,609.344 m, NIST) and per km.

When both races are entered, predictions start from the longer race, as in the study's approach.

A runner has a recent 5K in 25:00, a pace of 8:03 per mile (5:00 per km).

Riegel with k = 1.06: 10K = 1,500 s x 2^1.06 = 52:07. The mile predicts 7:31, the half marathon 1:55:00 and the marathon 3:59:47. With k = 1.08, the marathon becomes 4:10:14.

Adding a mile in 7:00: k = ln(1500 / 420) / ln(5000 / 1609.344) = 1.12. Critical speed = (5000 - 1609.344) / (1500 - 420) = 3.14 m/s, a pace of 8:33 per mile (5:19 per km). D prime = 1609.344 - 3.14 x 420 = about 291 m.

Meaning: this runner slows more with distance than the default assumes, so the personal k predicts a 54:27 10K and a 4:34:13 marathon. Endurance, not speed, is the gap to work on. The old version of this tool would have shown a marathon of about 3 hours 31 minutes from the same 5K, because it held 5K pace for every distance.

The fatigue exponent, the gap between distances and your training for the longer race all move the result.

The Fatigue Exponent

Vickers and Vertosick report that Riegel cited k of about 1.08 for elite runners and 1.05 to 1.06 for male recreational runners aged 40 to 70. A small change in k makes a big change over a long jump in distance.

Distance of the Jump

The study found Riegel well calibrated up to the half marathon but too fast for the marathon. About half of runners ran at least 10 minutes slower than predicted.

Training Volume

The same study found that weekly mileage predicted marathon speed. A runner with low mileage should expect a slower marathon than any formula shows.

Course and Weather

Hills, heat, wind and surface all slow a race. Use a flat, cool race as the input when you can.

Race Selection for Critical Speed

Critical speed studies used exhaustive efforts of roughly 2 to 20 minutes. Two races far longer than that give a rougher estimate.

The two methods answer different questions, and they work well together.

What Happened to the Old Training Paces?

The previous tool multiplied race speed by fixed percentages from 58% to 130% and labelled them as the Tinman formula, without a source. It also held one pace from 100 m to 100 miles. Those outputs were removed, because they could not be verified and the equal-pace times were wrong.

Setting a Goal Time

Use a recent race to pick a realistic target for your next event, then check the pace in the 5K, 10K and marathon pace charts.

Planning Training Intensity

With two races, use critical speed as a guide: steady runs below it, hard intervals above it. Pair it with effort guides in heart rate zones explained.

Tracking Fitness

Re-enter a new race every few weeks. A faster critical speed or a lower personal k shows progress.

Learning the Method

Read more about prediction limits in running pace and race time predictions.

1. Predicting a Marathon from a Short Race

The jump is large, and the study shows Riegel runs fast for the marathon. Add time, or use a half marathon as the input.

2. Using a Training Run as the Input

The formula assumes an all-out effort. A comfortable run gives slow predictions.

3. Mixing Old and New Races

For critical speed, use two races from the same few weeks, when fitness was similar.

4. Using Two Very Similar Distances

A 5K and an 8K sit close together, so small timing errors swing k and CS a lot.

5. Running Every Workout at Critical Speed

It is a boundary, not a daily pace. Most running is easier.

6. Ignoring Conditions

A hot or hilly race understates your fitness. Pick a fast, fair course as the input.

The formulas are computed exactly, but a prediction is only as good as the model and the input race. Riegel is reliable up to the half marathon and optimistic for the marathon.

No. This page is independent and not affiliated with the Tinman coach. It uses the published Riegel formula and critical speed instead of his formulas.

Vickers and Vertosick found it well calibrated for races up to a half marathon. For the marathon it was too fast, by 10 minutes or more for about half of runners.

It means each doubling of distance multiplies your time by about 2.085. So your pace slows about 4% every time the distance doubles.

It is the highest speed you can hold in a metabolic steady state. Research uses it to separate the heavy and severe intensity domains.

D prime is the fixed distance you can cover above critical speed before you must slow down. It works like a reserve that hard surges use up.

Use two all-out efforts at clearly different distances from the same few weeks, such as a mile and a 5K.

A higher k means you slow more as distance grows. It often shows speed that is ahead of endurance.

You can, but treat it as a best case. A half marathon makes a better input for a marathon goal.

Not well. Hills and terrain change pace in ways the formulas do not model.

No. The math runs in your browser and nothing is sent to us. Save keeps a result only in this browser.

• An empirical study of race times in recreational endurance runners (Vickers and Vertosick, 2016) (BMC Sports Science, Medicine and Rehabilitation, via PubMed Central; Riegel formula, exponent values, calibration).
• Critical speed estimated by statistically appropriate fitting procedures (European Journal of Applied Physiology, via PubMed Central; linear distance-time model and intensity domains).
• Optimization of the Critical Speed Concept for Tactical Professionals: A Brief Review (via PubMed Central; critical speed, D prime and test durations).
• NIST Guide to the SI, Appendix B.8 conversion factors (NIST; the mile as 1,609.344 m).