Critical Running Speed CalculatorFree online fitness & health calculator — instant results, no sign-up
Fit a two-trial critical speed model from maximal running efforts.
For general information only. This is not medical advice, diagnosis, dosing guidance or a treatment recommendation. Talk to a doctor or other qualified health professional about your health, pregnancy, or diet.
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About the Critical Running Speed Calculator
The Critical Running Speed Calculator fits a two-trial critical speed model using the distances and times from a short and a long maximal running effort. It estimates critical speed and distance reserve D′ from the straight-line relationship between distance and time. The results describe a simplified running-performance model, not a guaranteed sustainable pace.
- Short trial distance (m)
- The distance covered during the shorter maximal running trial, entered in meters; the default is 1000 m.
- Short trial time (seconds)
- The elapsed time for the shorter maximal running trial, entered in seconds; the default is 240 seconds.
- Long trial distance (m)
- The distance covered during the longer maximal running trial, entered in meters; the default is 3000 m.
- Long trial time (seconds)
- The elapsed time for the longer maximal running trial, entered in seconds; the default is 780 seconds.
Formula and method
Distance–time model: d = CS × t + D′. Two-trial fit: CS = (d_l − d_s) / (t_l − t_s); D′ = d_s − CS × t_s. With the defaults: CS = (3000 − 1000) / (780 − 240) = 2000 / 540 ≈ 3.7 m/s; D′ = 1000 − (2000 / 540) × 240 ≈ 111.11 m. Calculate D′ using the unrounded CS.
- dModeled running distance in meters.
- tRunning duration in seconds.
- d_sShort trial distance in meters.
- t_sShort trial time in seconds.
- d_lLong trial distance in meters.
- t_lLong trial time in seconds.
- CSCritical speed in meters per second, represented by the slope of the fitted distance–time line.
- D′Distance reserve in meters, represented by the intercept of the fitted distance–time line.
Subtract the short trial distance from the long trial distance and divide by the difference in trial times to obtain critical speed. Substitute that unrounded speed and either trial's distance and time into D′ = d − CS × t to obtain distance reserve. Round only the displayed results. The two observations determine the line exactly; they do not independently establish how well the model predicts other efforts.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Short trial distance1000 m
- Short trial time240 seconds
- Long trial distance3000 m
- Long trial time780 seconds
Results
- Critical speed3.7 m/s
- Distance reserve D′111.11 m
- NoteApproximation; individual results vary.
How to use the Critical Running Speed Calculator
- 1Choose two maximal running trials of different durations, completed with adequate recovery and under comparable conditions.
- 2Enter the short trial distance in meters and its elapsed time in seconds; the default entries are 1000 and 240.
- 3Enter the long trial distance in meters and its elapsed time in seconds; the default entries are 3000 and 780.
- 4Check that all entries are positive, the long trial takes more time and covers more distance, and the shorter trial has the higher average speed.
- 5Run the calculation and review critical speed, distance reserve D′, and the approximation note together.
Reading your result
Critical speed = 3.7 m/s: this is the fitted slope for the default trials, estimating the boundary between running intensities where physiological responses may stabilize and those where fatigue progressively develops; it is not an indefinitely sustainable speed. Distance reserve D′ = 111.11 m: this is the model's finite distance capacity above critical speed, not an extra distance you can necessarily run after any workout. Note = Approximation; individual results vary: treat both estimates as model-based guidance rather than precise physiological measurements.
Limitations
The model assumes both trials reflect maximal performance at a similar fitness level, with accurate distance and time measurements and comparable terrain, weather, and recovery. Pacing errors, fatigue, wind, hills, or trials that are too similar in duration can substantially affect the estimates. Two trials provide no redundancy for assessing fit quality, and extrapolation to very short sprints or long endurance events can be misleading. Equal trial times make the calculation undefined; nonpositive critical speed or a negative D′ suggests unsuitable data or a poor model match. Maximal testing is strenuous and may not be appropriate for every runner.
Common questions
Why does using 3.7 m/s in the D′ formula not reproduce 111.11 m?+
The displayed critical speed is rounded. For the default trials, the calculation retains CS = 2000 / 540 m/s when computing D′ = 1000 − CS × 240, which rounds to 111.11 m.
Can I use an easy run as one of the two trials?+
No, not for a meaningful maximal-performance estimate. Both trials should be maximal efforts for their respective distances; an easy run can shift both the fitted critical speed and D′ away from your actual performance profile.
What does a negative distance reserve D′ mean?+
It is not a useful physiological reserve estimate in this model. Check the entries and whether the shorter trial was genuinely maximal: with a longer-distance, longer-duration second trial, a negative D′ occurs when the shorter trial's average speed is lower than the longer trial's.
Can I predict another running time from these outputs?+
The fitted model can be rearranged to t = (d − D′) / CS, using unrounded values. Such predictions are approximations and are most defensible for comparable maximal efforts near the tested duration range, not for arbitrary sprint or marathon distances.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.