Critical Speed Calculator
Fit critical speed and D′ from multiple timed running efforts. Inspect distance-time fit, residuals and the speed-duration curve.
Running performance inputs
Your critical speed profile
4 m/s · estimated critical speed
D′: 280.00 m · fitted intercept
Full result table
| Test | Seconds | Entered metres | Distance (m) | Fitted distance (m) | Residual (m) |
|---|---|---|---|---|---|
| 1 | 180 | 1,000 | 1,000 | 1,000 | 0 |
| 2 | 360 | 1,720 | 1,720 | 1,720 | 0 |
| 3 | 540 | 2,440 | 2,440 | 2,440 | 0 |
Use 3–6 comparable maximal efforts lasting 2–20 minutes. Positive slope and positive intercept are required. R² describes fit to these entries, not physiological accuracy. Extrapolations outside the entered duration range are not shown. This model does not give a safe exercise duration or recovery prescription.
Let’s work it out.
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How to use Critical Speed Calculator
- Enter one list of durations in seconds and a second list of metres.
- The model uses ordinary least squares with an intercept.
- Switch between the fitted relationship, the duration curve and the data table.
Worked example
Distances 1,000, 1,720 and 2,440 metres at 180, 360 and 540 seconds give CS = 4 m/s and D′ = 280 m, an exactly linear distance-time example.
Formula, accuracy & limitations
Ordinary least squares fits distance (m) = CS × time (s) + D′. Modelled average speed at t seconds = CS + D′/t.
Use 3–6 comparable maximal efforts lasting 2–20 minutes. Positive slope and positive intercept are required. R² describes fit to these entries, not physiological accuracy. Extrapolations outside the entered duration range are not shown. This model does not give a safe exercise duration or recovery prescription.
These outputs use the stated model and your supplied inputs. A mathematically consistent model can still differ from personal measurements. Scenario curves and formula comparisons are not statistical confidence intervals.
Read the research and method reference ↗Enter matched test pairs
Enter one list of durations in seconds and a second list of metres. The order must match. Use three to six distinct durations, and keep equipment, measurement method and conditions as comparable as possible. This is a test-analysis tool, not a request to perform maximal efforts without appropriate preparation.
Inspect fit before interpreting the headline
The model uses ordinary least squares with an intercept. Residuals show each entered value minus the fitted value. Poor alignment, non-decreasing average output or an implausible intercept can indicate inconsistent efforts or a model that does not fit the data. A high R² alone cannot establish a valid physiological threshold.
Keep the curve inside the tested range
Switch between the fitted relationship, the duration curve and the data table. Predictions stay between your shortest and longest entered efforts. The intercept represents a fitted model parameter, not an independently measured tank of energy or distance that can be freely spent and refilled.
Frequently asked questions
Can I use only two tests?
This version requires at least three so it can show residuals and fit quality. Two points always define a straight line and cannot provide the same internal consistency check.
Why was my intercept rejected?
A zero or negative intercept does not support this positive-capacity two-parameter model. Check the order, units and comparability of the tests instead of forcing the result to look plausible.
Does R² close to one prove accuracy?
It means these points lie close to the fitted line. Shared measurement error, unsuitable protocols or too narrow a duration range can still yield a misleading physiological estimate.
Can I predict an hour-long effort?
The output is limited to the entered duration range. Extending a short-effort model to an hour would imply more certainty than these inputs support.
