Calculator Inputs
Example Data Table
Use similar maximal efforts from fresh sessions. Distances should not be too close together.
| Trial | Distance | Time | Use |
|---|---|---|---|
| Short trial | 1500 m | 5:00 | Captures faster race ability. |
| Middle trial | 3000 m | 10:45 | Anchors the linear model. |
| Long trial | 5000 m | 18:30 | Checks endurance durability. |
| Target | 10000 m | Projected | Creates race estimate and pace. |
Formula Used
The calculator models distance as a linear function of time:
Distance = Critical Velocity × Time + D-prime
For two trials, critical velocity is calculated as:
CV = (Distance2 - Distance1) / (Time2 - Time1)
For three trials, it uses least-squares regression. The slope is critical velocity. The intercept is D-prime. Pace is calculated with Pace = Distance unit / CV. Race projection uses Time = (Target distance - D-prime) / CV. The fatigue allowance increases the projected time.
How to Use This Calculator
- Enter two or three recent maximal trial results.
- Choose the trial distance unit.
- Enter a target race distance.
- Add a fatigue allowance for conservative pacing.
- Use zone adjustment for heat, hills, or training load.
- Press the calculate button.
- Review the result cards, graph, fit table, and zones.
- Download the CSV or PDF report for your records.
Critical Velocity Pace Guide
What Critical Velocity Means
Critical velocity is a physics based estimate of sustainable speed. It comes from the distance and time relationship. When maximal efforts are plotted, the slope of the best fit line gives velocity. This value is useful because it is tied to real performance. It is not a guess from heart rate alone.
Why Runners Use It
Runners and coaches use critical velocity to set repeat paces. The number often sits near strong threshold intensity. It can guide tempo runs, long intervals, and race planning. It also helps compare fitness across training blocks. If the same trials produce a faster slope, the athlete has improved.
Understanding D-prime
D-prime is the distance intercept. It represents a limited reserve above the critical pace. A larger value may show better short duration capacity. It should not be treated as endless energy. It is best used as a supporting metric with the main velocity estimate.
Choosing Good Trials
Use maximal efforts from similar conditions. Good trial pairs may include 1500 m and 3000 m. A third trial can improve confidence. Avoid using a tired workout as a test. Avoid mixing road, track, and steep hill results without adjustment. The model assumes honest efforts and stable conditions.
Using The Projection
The projected time is a planning tool. It is not a promise. Weather, pacing, fueling, and terrain can change the result. The fatigue allowance adds a safer margin. Training zones should also be adjusted when the athlete is tired. Use the chart to see whether trial points follow a clean line.
Coaching Note
Review the R squared value before making decisions. A high value suggests that the trial set fits the model. A lower value means the tests may be uneven. Repeat testing every few weeks can show progress. Keep the same distances when possible. This makes comparisons clearer and more useful.
FAQs
What is critical velocity?
Critical velocity is the estimated speed an athlete can sustain near the boundary between heavy and severe effort. It is found from maximal time trials.
How many trials are needed?
Two trials are enough for a basic model. Three trials are better because they allow a fit check and reduce single-test error.
Should trials be done on the same day?
They can be, but fatigue may distort results. Many athletes get cleaner data by testing on separate days under similar conditions.
What does D-prime mean?
D-prime is the distance reserve above critical velocity. It reflects short duration capacity, but it should not be viewed as unlimited energy.
Why is my D-prime negative?
A negative value often means the trials were uneven, not maximal, or too similar. Recheck distances, times, and testing conditions.
Can this predict race times?
It can estimate race time from your model. Actual performance still depends on terrain, weather, pacing, fueling, and race execution.
What is a good R squared value?
A value near 1.0000 means the trial points fit the line well. Lower values suggest more testing or cleaner data may help.
How often should I recalculate?
Recalculate every four to eight weeks, or after a major training block. Use similar trials so progress comparisons remain fair.