Critical Speed Calculator
Determine your CS and D' from time trial efforts — unlock your speed-duration profile
Critical Speed (CS) is the highest running speed you can sustain aerobically without progressive fatigue. D' (D prime) is your finite distance capacity above CS — think of it as your battery. Together, CS and D' define your entire speed-duration relationship. Enter 2 to 5 maximal efforts of different durations and we'll calculate your running profile using the Monod & Scherrer (1965) model.
This calculator provides estimates based on the 2-parameter Critical Speed model. Results depend on effort quality — all trials must be true maximal efforts. CS is not a single-session measurement: validate with field testing. Consult a coach or sports scientist for personalized training advice. TrainingZones.io is for informational purposes only.
Runner Levels — Where Do You Stand?
Classification based on estimated VMA from Critical Speed. CS is approximately 83-90% of VMA for trained runners.
| Level | VMA (km/h) | CS (km/h) |
|---|---|---|
🛋️Sedentary | 0-8 | 0-7 |
🚶Beginner | 8-10 | 7-8.7 |
🏃Jogger | 10-12 | 8.7-10.4 |
💪Active Runner | 12-14 | 10.4-12.2 |
⚡Good Runner | 14-15.5 | 12.2-13.5 |
🔥Athletic | 15.5-17 | 13.5-14.8 |
🏅Competitive | 17-18.5 | 14.8-16.1 |
🏆Elite | 18.5-20 | 16.1-17.4 |
🇫🇷National Level | 20-21.5 | 17.4-18.7 |
👑World Class | >21.5 | >18.7 |
Testing Protocols
Two proven methods to determine your Critical Speed and D'
The Science Behind Critical Speed
The CS model is the running equivalent of Critical Power, first described by Monod & Scherrer in 1965 and validated for running by Vanhatalo et al. (2011).
Linear Model — Distance vs Time
Total distance d increases linearly with time. The slope of this line is CS (m/s), and the y-intercept is D' (meters). This is how we calculate CS from your time trial data using linear regression.
Hyperbolic Model — Speed vs Time
Running speed v for a given duration t follows a hyperbola. As time increases, speed approaches CS asymptotically. The curve is fully defined by just two parameters: CS (the asymptote) and D' (the curvature constant).
Time to Exhaustion — The Countdown
Rearranging the formula gives the predicted time until exhaustion at any speed above CS. Your D' empties at a rate of (v - CS) meters per second, so higher speed means shorter time. Below CS, the model predicts infinite endurance (in theory).
Key Variables
Critical Speed — the boundary between sustainable and unsustainable running intensities, in m/s or km/h
D prime — your distance capacity above CS, measured in meters. The running equivalent of W' in cycling.
Time to exhaustion — how long you can hold a given speed above CS before D' is fully depleted
Maximal Aerobic Speed — estimated from CS (VMA ≈ CS / 0.87). Your top speed using only aerobic energy.