Quick answer
Jack Daniels' VDOT converts a race result into a fitness score and training paces using VO₂ = −4.60 + 0.182258v + 0.000104v² and %VO₂max = 0.8 + 0.1894393e^(−0.012778t) + 0.2989558e^(−0.1932605t). A 19:57 5 km gives a VDOT of about 50, with easy running at 5:52 to 4:54 per km and threshold pace of 4:15 per km.
Enter a recent race distance and time. The calculator returns the VDOT estimate and training paces.
Related tools: Race Time Prediction Calculator: Predict a finish time at another distance with Riegel's formula. Marathon Pace Calculator: Pace needed to finish a race distance in a target time. Pace Distance Calculator: Distance covered at a steady pace for a given time.
How to use the Running Training Pace Calculator
- Choose race distance: 1500 m, 1 mile, 3000 m, 2 miles, 5 km and 10 km and 4 more.
- Enter hours (a whole number, between 0 and 9). It starts at 0.
- Enter minutes (a whole number, between 0 and 59). It starts at 0.
- Enter seconds (between 0 and 59.99). It starts at 0.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Race distance | Choose one: 1500 m; 1 mile; 3000 m; 2 miles; 5 km; 10 km; 15 km; 10 miles; … | Starts at 5 km |
| Hours | A whole number | ≥ 0, ≤ 9, starts at 0 |
| Minutes | A whole number | ≥ 0, ≤ 59, starts at 0 |
| Seconds | A number | ≥ 0, ≤ 59.99, starts at 0 |
Formula and method
Formula
VO₂ = −4.60 + 0.182258 v + 0.000104 v²; %VO₂max = 0.8 + 0.1894393 e^(−0.012778 t) + 0.2989558 e^(−0.1932605 t); VDOT = VO₂ ÷ %VO₂max; training speed = the v whose VO₂ equals the chosen share of VDOT
IEEE-754 double precision; shown to at most 6 decimal places.
Applies the Daniels–Gilbert equations (v in metres per minute, t in minutes): the oxygen cost of running at a speed, and the fraction of maximal oxygen uptake a runner can sustain for a race of that duration. Dividing gives a performance-based VO₂max estimate. Training paces are the speeds that cost 59–74% (easy), 88% (threshold) and 98% (interval) of that value. The result is a formula-based estimate for flat running, not a lab test, and it fits races of roughly 3 to 240 minutes best. Easy paces should feel conversational; heat, hills and fatigue change the right pace.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Race distance = 5 km; Hours = 0; Minutes = 19; Seconds = 57.
| Result | Value |
|---|---|
| VDOT (estimated VO₂max) | 50 |
| Easy pace per km | 5:52 to 4:54 (slow to fast end) |
| Easy pace per mile | 9:27 to 7:53 |
| Threshold pace (88%) per km | 4:15 |
| Threshold pace per mile | 6:51 |
| Interval pace (98%) per km | 3:54 |
| Interval pace per mile | 6:17 |
Example 2
Inputs: Race distance = 5 km; Hours = 0; Minutes = 25; Seconds = 0.
| Result | Value |
|---|---|
| VDOT (estimated VO₂max) | 38.3 |
| Easy pace per km | 7:14 to 6:03 (slow to fast end) |
| Easy pace per mile | 11:38 to 9:44 |
| Threshold pace (88%) per km | 5:16 |
| Threshold pace per mile | 8:29 |
| Interval pace (98%) per km | 4:50 |
| Interval pace per mile | 7:47 |
Example 3
Inputs: Race distance = Half marathon; Hours = 1; Minutes = 45; Seconds = 0.
| Result | Value |
|---|---|
| VDOT (estimated VO₂max) | 42.6 |
| Easy pace per km | 6:39 to 5:34 (slow to fast end) |
| Easy pace per mile | 10:42 to 8:57 |
| Threshold pace (88%) per km | 4:50 |
| Threshold pace per mile | 7:47 |
| Interval pace (98%) per km | 4:26 |
| Interval pace per mile | 7:08 |
The first line is the headline result (vDOT (estimated VO₂max)). Below it the running Training Pace Calculator lists easy pace per km, easy pace per mile, threshold pace (88%) per km, threshold pace per mile, interval pace (98%) per km and interval pace per mile, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
How VDOT works
The first equation estimates oxygen cost from running speed v (m/min); the second estimates the fraction of VO₂max you can sustain for a race of t minutes. Dividing gives VDOT, an 'effective' VO₂max that predicts training paces from one result.
Use the right inputs
The equations work best for races between about 3 minutes and 4 hours. Use a recent, all-out effort. Paces shown are guides; adjust for heat, hills and fatigue. This is not a coaching or medical programme.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Minutes: entering "0" shows "Enter your finishing time." beside that field and no result.
Choosing between the Running Training Pace Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Race Time Prediction Calculator](/fitness/race-time-prediction-calculator/) | known race distance, unit and target distance | Predicted time |
| [Marathon Pace Calculator](/fitness/marathon-pace-calculator/) | race | Pace per km |
| [Pace Distance Calculator](/fitness/pace-distance-calculator/) | pace minutes and pace per | Distance |
| [Pace Calculator](/fitness/pace-calculator/) | distance and distance unit | Pace per km |
| [Calories per Mile Calculator](/fitness/calories-per-mile-calculator/) | body weight and pace | Calories per mile |
Background: fitness estimates
Fitness formulas are estimates whose accuracy depends on the input. One-rep-max formulas such as Epley and Brzycki give different answers, and predictions from hard sets of a few repetitions are better than from sets of ten or more. Age-based maximum heart rate formulas can be off by 10 to 30 beats a minute for an individual; Tanaka's 208 − 0.7 × age is generally preferred to 220 − age but is still an estimate.
Pace models built from a race result assume a maximal effort and work best for distances from about 5 km to the marathon. Use the output as a guide, not a prescription.
Assumptions and limitations
- Races shorter than about 3 minutes or longer than 4 hours are outside the equations' best-fit range
- Flat course assumed
Estimates from formulas describe averages. They are not a training or medical prescription; check with a qualified professional before changing your exercise or diet.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for minutes to confirm this.
Frequently asked questions
What is VDOT?
A running-fitness score derived from race performance.
What is threshold pace?
A comfortably hard pace you could hold for about an hour.
Are easy runs really that slow?
Yes, most running should be easy.
What does the Running Training Pace Calculator calculate?
Estimate VO₂max (VDOT) from a race result and get easy, threshold and interval training paces. It returns VDOT (estimated VO₂max), Easy pace per km, Easy pace per mile, Threshold pace (88%) per km and Threshold pace per mile.
What formula does the Running Training Pace Calculator use?
VO₂ = −4.60 + 0.182258 v + 0.000104 v²; %VO₂max = 0.8 + 0.1894393 e^(−0.012778 t) + 0.2989558 e^(−0.1932605 t); VDOT = VO₂ ÷ %VO₂max; training speed = the v whose VO₂ equals the chosen share of VDOT. Applies the Daniels–Gilbert equations (v in metres per minute, t in minutes): the oxygen cost of running at a speed, and the fraction of maximal oxygen uptake a runner can sustain for a race of that duration.
What do I need to enter in the running Training Pace Calculator?
You enter Race distance, Hours, Minutes and Seconds.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Races shorter than about 3 minutes or longer than 4 hours are outside the equations' best-fit range.
What are the limits of this calculator?
Races shorter than about 3 minutes or longer than 4 hours are outside the equations' best-fit range. Flat course assumed.
What is an example of a running Training Pace result?
With race distance 5 km, hours 0, minutes 19 and seconds 57, the vDOT (estimated VO₂max) is 50.
Where does the method come from?
The method follows: Daniels J.T., Gilbert J.R., Oxygen Power: Performance Tables for Distance Runners (1979); Daniels, Daniels' Running Formula: oxygen cost and %VO₂max equations (computed here from the published equations; no tables are reproduced); Intensity shares of VO₂max for easy, threshold and interval training as described in Daniels' Running Formula.
Can I rely on this calculator for a decision?
Estimates from formulas describe averages. They are not a training or medical prescription; check with a qualified professional before changing your exercise or diet. For this calculator in particular: Races shorter than about 3 minutes or longer than 4 hours are outside the equations' best-fit range.
Related calculators
- Race Time Prediction Calculator — Predict a finish time at another distance with Riegel's formula.
- Marathon Pace Calculator — Pace needed to finish a race distance in a target time.
- Pace Distance Calculator — Distance covered at a steady pace for a given time.
- Pace Calculator — Pace and speed from a distance and a time.
- Calories per Mile Calculator — Energy cost of running a mile from body weight and pace (ACSM equation).
- Swimming Pace Calculator — Pace per 100 meters or yards from a distance and a time.
- Training Load Calculator — Session load from perceived exertion and duration.
Sources
- Daniels J.T., Gilbert J.R., Oxygen Power: Performance Tables for Distance Runners (1979); Daniels, Daniels' Running Formula: oxygen cost and %VO₂max equations (computed here from the published equations; no tables are reproduced)
- Intensity shares of VO₂max for easy, threshold and interval training as described in Daniels' Running Formula
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.