acalculator

What is my VDOT?

Type the distance and finishing time of a recent race. The VDOT calculator uses the Daniels and Gilbert equations to give your VDOT and the times you could run at other distances on the same fitness.

Your numbers

Units
Type up to two parts, for example 20 min or 3 h 30 min.
VDOT
49.8

3.107 mi in 20 min is a VDOT of 49.8.

Oxygen cost of the race pacemL/kg/min
47.5
Share of VO2max held
95.3%
1,500 m time
5:25
1 mile time
5:51
5 km time
20:00
10 km time
41:28
Half marathon time
1:31:50
Marathon time
3:11:17
Pace at VO2max, per km
3:51
Pace at VO2max, per mile
6:11

VDOT: 49.8. 3.107 mi in 20 min is a VDOT of 49.8.

How to calculate

Computes a runner’s VDOT from one race distance and time with the Daniels and Gilbert equations, with equal-effort times for 1,500 m to the marathon and the pace at VO2max.

Example with the default inputs (Race distance 3.10685596118667 mi, Race time 20 min): 3.107 mi in 20 min is a VDOT of 49.8.

Method: v = distance ÷ time (m/min); VO2 = −4.60 + 0.182258 v + 0.000104 v²; %max = 0.8 + 0.1894393 e^(−0.012778 t) + 0.2989558 e^(−0.1932605 t), t in minutes; VDOT = VO2 ÷ %max.

  • The race was run at full effort on a flat course in good conditions.
  • Equal-VDOT times assume the runner is as well trained for the other distance.
  • VDOT is a performance score, not a measured VO2max from a lab test.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Race distance 3.107 mi, Race time 20 min gives VDOT 49.806233, Oxygen cost of the race pace 47.4645, 10 km time 41:28, Half marathon time 1:31:50, Marathon time 3:11:17, Pace at VO2max, per km 3:51, Pace at VO2max, per mile 6:11.Source: Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners, 1979 (equations as given in Daniels’ Running Formula); equations written out at https://dev.to/keepknow/how-race-time-predictors-actually-work-daniels-vdot-vs-riegel-with-the-javascript-55k1 (retrieved 2026-10-01)
  2. Race distance 26.22 mi, Race time 210 min gives VDOT 44.553531, 5 km time 22:00, 10 km time 45:37.Source: Daniels and Gilbert 1979, Oxygen Power (VO2 and %VO2max equations)
  3. Race distance 3.107 mi, Race time 19.93 min gives VDOT 50.Source: Daniels and Gilbert 1979, Oxygen Power

How it works

Type a race distance d (metres) and time T. With t = T in minutes and v = d ÷ t the speed in metres per minute:

  • Oxygen cost VO2 = −4.60 + 0.182258 × v + 0.000104 × v² (mL/kg/min)
  • Share of VO2max held = 0.8 + 0.1894393 × e^(−0.012778 × t) + 0.2989558 × e^(−0.1932605 × t)
  • VDOT = VO2 ÷ share

Then:

  • Equal-effort times for 1,500 m, 1 mile (1,609.344 m), 5 km, 10 km, the half marathon (21,097.5 m) and the marathon (42,195 m): the time t at which the formula above gives the same VDOT for that distance. VDOT falls as t grows, so the calculator halves the range from 0.5 to 2,000 minutes 100 times.
  • Pace at VO2max: the speed v whose oxygen cost equals the VDOT, v = (−0.182258 + √(0.182258² + 4 × 0.000104 × (4.60 + VDOT))) ÷ (2 × 0.000104), shown as time per kilometre (1,000 ÷ v) and per mile (1,609.344 ÷ v).

VDOT, the oxygen cost and the share show to 1 decimal. Times show to the nearest second, halves rounded up, as m:ss below an hour and h:mm:ss from an hour. The maths runs in floating point.

Rules

  • The distance is from 800 m to 50 km; the time is from 2 minutes to 10 hours. 1 km = 1,000 m and 1 mi = 1,609.344 m exactly.
  • A VDOT outside 10 to 100 has no answer: "This race gives a VDOT of x, outside 10 to 100, where the formulas do not apply. Check the distance and time."

Worked examples by hand

5 km in 20:00. v = 5,000 ÷ 20 = 250 m/min. VO2 = −4.60 + 0.182258 × 250 + 0.000104 × 250² = −4.60 + 45.5645 + 6.5 = 47.4645. Share = 0.8 + 0.1894393 × e^(−0.25556) + 0.2989558 × e^(−3.86521) = 0.8 + 0.146720 + 0.006265 = 0.952983. VDOT = 47.4645 ÷ 0.952983 = 49.8. Pace at VO2max: v = 259.95 m/min, so 1,000 ÷ 259.95 = 3.847 min = 3:51 per km, and 6:11 per mile.

A marathon in 3:30:00. t = 210, v = 42,195 ÷ 210 = 200.93 m/min. VO2 = 36.2196; share = 0.812945; VDOT = 44.6. The same VDOT gives 22:00 for 5 km.

Other questions people ask

What is VDOT?

A running fitness score from Jack Daniels and Jimmy Gilbert. It is the VO2max that would explain your race time, if you ran with average running economy. Higher is fitter: a 20:00 5 km gives a VDOT of about 49.8.

How is VDOT calculated?

From two equations. The oxygen cost of the race speed v (metres per minute) is −4.60 + 0.182258 v + 0.000104 v². The share of VO2max you can hold for t minutes is 0.8 + 0.1894393 e^(−0.012778 t) + 0.2989558 e^(−0.1932605 t). VDOT is the first divided by the second.

How does the calculator predict my other race times?

For each distance it finds the time that gives the same VDOT. From a 20:00 5 km that is 41:28 for 10 km, 1:31:50 for the half marathon and 3:11:17 for the marathon.

Is VDOT the same as VO2max?

No. VO2max is measured in a lab. VDOT is worked out from a race, so it also reflects running economy and race skill. Two runners with the same VO2max can have different VDOTs.

Why does my marathon prediction feel too fast?

The prediction assumes you are as well trained for the marathon as for the race you typed. Without long runs and marathon-specific training, most runners are slower than a 5 km time predicts.

Why are the times a second or two off Daniels’ tables?

The book’s tables were rounded when they were printed; the calculator solves the equations to the second. At VDOT 50 the equations give 19:56 for 5 km, and the table lists 19:57.