Oxygen cost of running
VO2 = −4.60 + 0.182258 × v + 0.000104 × v2
With v in meters per minute and VO2 in ml/kg/min. At 8:00 per mile (201 m/min), that’s about 36 ml/kg/min.
VO2 max calculator for runners
A recent race time gives you an estimated VO2max (Daniels-Gilbert), and with it equivalent times for the 5K, 10K, half and marathon. Treat it as a fitness number you track race to race, not a lab measurement.
h:mm:ss
e.g. 24:30 or 1:52:00
Daniels-Gilbert, and Cooper for the 12-minute
Your race gives a speed and a duration. One equation says how much oxygen that speed costs, the other what share of your VO2max you can hold that long. Divide the first by the second and you get your VO2max.
Share of VO2max you can hold
0.8 + 0.1894393 × e−0.012778 t + 0.2989558 × e −0.1932605 t
With t in minutes. You can hold about 100% for 11 minutes, 89% for an hour, and the curve flattens toward 80% on very long races. It also colors the equivalent times: Z5 above 95%, Z4 from 83 to 95%, Z3 below.
For each distance, the tool finds the finish time that gives your VO2max. Results match the published tables within 0.1 ml/kg/min.
Turn it into training
The same equations give your easy, marathon, threshold and interval paces in the training pace calculator. No recent race? A Cooper test gives you an estimate from a 12-minute run.
Frequently asked questions
How accurate is a VO2max estimated from a race?
It’s the VO2max that would explain your race if your running economy were average. If you’re economical, you get a number above your lab value; if not, below. Two runners with the same time can come out with different numbers.
Why doesn’t it match the VO2max on my Garmin or Apple Watch?
Your watch estimates VO2max from heart rate and pace on everyday runs, with its own model. This calculator only looks at one all-out race. A 2 to 5 point gap is common, so stick to one source.
Which race should I enter?
A recent, flat, all-out race between the mile and the half marathon. A marathon works too, but heat, fueling and pacing mistakes drag it down more. Skip training runs and hilly trail races.
Can I run the equivalent marathon time from my 5K?
Only if you’ve put in the endurance training. The equivalents assume you’re as well prepared for every distance. Most runners coming from short races run their first marathon slower than predicted.
What is a good VO2max for a runner?
On this scale, a 30:41 5K gives 30 ml/kg/min, 24:06 gives 40, 19:56 gives 50 and 17:03 gives 60. A 25-minute 5K, a 50-minute 10K and a 4-hour marathon all land near 38 to 40. Age and sex shift the averages.
Guides that use this calculator
- Cooper test: how to test your maximal aerobic speed Kenneth Cooper's 12-minute run, from warm-up to the last lap. What your distance in miles says about your VO2max, and the treadmill speeds it gives you. Updated
- Predict your marathon time from a half marathon A 1:55 half says 3:59:46 with Riegel. Checked on 2,303 recreational runners, half of them finished at least 10 minutes slower than that. Updated
- Training paces from a race time: easy to intervals A 25:00 5K puts your easy runs at 9:44 to 11:38 per mile. Five training paces from one race, and the days to ignore them. Updated
Sources
- Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ, 1979, appendix A.
- Daniels J, Fitts R, Sheehan G. Conditioning for Distance Running: The Scientific Aspects. New York: John Wiley & Sons, 1978.