# Reverse VO_{2} Max Calculator

# Description

## Introduction

This calculator predicts times for popular track and road race distances based on a runner's VO_{2} max.

Predictions for track distances from 800 meters to 3000 meters and for road distances from 1 mile to the marathon are provided.

We refer to it as a *reverse* calculator, in contrast to our calculator that estimates VO_{2} max based on a recent race time.

## VO_{2} max and performance

VO_{2} max is well-established as a reliable predictor of running performance. It can be estimated from a recent race performance, or from a specific test, such as the Cooper test. Many modern running watches can also predict your VO_{2} max based on training data.

Taking a VO_{2} max value and using it to predict race times can be especially useful as a pacing guide for those runners attempting an unfamiliar distance, or for those who haven't raced in a while.

## Difficulties and limitations

All predicted times are estimates. VO_{2} max becomes less and less important for shorter distances, especially sprints, and for this reason track distances less then 400 metres are not included in the results.

Also note that other factors will contribute to performance in an event. Thus, the race time predictions are more likely to be accurate for distances similar to that which yielded the VO_{2} max estimate in the first place. For example, if your VO_{2} max estimate is based on a 5,000 meter treadmill test, then you will have more confidence in the predicted time for 10k than you will for 800 meters or for a marathon.

It's worth remembering that the formula for VDOT is based on performances by elite runners. And what is true for elite runners isn't necessarily accurate for runners of other levels.

Finally, if your VO_{2} max is estimated from a sport other than running then the predicted times are likely to be less accurate, since much of running fitness is specific to the biomechanics of, and the adaptations that take place as a result of, the activity itself.

## Using the calculator

Simply enter your VO_{2} max. Values from 10 to 100 are permitted.

# How It Works

## VO_{2} max formula

The calculator is based on the Daniels and Gilbert formula for estimating VO_{2} Max.

It may be better thought of as a reverse *VDOT* calculator, VDOT being the term used by Daniels.

The Daniels and Gilbert formula is:

```
``````
VO
```_{2} Max = (−4.60 + 0.182258 × S + 0.000104 × S^{2})/(0.8 + 0.1894393 × e^{(-0.012778 × T)} + 0.2989558 × e^{(−0.1932605 × T)})

where:

`S`

is speed in metres per second

`T`

is time in seconds

That formula will give you a VDOT value based on a distance and time. But since this is a reverse calculator we want a time for a distance based on a VDOT. We achieve this via an algorithm that, for each distance of interest, iteratively generates VDOT values for a time and uses the result to use better-fitting times until an exact (or very close) VDOT match is found.