# The Calculator

# Description

## Introduction

This tool uses some of the most-popular race time predictors to estimate race times for popular distances. Estimated finish times for popular track and road race distances are generated using the Reigel, Cameron and VO_{2} Max formulas and age grading tables. The results are presented as tables that allow quick comparison of the different estimates.

## Difficulties

Race time prediction is difficult, particularly for the most-common approach, which is to try to derive a single formula to cater for all runners and all distances. This is problematic since runners vary wildly in their ability to convert performances from one event to another. For example, top speed tends to decrease more rapidly than endurance as runners age.

The characteristics that enable an athlete to generate power are not entirely in line - and even sometimes at odds - with those that enable a good performance in endurance events. A 100 metre sprinter is unlikely to be able to perform well over a marathon, and the reverse is also true. A good example is presented by decathletes, who tend to perform relatively less well over 1500m (a primarily aerobic event) than they do in the other events (primarily anaerobic and power-based).

The Age Grading approach could be considered the most sophisticated of these prediction models since it at least considers age and sex. The Reigel, Cameron and the VO_{2} Max models do not take these parameters into account.

Because of these limitations, the results generated by this tool should be considered estimates only.

## Using the calculator

To use the calculator simply choose or specify a race distance, enter a race time and your age and indicate your sex.

Predictions are more likely to be accurate for distances that are close to the distance entered.

# How It Works

The descriptions below detail how each model achieves its predictions. There's no need to read them or understand how they work before you use the calculator.

## Riegel

Peter Reigel developed a formula to predict race times. It's probably the most-widely-known and used formula.

The formula is:

`T2 = T1×(D2÷D1)`

^{1.06}

where:

`D1`

is the distance run in metres

`T1`

is the time in seconds achieved for D1

`D2`

is the distance in metres for which a prediction is desired

`T2`

is the predicted time in seconds

Reigel claims that the formula is most accurate for runs lasting from three and a half minutes to three hours fifty minutes.

## Cameron

Dave Cameron's formula was developed by considering the top times in the world for various distances.

The formula is:

`T2 = (T1÷D1) × D2 × (f(D1)÷f(D2)) `

where:

`f(x) = 13.49681 − (0.000030363×D1) + (835.7114÷x`

^{0.7905}

`D1`

is the distance run in metres

`T1`

is the time in seconds achieved for D1

`D2`

is the distance in metres for which a prediction is desired

`T2`

is the predicted time in seconds

It's claimed to work best for distances from 800m to the marathon

## VO_{2} Max

The Daniels and Gilbert formula for estimating VO_{2} Max 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

It's possible to estimate equivalent perfomances across different distances by using the formula to convert a time to an estimated VO_{2} Max value, and then using that estimated VO_{2} Max value to generate predicted times.

## Age Grading Tables

Predictions can be made by converting a performance to an age-grading percentage and then using that age-grading percentage to generate predicted times for various distances.

For more information see our age grading calculator.