# Finish time predictor. How fast can you run?

## Predict your potential finish time

### 4 methods to predict your potential running race time.

What is my potential running race time?

For example, I can run 10 km in 50 minutes: what could be the half marathon marathon finish time? And for a marathon?

This page shows 4 methods to estimate theoretical times at different distances based on a performance at an input distance. In one case it is also necessary to know sex and age.

The results can be used as a reference for planning future goals. The lower the difference between the distance used as a reference and the distance of which you want to estimate the travel time, and more reliable will be the calculation. It is therefore not advisable to estimate the theoretical time of a marathon, for example, by using the time of a 10 km, but rather that of a half marathon, or better the average of 2-3 recent half marathons.
A table will show the theoretical times and the relative pace in min/km. In the last line the averages of the 4 methods.

### Riegel formula

An empirical way to estimate the race time is to use the time and the distance of a recent run in the so-called Riegel formula. Pete Riegel proposed the formula in 1977.

### Dave F. Cameron's Model

This model uses the top 10 times in the world at various distances to compute performances across distances. In his article Cameron obtain a formula by using a non-linear regression method.

### Estimate based on VO2 Max

VO2 Max (also maximal oxygen consumption or maximal aerobic capacity) is the maximum rate of oxygen consumption as measured during incremental exercise.
The estimate based on the VO2 Max first computes the VO2 Max, given the performance entered, using the Daniels and Gilbert VO2 Max formula:

VO2 Max = (-4.60 + 0.182258 * v + 0.000104 * v2) / (0.8 + 0.1894393 * e-0.012778*tin + 0.2989558 * e-0.1932605*tin)

with v = din/tin, where din the distance in meters and tin the time in seconds of the performance entered. VO2max is expressed in millilitres of oxygen per kilogram of body mass per minute (e.g., ml/(kg·min)).
The same formula is then used in reverse to estimate the times by using the same VO2 Max found at the beginning. There is no analytic solution to solve this problem, but the solution can be found numerically (we use the Newton's Method).