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Race time predictor

What are your theoretical performance?
This page shows 4 methods to estimate theoretical times at different distances based on a performance at a 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 following formula in 1977:

t = t_in * (d/d_in)^1.06

with t_in and d_in respectively the time and the distance of the known performance and t is the estimated time to travel the distance d.

Dave 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 states that to obtain the following formulas he used non-linear regression methods:

t = (t_in/d_in) * d *(13.49681 - 0.000030363 * d_in + 835.7114/d_in^0.7905) / (13.49681 - 0.000030363 * d + 835.7114/d^0.7905)

with t_in and d_in respectively the time [s] and the distance [m] of the known performance and t [s] is the estimated time to travel the distance d [m].

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*t_in} + 0.2989558 * e^{-0.1932605*t_in)}

with v = d_in/t_in, where d_in the distance in meters and t_in 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).

Age grading

This method is the only that uses age and gender of the runner. With the so called age grading prediction we assume that you will able to run the same age-graded performance at every distance. The age-graded score is the percentage ratio between the world record for your age and gender and the time of your performance.
So, for example, a 40-year-old man that runs 10 km in 50 minutes has a age-graded score equal to 55.4%. This value is used to predit times at differen distances.

Distance	Unit	Time [hh:mm:ss]	Gender	Age

VO₂ Max - Scores for adult men
Age	18-25	26-35	36-45	46-55	56-65	65+
excellent	>60	>56	>51	>45	>41	>37
good	52-60	49-56	43-51	39-45	36-41	33-37
above average	47-51	43-48	39-42	36-38	32-35	29-32
average	42-46	40-42	35-38	32-35	30-31	26-28
below average	37-41	35-39	31-34	29-31	26-29	22-25
poor	30-36	30-34	26-30	25-28	22-25	20-21
very poor	<30	<30	<26	<25	<22	<20

VO₂ Max scores for adult female
Age	18-25	26-35	36-45	46-55	56-65	65+
excellent	>56	>52	>45	>40	>37	>32
good	47-56	45-52	38-45	34-40	32-37	28-32
above average	42-46	39-44	34-37	31-33	28-31	25-27
average	38-41	35-38	31-33	28-30	25-27	22-24
below average	33-37	31-34	27-30	25-27	22-24	19-21
poor	28-32	26-30	22-26	20-24	18-21	17-18
very poor	<28	<26	<22	<20	<18	<17