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.
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 = tin * (d/din)1.06
with tin and din respectively the time and the distance of the known performance and t is the estimated time to travel the distance d.
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 = (tin/din) * d *(13.49681 - 0.000030363 * din + 835.7114/din0.7905) / (13.49681 - 0.000030363 * d + 835.7114/d0.7905)
with tin and din 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].
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).
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.
|VO2 Max - Scores for adult men|
|VO2 Max scores for adult female|
Tools for runners: 10 km training plan.
Do you want to run a 10 K (6.2 mi)?
Create your 10 km training plan! Tables for times from 35 minutes to 1 hour and 15 minutes, with customizations in 1 minute steps (that is, for example, you can choose 40 minutes, or 41 minutes, and so on). Fast link:
10 km in 35 minutes
10 km in 40 minutes
10 km in 45 minutes
10 km in 50 minutes
10 km in 55 minutes
10 km in 1 hour
10 km in 1 hour and 15 minutes
Tools for runners: half-marathon training plan.
Do you want to run a 21 K (13.1 mi)?
Create your half-marathon training plan. Tables for times from 1 hour and 20 minutes to 2 hours and 30 minutes, with customizations in 1 minutes steps (that is, for example, you can choose 1 hour and 47 minutes, or 1 hour and 48 minutes, and so on). Fast link:
Half-Marathon in 1 hour and 30 minutes
Half-Marathon in 1 hour and 45 minutes
Half-Marathon in 2 hours
Half-Marathon in 2 hours and 15 minutes
Half-Marathon in 2 hours and 30 minutes
Tools for runners: marathon training plan.
Do you want to run a 42 K (26.2 mi)?
Create your marathon training plan! Tables for times from 3 hours to 6 hours, with customizations in 1 minute steps (that is, for example, you can choose 4 hours and 5 minutes, or 4 hours and 6 minutes, and so on). Fast link:
Marathon in 3 hours
Marathon in 3 hours and 30 minutes
Marathon in 4 hours
Marathon in 4 hours and 30 minutes
Marathon in 5 hours
Marathon in 5 hours and 30 minutes
Marathon in 6 hours