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Running: what should be my speed for a given ETA?

With all the techno onboard, on your wrist or on your humerus (upper arm), you now have access to your instant speed, and in particular, to your average speed.  The benefit of knowing your average speed is to manage your energy and your reserves while racing to reach your goal: covering the distance in a given time or less.
In this article, I will reveal the formula that gives ETA as a function of your average speed, and I will also display reference charts, with speeds, times and paces, that you can refer to for your next training or races.
Running: what should be my speed for a given ETA?

The speed = f(race time) equation

Below are the different expressions of the equation that binds average speed and ETA (race time).
Running: what should be my speed for a given ETA?

Légend :
d : distance ; t : time ; v : velocity (speed)
dkm : distance, expressed in kilometers
tmin : time, expressed in minutes
vkm/h : speed, in kilometers per hour.

Attention if you evaluate these equations with numerical values: if you want to use seconds on top of minutes (which is not common in these kind of problem), you will have to convert the seconds into minute decimals, i.e.  divide the seconds by 60.
Example : 43 minutes and 20 seconds, don’t use 43.20 in the equation, but rather 43 + 20/60, so 43.3333.

Example of a numerical evaluation to calculate the necessary average speed

Example of a 10 km run, thus dkm=10 ; you’re aiming at 50 minutes, thus tmin = 50 ; the equation supplies vkm/h = 60*10/50 = 12 km/h.  Meaning you will have to run at an average speed of 12 km/h to cover the distance in 50 minutes.

Pace

The Pace, that I note p herein, is the reverse expression of the speed.  It means that it represents the time needed to run a unit of distance.  It is usually expressed in minutes per kilometer, or in minutes per mile in some English-speaking countries (e.g.  the USA).

1 mile = 1609 m, not to be confused with one nautical mille = 1852 m .

Smartphone apps and an increasing number of smartwatches display the pace while you’re running.  The lower the pace the faster you’re running, and vice-versa.
E.g.  if you ran 10 km in one hour, then your pace was 60 minutes / 10 km = 6:00 minutes per kilometer.

Pace : speed conversion

The equations

Let’s note p the pace, and v the speed (velocity), thefore we have the equivalence:
Running: what should be my speed for a given ETA?

Practical application

Let’s consider a speed of v = 14.5 km/h, what is the corresponding pace?

Answer:

p = 3600 / 14.5 = 248 seconds, (we neglected the decimal part)
which is 4 minutes (4 x 60 = 240 seconds) and 8 seconds, simply noted 4:08.

What about a pace of 5:25 (minutes per km), what is the corresponding speed?

Answer:

v = 3600 / (5 x 60 + 25), therefore 11.08 km/h (rounded to the second decimal).

Running time : pace conversion

The formula

Let ps be the pace in seconds per km, let t be the running time in seconds, and d the distance run in meters.  Therefore we have the following equivalence :
Running: what should be my speed for a given ETA?

Practical application

Let’s consider a running time of t = 1:42:47 over a half-marathon.  What is the corresponding pace?

Answer:

*Always exploit the equations given using International System units: meters and seconds!
Convert the running time in seconds : t = 1x3600 + 42x60 + 47 = 6167 seconds,
Convert the distance in meters; a half-marathon is 21,097 m .
Finally, apply the above formula p = t/d, i.e.  p = 1000 x 6167 / 21097 = 292 seconds per km.  That we will now convert into minutes and seconds, which are 4 minutes and 52 secondes, simply noted 4:52 .

How did the guy do to convert seconds into minutes + seconds?

An easy way to convert 292 seconds into minutes, mentally, is to look for the closest multiple of 60.
We know that 5 times 60 equals 300, so the pace will be very close to 5:00 per km.  But since 292 is only 8 seconds less than this multiple, we take them off, giving 5:00 - 0:08 = 4:52/km .

Make sure you respect the units used in the formulae.  A frequent error is to forget to convert pace minutes into seconds.

Reference charts

I’ve drawn up these charts for your convenience, with classical distances and running times.
The values in the charts are the average speeds in km/h that you need to run at for the corresponding ETAs.

Too low or unlikely speeds have been removed.
Reminder: 21 097 m is a half-marathon’s distance,
42 195 m is a marathon’s.

Speed chart, in km/h

distance / time 20 min 25 min 30 min 35 min 40 min 45 min 50 min 55 min 1:00 1:05 1:10 1:15 1:20 1:25
5 km 15.00 12.00 10.00 8.57 7.50 6.67 6.00              
10 km     20.00 17.14 15.00 13.33 12.00 10.91 10.00 9.23 8.57 8.00 7.50 7.06
20 km               21.82 20.00 18.46 17.14 16.00 15.00 14.12
half-marathon               23.01 21.10 19.47 18.08 16.88 15.82 14.89

(continued)

distance / time 1:30 1:35 1:40 1:45 1:50 1:55 2:00 2:05 2:10 2:15 2:20 2:25 2:30 3:00
10 km 6.67 6.32 6.00 5.71 5.45 5.22 5.00              
20 km 13.33 12.63 12.00 11.43 10.91 10.43 10.00 9.60 9.23 8.57 8.00 7.50 7.06 6.67
half-marathon 14.06 13.32 12.66 12.06 11.51 11.01 10.55 10.13 9.74 9.04 8.44 7.91 7.45 7.03
marathon             21.10 20.25 19.47 18.08 16.88 15.82 14.89 14.07

(continued)

distance / time 3:10 3:20 3:30 3:40 3:50 4:00 4:20 4:40 5:00 5:20 5:40 6:00 6:30
5 km                          
10 km                          
20 km 6.32 6.00 5.71 5.45 5.22 5.00              
half-marathon 6.66 6.33 6.03 5.75 5.50 5.27              
marathon 13.32 12.66 12.06 11.51 11.01 10.55 9.74 9.04 8.44 7.91 7.45 7.03 6.49

pace/speed conversion chart, time per kilometre.

pace (min/km) 2:45 2:50 2:55 3:00 3:05 3:10 3:15 3:20 3:25 3:30 3:35 3:40 3:45 3:50 3:55
speed (km/h) 21.82 21.18 20.57 20.00 19.46 18.95 18.46 18.00 17.56 17.14 16.74 16.36 16.00 15.65 15.32

(continued)

pace (min/km) 4:00 4:05 4:10 4:15 4:20 4:25 4:30 4:35 4:40 4:45 4:50 4:55
speed (km/h) 15.00 14.69 14.40 14.12 13.85 13.58 13.33 13.09 12.86 12.63 12.41 12.20

(continued)

pace (min/km) 5:00 5:05 5:10 5:15 5:20 5:25 5:30 5:35 5:40 5:45 5:50 5:55
speed (km/h) 12.00 11.80 11.61 11.43 11.25 11.08 10.91 10.75 10.59 10.43 10.29 10.14

(continued)

pace (min/km) 6:00 6:15 6:30 6:45 7:00 7:15 7:30
speed (km/h) 10.00 9.60 9.23 8.89 8.57 8.27 8.00

All right, I’ve gone down to 7:30/km because it was the aerobic running speed of my younger son over 4 km when he was five . . . don’t feel bad if this is your running speed! What is more important is to progress, or even at least to run! So many can’t!

Practical application: the possible race strategies to reach your goal

Start your race at the same speed as the average speed supplied by the reference chart.  Or . . . start slower, then accelerate over the last kilometers to increase it, until your average speed equals the one given in the charts.
This latter method ensures a good warm up, then a steady and controlled cruise speed, and finally will allow you to gauge the amount of risk you can take towards the end if you tap in to your reserves, to grab a few seconds or minutes.  However, don’t accelerate too late towards the end, especially during long races, as your average speed will barely vary . . .

What if I want to know my ETA for a given speed?

It is the reciprocal problem to the initial topic’s question.  The speed-time equation allows you to swap speed and time.Running: what should be my speed for a given ETA?

Example of a numerical evaluation for an ETA

Example of a half-marathon, thus dkm=21.1 ; you’re thinking of running at 10.5 km/h, what would your ETA be?
The equation gives tminutes = 60 x 21.1 / 10.5 = 120.57.  Therefore 2 hours and 0.57 minutes, wait, I didn’t say 57 seconds! So you have to multiply by 60 to get seconds, so 0.57 x 60 = 34 secondes, roughly.  Thus a total of 02:00:34.  Good luck!

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created 30 September 2015
revised 28 July 2018 by M. Fabien Haddadi M Sc. Fab
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