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

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.

### The speed = f(race time) equation

Below are the different expressions of the equation that binds average speed and ETA (race time).

*Légend* :

**d** : distance ; **t** : time ; **v** : velocity (speed)

**d _{km}** : distance, expressed in kilometers

**t**: time, expressed in minutes

_{min}**v**: speed, in kilometers per hour.

_{km/h}*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 **d _{km}**=10 ; you’re aiming at 50 minutes, thus

**t**= 50 ; the equation supplies

_{min}**v**= 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.

_{km/h}### L’allure

L’allure, que je note **p**, est l’expression inverse de la vitesse, ce qui veut dire que c’est le temps nécessaire à parcourir une unité de distance. Elle s’exprime en général en minutes par kilomètre, ou en minutes par miles dans certains pays anglo-saxons.

Des montres et applications mobiles spécialisées dans la course à pied affichent l’allure. Plus elle est faible, et plus vous courrez vite, et inversement.

Ex. Si vous couvrez 10 km en 1 heure (60 min), votre allure est de 60 / 10 = 6:00 minutes par kilomètre.

### Pace : speed conversion

#### The equations

Let’s note p the pace, and v the speed (velocity), thefore we have the equivalence:

##### 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).

### 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.

**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: |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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: | 4:20 | 4:40 | 5h | 5h20 | 5h40 | 6h00 | 6h30 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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.

#### Example of a numerical evaluation for an ETA

Example of a half-marathon, thus **d _{km}**=21.1 ; you’re thinking of running at 10.5 km/h, what would your ETA be?

The equation gives

**t**= 60 x 21.1 / 10.5 =

_{minutes}**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!