As a runner probably you came across the fact that we use pace to measure our speed and that is expressed in min/km or min/mile depending on the system used. Conversion between them requires a few simple calculations that can be done using pen and paper or even in your head.
Using Pen and Paper for Precise Calculations
You need to do a few simple mathematical calculations to get the converted pace. To make these calculations easier you will have to work only with natural numbers.
Step 1: Convert to Seconds
Convert your input data to seconds by multiplying the minutes part by 60 and adding the seconds to the result.
e.g. 5:30 min/km 5 x 60 + 30 = 300 + 30 = 330
e.g. 9:45 min/mile 9 x 60 + 45 = 540 + 45 = 585
Lets name the end result input seconds.
Step 2: Convert by Division or Multiplication
1 kilometer equals about 1.61 mile, lets call this the distance constant.
min/km → min/mile
To convert from min/km to min/mile multiply the input seconds by the distance constant.
Multiplications by real numbers can be harder, to simplify you can replace the distance constant with 161 / 100.
e.g. 5:30 min/km 330 x 1.61 = 330 x 161 / 100 = 53130 / 100 = 531
min/mile → min/km
To convert from min/mile to min/km divide the input seconds by the distance constant.
Divisions by real numbers can be challenging, but luckily you can use a trick described by this mathematical formula.
X / (A / B) = X * (B / A)
Therefore instead of dividing by 1.61 that equals to (161 / 100), multiply by (100 / 161).
e.g. 9:45 min/mile 585 / 1.61 = 585 / (161 / 100) = 585 x 100 / 161 = 58500 / 161 = 363
Lets name this result converted seconds.
Step 3: Convert Back the Seconds to Minutes and Seconds
To get the result in minutes and seconds, divide the converted seconds by 60. The result is the minutes, the remainder is the seconds you are looking for.
e.g. 5:30 min/km 531 / 60 = 8 remainder 51
Therefore the result is 8:51 min/mile
e.g. 9:45 min/mile 363 / 60 = 6 remainder 3
Therefore the result is 6:03 min/km.
Fast and Simple Approximation In Your Head
Sometimes you don’t have the time or the tools to do the conversion, but you want a good approximation of the result in a few seconds.
First, we simplify the distance constant to 1.6.
min/km → min/mile Simplified
Convert the input pace to a real number expressing it in minutes.
e.g. 5:30 min/km 5.5
Multiply this by 1.6 like you did it on pen and paper. How to do that in your head easily? Split up 1.6 into three parts: 1, .5 and .1. In other words the whole plus half of it plus ten percent of it.
These values are fairly easy to calculate in your head. You don’t need precise calculations, feel free to round the numbers.
e.g. 5:30 min/km 5.5 + (5.5 / 2) + (5.5 / 10) = 5.5 + 2.8 + 0.5 (with rounding) = 8.8
And 8.8 minutes is about 8:45.
To sum up, think of the input pace in minutes and do the math with it. The thinking process for the above example would go like this:
5:30 is 5 and a half minutes. Plus half of it, that is a bit less than 3 minutes, makes it a bit less than 8 and a half minutes. Plus ten percent of it, that is half minute, makes it about 9 minutes.
min/mile → min/km Simplified
Again, convert the input pace to a real number expressing the minutes.
e.g. 9:45 min/mile 9.75
This number should be divided by 1.6, which is the tricky part. We can use the trick from the pen and paper calculations and instead of division by (16 / 10) use multiplication by (10 / 16).
e.g. 9:45 min/mile 9.75 x 10 / 16 = 97 / 16 (with rounding)
How do you divide by 16 easily? By calculation the powers of 16 by addition.
1: 16 2: 16 + 16 = 32 3: 32 + 16 = 48 4: 48 + 16 = 64 5: 64 + 16 = 80 6: 80 + 16 = 96
You can stop here as 96 is close enough to 97 that we calculated in the previous step. So 96 is 16 on the power of 6.
Therefore 97 / 16 is about 6, this makes the result approximately 6:00 min/km.
To sum up, the thinking process would go like this:
9:45 is almost 10 minutes. Multiplying it with 10 makes it a hundred. 16 (one) plus 16 equals 32 (two), plus 16 equals 48 (three), plus 16 equals 54 (four), plus 16 equals 80 (five), plus 16 equals 96 (six). That is almost a 100, I added 16 six times, so the result is about 6 minutes.
If you want a simple solution head over to the pace converter that will do all the math for you. Don’t forget to add the page to your bookmarks so you can find it later easily.