Convert km to miles in your head!

While touring in Europe it's convenient to be able to convert between km and miles in your head. A rough & ready method involves memorising three numbers – 3, 5 and 8 – and the fact that 1 km in miles is approximately equal to the first of these numbers divided by the second, or alternatively the second divided by the third. That is:

1 km ≅ 3/5 or 5/8 miles

(Tip: To help memorise 3, 5 and 8, note that 3 + 5 = 8)

When converting a km figure to miles (or km/h to mph), look for ways to use the divisors 5 or 8. For every 5 km accounted for, substitute 3 miles; and for every 8 km accounted for, substitute 5 miles. When converting the other way, look for ways to use the divisors 3 or 5, then substitute 5 and 8 km respectively.

Some examples:

Imagine you're in France and you see a speed limit sign "45 km/h". This is an easy one because the figure can be divided by one of the two key divisors (5) with no remainder. 5 km is 3 miles. There are nine 5's in 45, so 45 km/h is 9 * 3 = 27 mph.

Further on you see a directions sign with "MONT VENTOUX 21". Focusing on the key divisors 5 and 8 you spot that 21 is 16 + 5, i.e. 2 * 8 + 5; so 21 km = 2 * 5 + 3 = 13 miles.

Your speedo says you're doing 70 mph. To calculate this value in local currency: 14 * 5 mph = 14 * 8 km/h = 112 km/h.

What if the best sum you can achieve leaves the odd unit unaccounted for (e.g. 31 km = 6 * 5 + 1)? Well, you never have to stop! 1 km = 2 * .5 km = 2 * .3 miles = 0.6 miles. So 31 km = 18.6 miles. However, remember this is only an approximation! In this case, because 1 km is a small proportion of the overall figure, just round up to 32 km, which is 4 * 8 km = 4 * 5 miles.

This might sound cumbersome at first but after a little practise you will soon become adept. And the practise can be done in your head while you're on the road. A few days into your trip and you'll be impressing your friends and family with your uncanny mental faculty.

Accuracy

According to Google, 1 kilometre = 0.621 miles. So:

3/5 = 0.6, i.e. -3.4% error

= 0.6, i.e. -3.4% error 5/8 = 0.625, i.e. +0.6% error

Hence, in cases where you have a choice between the two ratios (like when converting 40 km to miles) 5/8 should be preferred (i.e. 5 * 5 miles is a more accurate than 8 * 3 miles). And if you have stooped to using a calculator (hopefully you're not driving!), simply doing the whole conversion using 5/8 will give pretty good accuracy.

There are other methods of converting between miles and kms in your head, like this one based on the golden ratio.

Similar conversions

If you regularly need to convert other units you can apply the same method after memorising the applicable approximate conversion ratios. Examples:

miles ↔ nautical miles 1 mile ≅ 6/7 or 7/8 nm (-1.4%, +0.7% error) mph ↔ m/s 1 mph ≅ 4/9 or 5/11 m/s (-0.6%, +1.7% error) ft ↔ m 1 ft ≅ 3/10 or 4/13 m (-1.6%, +0.95% error)

Some of these figures aren't so easy to deal with and only miles ↔ nm exhibits the same '3 easily remembered digits' characteristic as km ↔ miles.

For ft ↔ m you can generally get by just memorising 3/10. It is, of course, very easy when converting feet to metres: just divide by 10 and multiple by 3 (e.g. 6' = 1.8 ). But how easy it is to convert metres to feet depends on how easy you find it to divide the particular value by 3; e.g.: 100 m ≅ 333 ft; 150 m ≅ 500 ft; 800 m ≅ ...hmmm

Side note: This kind of mental arithmetic would be easier in most cases if we adopted the dozenal system (base 12) rather than decimal (base 10).