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
• 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).

19 Feb 2011, easleyonline