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For example, when I need to talk with my American friends about body weight:

$\mathrm{KG}\times2+10\%$
($100\times2=200$, $200+10\%=220$... Pretty accurate and easy to do mentally, both ways)

However, when I need to talk with my British friends about body weight, how do I approximate from KG to Stones?
Additionally, if I have a similar formula for Stones-lbs, that will be useful too!
I mean, I know a Stone is 14 lbs, but how to approximate 247lbs in Stones without pulling out a calculator?

For your reference, a Stone is about 6.35 KG

I am thinking that a "good, practical" approximation follows these rules:

  1. 5% accuracy is kinda bad... Imagine weighing 100kg and wanting to lose 5kg - the error alone is making discussion about it difficult! I am thinking up to 2% error
  2. Maximum of 3 steps
  3. Only addition, subtraction, multiplication and division allowed (% also allowed)
  4. Multiplication only by "easy" factors: 2, 3, 4, 5, 10
  5. Division only by "easy divisors": 2, 10
  6. Only "easy" percentages like: 1%, 10%...
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    $\begingroup$ Can you do 13/2? $\endgroup$ Jan 8, 2021 at 11:37
  • $\begingroup$ I think the error is just above the acceptable but it does open a line of thinking: If we can change that "13" to add an extra step, this can make the approximation work! $\endgroup$ Jan 8, 2021 at 11:46
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    $\begingroup$ $6.35=127/20$. The approximation $19/3$ is better than $13/2$, but maybe less easy. $\endgroup$ Jan 8, 2021 at 11:50
  • $\begingroup$ yeah, I found 12.7 myself - interesting why this rings a lot like .50" to cm? Like, there's some hidden size conversion here! $\endgroup$ Jan 8, 2021 at 11:59
  • $\begingroup$ it's like: Stone x quarter inch x 10 = KG :) which is not easy to use for mental approximation, but a nice way of remembering what a stone equals to $\endgroup$ Jan 8, 2021 at 12:02

4 Answers 4

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To go from kilograms to stone, double the number of kilograms 4 times, then move the decimal point two places to the left. This is effectively the same as dividing by 6.25, which is only about 1.6% different from 6.35.

For example, how much is 98 kg in stone? Double 98 four times (-> 196 -> 392 -> 784 -> 1568), then move the decimal point 2 places to the left: about 15.68 stone.

The actual answer is about 15.43 stone, so 15.68 stone is a pretty good estimate.

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    $\begingroup$ this is beautiful, thanks! $\endgroup$ Jan 16, 2021 at 19:56
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20 stones are equal to 127 kilograms.

This is the best I could get and it's not good enough.

For the reverse (kgs to stones) there's no easy way, it seems.

You cannot rely there would be an easy conversion simply because
the metric system is not compatible with the British one
(in terms of "good" rational conversions).

So you cannot find easy to remember whole numbers $A$ and $B$ such that
$A$ stones are equal to $B$ kilograms. Let alone doing it both ways.

So in general you do need a calculator or... just wait for the British/US to adopt widely the metric system

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70 kg is extremely close to 11 stone (about $0.2\%$ out). Now that perhaps doesn't give a sufficiently easy conversion because of the difficulty of dividing by $7$, but for weights of people (which is basically the only time anyone uses stones) you will generally be able to do well by taking the nearest multiple of 70 kg, then approximating the remainder in some cruder way (such as $\mathrm{kg}\times3/20$). For example taking 100 kg, $100=70+30$ gives an approximation of $11+3\times30/20=15.5$ stone. The actual value is $15.72$ stone, so we are about $1.4\%$ out.

(For people with weight significantly below 70 kg you can do better by approximating the difference from 35 kg $\approx$ 5.5 stone.)

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I worked out another mental method for converting kilograms to stone that takes a little more work, but gives a more accurate answer. First, assuming you're not going to deal with weights much beyond 150 kg, you'll need to know your multiples of 19 from 1 to 8:

$\\19 \times 1 = 19 \ \ \ \ 19 \times 5 = 95\\19 \times 2 = 38 \ \ \ \ 19 \times 6 = 114\\19 \times 3 = 57 \ \ \ \ 19 \times 7 = 133\\19 \times 4 = 76 \ \ \ \ 19 \times 8 = 152$

In the steps below, I'll use the conversion of 86 kg to stone in the examples.

Step 1: Take the number of kilograms and divide it by 19, thinking of the answer as a mixed fraction. Since $86 = (19 \times 4) + 10$, we can quickly see that $\frac{86}{19} = 4\frac{10}{19}$

Step 2: Multiply the total you get in step 1 by 3. $3 \times 4\frac{10}{19} = 12\frac{30}{19} \Rightarrow 13\frac{11}{19}$

The total from step 2 is your estimate!

How good is this estimate? This method of estimation is equivalent to dividing by 6.33, and thus yields a good approximation of dividing by 6.35. Your estimate will be off by only about $\frac{3}{10} \%$!

Example: The estimate yields $13\frac{11}{19} \approx 13.57 \ stone$, while the actual conversion gives $86 \ kg = 13.54 \ stone$.

Bonus: If you want to be able to give your answer in decimals, learn to mentally divide by 19 with decimal precision here.

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