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I remember back in school thinking "when will I ever need to use this in real life" during math classes. Today was that day! I had to get the diameter of a copper water cooling pipe that's in my air conditioning utility cupboard and is quite hard to reach.

I do have callipers just for this purpose but when I tried to use them, I couldn't tell if they got all the way around the pipe or not. So I thought that I may as well use the formula for the circumference of a circle to confirm my measurement.

I used a flexible tape measure used for sewing to measure around the pipe, which gave me the circumference. In my case it was 243mm.

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Now the formula for the circumference is 2 × pi × r. With that and a little bit of algebra it's easy enough to work out the radius...
First write the formula and the measurements, which are equal one another
243 = 2 × pi × r
Substitute the value for pi, 4 decimal places is close enough
243 = 2 × 3.1415 × r
Multiply pi by 2
243 = 6.283 × r
Change sides for r and adjust to divide
r = 243 ÷ 6.283
Final result for radius
r = 38.675

Now that of course gives the radius and I was after the diameter, so just multiply by two (or I could have just not multiplied pi by 2 above).

Diameter is 2x the radius
d = r × 2
Substitute the value for radius
d = 38.675 × 2
Final result for diameter
d = 77.35

So the diameter of my pipe according to the calculation is 77.35mm. This is not a standard copper pipe size, which means my circumference measurement was wrong (confirmed later it was off by 5mm). It's important to get this measurement right, however it's not a show stopper if you just need an approximate value and can just match to the closest standard size (you're not likely to have non-standard sized pipes).

Incidentally this is what my callipers said...76mm, which was spot on after all.

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