Why is the pi circumference divided by the diameter

Calculate the circumference - formula 2 * π * r

Before we calculate the circumference with any formula, we should first ask ourselves what is meant by the circumference of a circle or the circumference of a circle. The circumference means the length of a circular line. Or the distance to go around a circle. In real life, there are many ways to measure the circumference. The most intuitive solutions are to wrap the circle with a string or to unroll the circle on a plane. The latter is shown in the following animated graphic.

Here we see a circle with the diameter 1, which when unrolled results in a segment of pi. The diameter of a circle has a fixed ratio to the number PI. People recognized this fixed connection between the circumference and pi early on, but at the time they could only roughly determine or calculate pi.


How is the circumference calculated?

In order to be able to calculate the circumference, you need the number PI. The more precisely we know PI, the more precise the result of our calculation will be. In school, one is often content with a value of PI rounded to two decimal places, namely 3.14. If you want to know more, there are a few more parts of Pi to be admired here. And that finally brings us to the formula for calculating the circumference:

U = d π or. U = 2 π r

Concerning the formula: diameter d of the circle multiplied by the number PI results in the circumference U of the circle. Since mathematicians prefer to work with the radius r of a circle instead of the diameter, the second circle circumference formula has become more ingrained in people's minds. It feels like this formula and the sequence of digits three point one four are the only things that students can remember for many years after school


Online circle calculator - calculate circle area + circumference

This circle calculator is based on Arndt Brünner's circle calculator.
Creative Commons Attribution Non-commercial Share Alike License 4.0

One more word about the online calculator. The use of such tools is convenient, but should not replace thinking and doing your own calculations. Learning always has something to do with practicing. Anyone who has understood the ideas and can also do the calculations by hand or pocket calculator is of course allowed to work excessively with such tools.


Finally, the master’s question. Why can't pirates calculate a circumference? Because they guess Pi 😉

Note on image rights:
Animated rolling of the circumference illustrating the number π - @John Reid - Wikipedia (the GNU Free Documentation License)
A circle with a center, radius and diameter - @ Sven