If you need incircle radius (apothem) (r), circumcircle radius (r) and diagonal (d) and you already have side a, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Pentagon Calculator?
The pentagon calculator works through side a to give you incircle radius (apothem) (r), circumcircle radius (r) and diagonal (d).
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Pentagon Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with side a set to 10, the calculator returns diagonal (d) of 16.18034, and height (h) of 15.38842, and perimeter of 50. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out incircle radius (apothem) (r)?
Enter side a. The calculator then works through the relationship and reports incircle radius (apothem) (r), circumcircle radius (r) and diagonal (d).
What does the pentagon actually calculate?
It takes side a and converts them into incircle radius (apothem) (r), circumcircle radius (r) and diagonal (d) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter side a?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.