The segment area calculator works out segment area (a), chord length (c) and arc length (l) from central angle (α), height (h), sin and cos. Enter what you have and the relationship is applied straight away, so you get the answer without working through the algebra yourself.
What Is the Segment Area Calculator?
The segment area calculator works through central angle (α), height (h), sin and cos to give you segment area (a), chord length (c) and arc length (l).
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 Segment Area 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 central angle (α) set to 10, height (h) set to 5, sin set to 2, the calculator returns radius (r) of 6.97995, and arc length (l) of 69.7995, and segment area (a) of 256.8506. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out segment area (a)?
Enter central angle (α), height (h), sin and cos. The calculator then works through the relationship and reports segment area (a), chord length (c) and arc length (l).
What does the segment area actually calculate?
It takes central angle (α), height (h), sin and cos and converts them into segment area (a), chord length (c) and arc length (l) 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 central angle (α)?
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.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
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.