If you need perimeter of cycloid or area of cycloid (a) or hump height (d) and you already know radius of rolling circle (r), this calculator does the substitution for you. It is built for quick answers, for checking somebody else’s arithmetic, and for the moments when a formula book is not within reach.
What Is the Cycloid Calculator?
It is built around perimeter of cycloid, area of cycloid (a), hump height (d), and it works the same way whether you are checking a homework answer, confirming a colleague's figure, or working something out for yourself. Everything runs in your browser, so nothing you enter is uploaded anywhere.
How the Cycloid Calculation Works
The calculator works through the relationship one step at a time, so a change in any input flows straight through to the result.
The relationship between radius of rolling circle (r) and perimeter of cycloid, area of cycloid (a), hump height (d), hump length (c), arc length (s) is fixed, so the same figures always give the same answer. That makes it a good cross-check: run the numbers a second way and see whether the result agrees.
Getting a Result You Can Trust
It is worth running the figures twice with slightly different inputs. A calculator that behaves sensibly will move its outputs by a proportionate amount; if a small change produces a wildly different answer, there is usually a unit or a decimal point issue somewhere in the inputs.
Frequently Asked Questions
What do I need to work out perimeter of cycloid?
Enter radius of rolling circle (r). The calculator then works through the relationship and reports perimeter of cycloid, area of cycloid (a), hump height (d).
What does the cycloid actually calculate?
It takes radius of rolling circle (r) and converts them into perimeter of cycloid, area of cycloid (a), hump height (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 radius of rolling circle (r)?
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.
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.