This rotation calculator takes the figures you already have and applies the relationship behind rotation calculations for you, giving x10, y10 and x1 from x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, pivot x0, pivot y0 and angle of the rotation θ.
What Is the Rotation Calculator?
The rotation calculator works through x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, pivot x0, pivot y0 and angle of the rotation θ to give you x10, y10 and x1.
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 Rotation 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 x1 set to 10, x2 set to 5, x3 set to 2, the calculator returns x1 of 12.72789, and y1 of 6.24844, and x2 of -74.30252. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out x10?
Enter x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, pivot x0, pivot y0 and angle of the rotation θ. The calculator then works through the relationship and reports x10, y10 and x1.
What does the rotation actually calculate?
It takes x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, pivot x0, pivot y0 and angle of the rotation θ and converts them into x10, y10 and x1 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 x1?
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.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.