Whether you are estimating on the spot or checking a result somebody else gave you, the polar to rectangular coordinates calculator is the quickest way to get from r, θ, x, y, one way, cos, sin, atan2 and θ to x, y and r.
What Is the Polar to Rectangular Coordinates Calculator?
The polar to rectangular coordinates calculator works through r, θ, x, y, one way, cos, sin, atan2 and θ to give you x, y and r.
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 Polar to Rectangular Coordinates 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 r set to 10, θ set to 5, x set to 2, the calculator returns x of 2.84, and y of -9.59, and r of 100.02. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out x?
Enter r, θ, x, y, one way, cos, sin, atan2 and θ. The calculator then works through the relationship and reports x, y and r.
What does the polar to rectangular coordinates actually calculate?
It takes r, θ, x, y, one way, cos, sin, atan2 and θ and converts them into x, y and r 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 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.
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.
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.