Cartesian to polar coordinates
Enter x and y and get the polar coordinates: the distance r to the origin and the angle θ, in degrees or radians, plus the quadrant the point lies in.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The formulas
- r = √(x² + y²)
- θ = atan2(y, x)
atan2 takes the signs of x and y into account, so the angle is right in every quadrant. For (−1, −1), θ is −135° (or 225° measured from 0° to 360°), not 45°.
Polar coordinates
Instead of "3 right and 4 up", polar coordinates say "5 away at an angle of 53.13°". They are handy for anything that turns or radiates from a centre, such as radar, antennas and complex numbers. The other way round is the polar to Cartesian converter.
Frequently asked questions
Is the cartesian to polar free?
Yes. The cartesian to polar is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.