Cartesian to Polar Calculator
Convert x, y coordinates to polar coordinates.
Results update as you type.
How it works
This calculator converts Cartesian coordinates to polar form, the reverse of the polar-to-Cartesian conversion. You enter the x and y coordinates of a point, and it returns the radius and the angle in degrees. The radius is the straight-line distance from the origin to the point, computed with the Pythagorean theorem as the square root of x squared plus y squared. The angle is the direction of the point measured counterclockwise from the positive x-axis. Finding the angle correctly requires care about which quadrant the point is in, so the calculator uses the two-argument arctangent function, which accounts for the signs of both x and y to place the angle in the right quadrant, then reports it in the range 0 to 360 degrees. Converting to polar form is useful whenever a problem is more naturally expressed in terms of distance and direction rather than horizontal and vertical position, such as in navigation, physics involving rotation or central forces, signal processing, and computer graphics. The point at the origin, where both x and y are zero, has a radius of zero and an undefined angle, since no direction is meaningful there. Enter the x and y coordinates to convert them to polar radius and angle.
r = √(x² + y²) ; θ = atan2(y, x)
The radius is the straight-line distance from the origin to the point, found with the Pythagorean theorem as the square root of x squared plus y squared. The angle is the direction from the positive x-axis, computed with the two-argument arctangent so it lands in the correct quadrant, then reported in degrees from 0 to 360.
Source:Coordinate geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter x-coordinate and y-coordinate.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Radius (r) updates instantly as you type — no button to press.
Frequently asked questions
How do you convert Cartesian to polar coordinates?
Find the radius as the square root of x squared plus y squared, the distance from the origin. Find the angle using the two-argument arctangent of y and x, which gives the direction from the positive x-axis in the correct quadrant. The calculator returns the radius and the angle in degrees, converting a point from rectangular to polar form.
Why use the two-argument arctangent?
The ordinary arctangent of y divided by x cannot tell which quadrant a point is in, because dividing loses the individual signs of x and y. The two-argument arctangent, atan2, takes x and y separately, so it returns the correct angle in all four quadrants. This avoids the errors that arise from the plain arctangent.
What range is the angle given in?
This calculator reports the angle from 0 to 360 degrees, measured counterclockwise from the positive x-axis. Some conventions use minus 180 to 180 degrees instead. If you need a different range, you can add or subtract 360 degrees as appropriate. The radius is always non-negative, so direction is fully captured by the angle.
What happens at the origin?
At the origin, where both x and y are zero, the radius is zero and the angle is undefined, because a point with no distance from the origin has no meaningful direction. Any angle would describe the same point. In practice, the origin is a special case, and calculations involving it should handle the undefined angle separately.
When are polar coordinates preferable?
Polar coordinates shine when distance and direction are the natural way to describe a situation, such as radar and navigation, circular or orbital motion, central forces in physics, antenna patterns, and certain graphics or spiral shapes. Converting Cartesian data to polar can reveal rotational symmetry or simplify equations that are awkward in rectangular form.