Polar to Cartesian Calculator
Convert polar coordinates (r, θ) to Cartesian (x, y) using x = r·cos θ and y = r·sin θ, with the angle in degrees.
How it works
x = r · cos θ · y = r · sin θ (θ in degrees, converted internally to radians)
Polar coordinates locate a point by how far it is from the origin (r) and the angle θ it makes with the positive x-axis. To get the familiar Cartesian x and y, drop a right triangle from the point to the x-axis: the horizontal leg is r·cos θ and the vertical leg is r·sin θ. A negative radius simply points the other way along the angle, and the calculator converts your degrees to radians before applying the trig functions.
Worked example
Convert (r = 5, θ = 53.13°). x = 5 × cos 53.13° ≈ 5 × 0.6 = 3.0000 and y = 5 × sin 53.13° ≈ 5 × 0.8 = 4.0000, so the point is (3, 4). Checking with the Pythagorean theorem, √(3² + 4²) = 5, which recovers the original radius.
Sources: Polar coordinate system — Wikipedia
Frequently asked questions
Which way is the angle measured?
Counter-clockwise from the positive x-axis. So 0° points right along the x-axis, 90° points straight up, 180° points left, and 270° points down. Enter the angle in degrees and the calculator handles the radian conversion.
What does a negative radius do?
A negative r reflects the point through the origin — it lands in the opposite direction from the given angle, the same as adding 180° to θ and using a positive radius.
How do I go back from Cartesian to polar?
Use the reverse conversion: r = √(x² + y²) and θ = atan2(y, x). Our Cartesian to Polar Calculator does exactly that, turning an (x, y) pair back into (r, θ).
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This calculator is for educational purposes. Double-check important results before acting on them.