Polar to Rectangular Converter
Convert polar coordinates (r, θ) to rectangular (x, y) coordinates, with the angle entered in degrees or radians.
How it works
x = r·cos θ · y = r·sin θ
Polar coordinates describe a point by its distance r from the origin and the angle θ its ray makes with the positive x-axis. Dropping perpendiculars to the axes recovers the rectangular coordinates: the horizontal leg is r·cos θ and the vertical leg is r·sin θ. Make sure the angle unit matches your data — degrees and radians give very different points.
Worked example
For r = 5 and θ = 53.13°: x = 5·cos 53.13° ≈ 5·0.6 = 3.0 and y = 5·sin 53.13° ≈ 5·0.8 = 4.0, so the rectangular coordinates are approximately (3, 4).
Sources: Polar coordinate system (Wikipedia)
Frequently asked questions
Do I enter the angle in degrees or radians?
Either — pick the matching unit from the selector. The calculator converts internally to radians (the form the trig functions need) and reports the angle it actually used.
What happens with a negative radius?
A negative r points in the opposite direction, i.e. 180° away from θ. The formulas x = r·cos θ and y = r·sin θ handle this automatically, placing the point on the far side of the origin.
How is this different from converting back to polar?
This direction goes (r, θ) → (x, y) using cosine and sine. The reverse, (x, y) → (r, θ), uses the Pythagorean theorem for r and atan2 for θ — use the rectangular-to-polar converter for that.
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This calculator is for educational purposes. Double-check important results before acting on them.