Polar to Cartesian Converter (and Back)
Choose the direction and enter the coordinates.
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Cartesian (x, y)
Cartesian (x, y)
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Polar (r, θ in degrees)
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θ in radians
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Quadrant
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Polar to Cartesian Converter (and Back) by TheCalcTools
How the Polar to Cartesian Converter (and Back) works
Polar coordinates give a point by its distance r from the origin and its angle θ from the positive x-axis. x = r cos θ and y = r sin θ.
Going back, r = √(x² + y²) and θ = atan2(y, x), which picks the correct quadrant. Angles here are reported from 0° to 360°.
The formula
x = r cos θ, y = r sin θ; r = √(x² + y²), θ = atan2(y, x)
Worked example
Using the default values shown in the calculator:
| Convert | Cartesian (x, y) to polar (r, θ) |
|---|---|
| x | 3 |
| y | -4 |
| r (distance from the origin) | 5 |
| θ (degrees) | 30 |
- (3, −4) is r = 5 at θ = 5.355890 radians: (5, 306.869898°).
Result:
| Cartesian (x, y) | (3, -4) |
|---|---|
| Polar (r, θ in degrees) | (5, 306.869898°) |
| θ in radians | 5.3559 |
| Quadrant | IV |
Frequently asked questions
Why use atan2 rather than atan(y/x)?
atan(y/x) cannot tell (1, 1) from (−1, −1). atan2 looks at both signs and returns the right quadrant.
Sources and further reading
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