Rectangular to Polar Converter
Convert any Cartesian point (x, y) into its polar form (r, θ) using the magnitude and a quadrant-correct atan2 angle.
Angle unit
Angle θ: 53.1301°
- 1
x²
3² = 3 × 3 = 9 - 2
y²
4² = 4 × 4 = 16 - 3
Magnitude r
√(9 + 16) = 5r is the straight-line distance from the origin to the point.
How does this calculator work?
To convert (x, y) to polar form, compute the magnitude r = √(x² + y²) and the angle θ = atan2(y, x). Using atan2 keeps the angle in the correct quadrant. The result is written r ∠ θ, with θ available in degrees or radians and in either the −180°-to-180° or 0°-to-360° range.
Formula
How this is calculated
Enter the x (horizontal) and y (vertical) coordinates of a point, then pick whether you want the resulting angle in degrees or radians. The magnitude r is the straight-line distance from the origin to the point, computed as r = √(x² + y²) using Math.hypot for numerical stability.
The angle θ is found with atan2(y, x) rather than plain arctan(y/x), because atan2 inspects the signs of both x and y to place the angle in the correct quadrant. Its principal range is −π to π (−180° to 180°). We also report the angle normalized to a full turn, [0, 2π) or [0°, 360°), by adding one full revolution to any negative result. Degrees are obtained by multiplying the radian value by 180/π.
At the origin (x = 0, y = 0) the magnitude is 0 and the angle is conventionally 0; atan2(0, 0) returns 0 here. Both inputs must be finite numbers. The polar form is shown as r ∠ θ, the standard phasor notation used in engineering and complex-number work.
Frequently asked questions
arctan(y/x) loses the sign information of x and y, so it cannot distinguish opposite quadrants and divides by zero when x = 0. atan2(y, x) uses both signs to return the correct angle across all four quadrants.
The principal angle from atan2 lies in −180° to 180° (−π to π). We additionally provide the same direction expressed in the 0° to 360° (0 to 2π) range for convenience.
Use x = r·cos(θ) and y = r·sin(θ), with θ in radians (multiply degrees by π/180 first).
Also known as
TG we-Calculate Editorial Team. (2026). Rectangular to Polar Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rectangular-to-polar-calculator
TG we-Calculate Editorial Team. "Rectangular to Polar Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/rectangular-to-polar-calculator.
TG we-Calculate Editorial Team, "Rectangular to Polar Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rectangular-to-polar-calculator
@misc{wecalculate_rectangular_to_polar_calculator, title = {Rectangular to Polar Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rectangular-to-polar-calculator}}, year = {2026}, note = {TG we-Calculate} }
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