Rotation Calculator

Our rotation calculator implements this basic geometric transformation for up to ten points at the same time!

Clear
Cartesian (x, y)(3, 4)
Polar (r, θ)(5, 53.130102°)
r5
θ in degrees53.13010235°
θ in radians0.927295218
Quadrant1

The formula

r = √(x² + y²), θ = atan2(y, x)

Why atan2 rather than atan

atan(y/x) loses the quadrant: (1, 1) and (−1, −1) give the same ratio and so the same angle, though they point in opposite directions. atan2(y, x) takes both coordinates separately and returns the correct angle across all four quadrants, from −180° to 180°. Always use atan2 for this conversion.