Charts & Data Visualization
Polar Plot Coordinate Formula: Convert Radius & Angle (r, theta) to XY Scatter
Plot true continuous-angle Polar Charts (antenna radiation lobes, wind roses, acoustic microphone patterns) on an XY Scatter grid by converting Polar (r, theta_deg) into Cartesian X = r * COS(RADIANS(theta)) and Y = r * SIN(RADIANS(theta)).
Why Radar Charts distort unequal angles — and how Polar-to-Cartesian XY Scatter fixes it!
Built-in spreadsheet Radar/Spider charts treat angles as equally spaced categorical text labels — so plotting measurements at 0°, 15°, 30°, and 120° places 120° right next to 30° at equal 90° visual spacing, severely distorting directional lobes! Converting Polar coordinates (Radius r >= 0, Angle theta in degrees) into Cartesian coordinates plots exact continuous geometry on a standard XY Scatter chart!
Under standard counterclockwise (CCW from +X East axis) mathematical convention, X = r * COS(RADIANS(theta_deg)) and Y = r * SIN(RADIANS(theta_deg)); under clockwise compass/navigation azimuth convention (CW from +Y North = 0°, East = 90°), simply swap trigonometric axes: X_compass = r * SIN(RADIANS(azimuth_deg)) and Y_compass = r * COS(RADIANS(azimuth_deg))!
| Polar Point (Radius r = 10.0) | Math CCW X = r * COS(theta) | Math CCW Y = r * SIN(theta) | Compass CW (0° = North) (X, Y) |
|---|---|---|---|
| theta = 0° | X = 10.0000 | Y = 0.0000 | (0.0000, 10.0000) |
| theta = 30° | X = 8.6603 | Y = 5.0000 | (5.0000, 8.6603) |
| theta = 60° | X = 5.0000 | Y = 8.6603 | (8.6603, 5.0000) |
| theta = 135° | X = -7.0711 | Y = 7.0711 | (7.0711, -7.0711) |
Cartesian Abscissa X = r * COS(RADIANS(theta_deg))
Converts non-negative polar radius B2 and angle B3 (degrees CCW from +X axis) into horizontal scatter coordinate X.
=IF(B2 < 0, "Requires Polar Radius r >= 0", ROUND(B2 * COS(RADIANS(B3)), 4))Cartesian Ordinate Y = r * SIN(RADIANS(theta_deg))
Computes vertical scatter coordinate Y = r * SIN(RADIANS(theta_deg)), satisfying exact Euclidean verification SQRT(X^2 + Y^2) = r.
=IF(B2 < 0, "Requires Polar Radius r >= 0", ROUND(B2 * SIN(RADIANS(B3)), 4))Try the example
Use the original values or change them to test your understanding.