How to use it
- Cartesian to polar: type x and y. You get the distance r from the origin and the angle from the positive x-axis.
- Polar to cartesian: type the distance r and the angle in degrees. You get x and y.
- Degrees: type decimal degrees to see degrees, minutes and seconds, or type the three parts to get the decimal value.
- The address bar holds the numbers, so a link brings the same conversion back.
The formulas
From polar to cartesian: x = r cos v and y = r sin v. From cartesian to polar: r = √(x² + y²), and the angle v is found from the signs of x and y as well as their ratio.
| Point | r | Angle v |
|---|---|---|
| (3, 4) | 5 | 53.13° |
| (−3, 4) | 5 | 126.87° |
| (−3, −4) | 5 | 233.13° |
| (3, −4) | 5 | 306.87° |
The ratio y/x is the same for (3, 4) and (−3, −4), so arctan(y/x) alone gives 53.13° for both. The calculator uses atan2(y, x), which looks at both signs and so lands in the right quadrant. The angle is measured counter-clockwise from the positive x-axis and given from 0° to 360°.
Degrees, minutes and seconds
One degree is 60 minutes and one minute is 60 seconds. 40.7128° is 40° plus 0.7128 · 60 = 42.768′, and 0.768 · 60 = 46.08″, so 40° 42′ 46.08″.