Polar to Cartesian coordinate converter
Two ways of naming the same point on a plane, converted with high-precision trigonometry.
x from polar
3.000 000 000 29
- y from polar
- 3.999 999 999 78
- r from Cartesian
- 5
- Angle from Cartesian
- 53.130 102 degrees
Show the working
- Radius r = 5
- Angle = 53.1301
- x (for the reverse) = 3
- y (for the reverse) = 4
- rad = rad(53.1301) = 0.927 295
- x from polar = 5 * cos(0.927 295) = 3
- y from polar = 5 * sin(0.927 295) = 4
- r from Cartesian = hypot(3, 4) = 5
- Angle from Cartesian = (3 != 0 || 4 != 0) ? deg(atan2(4, 3)) : 0 = 53.1301
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- x = r cos(theta), y = r sin(theta)
- r = sqrt(x^2 + y^2), theta = atan2(y, x)