# How to translate plane coordinates x,y to equirectangular?

I have a procedural texture with a circle made by formula X ** 2 + Y ** 2 < R ** 2. It looks like a circle on a plane. But if I try to use this formula in the World environment - the circle is distorted.

How to convert XY coordinates in the formula to the equirectangular coordinates to have the clear circle in the environment?

It's not about especially for the circle, I need to have the formula to translate any procedurally generated plane texture to equirectangular. • It's very late, but still-- if you recreate equirectangular mapping in nodes, you're going to have the exact same distortion that you have with using equirectangular mapping. You're approaching this the wrong way. If you want a circle, do it by dot product >= constant; if you want to make an equirectangular map without distortion, do it by making an equirectangular render. – Nathan Apr 9 at 16:59

It seems to me, that the number, that used in Power node is not exactly equals 2. It can be like 2.0001, but in widget it rounds 2. Why is important? Coordinates are in range -1 ... 1 so part of coordinates are negative. And raising a negative number to a fractional degree is impossible (because of math), so it brakes the resulted circle.
Does not equal 2: 