I came up with a solution.
This is formula to calculate x and y of Mercator projected map:

Here is function for y:
function degreesToRadians(degrees){
return degrees / 180 * Math.PI;
}
function mercatorLatitudeToY(latitude){
return Math.log(Math.tan(Math.PI / 4 + degreesToRadians(latitude) / 2));
}
When R=1 the result you get is radians. So I calculate y for top and bottom latitudes.
Next, I calculate the same radians if the projection is Equirectangular - I simply need to convert top and bottom latitude to radians. And last thing - I just need to find aspect ratio of differences:
var scale = (mercatorLatitudeToY(topLatitude) - mercatorLatitudeToY(bottomLatitude))/ (degreesToRadians(topLatitude) - degreesToRadians(bottomLatitude));
For map without Antarctica, aspect ratio is ~1.5