Calculate the average alpha needed to get a foreground colour to be as close to a target colour, when used with transparency above a background colour.

rgba-calc.js

var rgb = (function(red, blue, green) {
  return {
    red: red,
    blue: blue,
    green: green
  };
});

var rgb1 = rgb(0, 0, 0); // colour to use
var rgb2 = rgb(255, 255, 255); // background colour
var rgb3 = rgb(219, 230, 226); // target colour

// calculate alphas
var alpha1 = (rgb3.red-rgb2.red) / (rgb1.red-rgb2.red),
    alpha2 = (rgb3.green-rgb2.green) / (rgb1.green-rgb2.green),
    alpha3 = (rgb3.blue-rgb2.blue) / (rgb1.blue-rgb2.blue);

// the average alpha to use to get rgb2 as close to rgb3 as possible
var averageAlpha = ((alpha1 + alpha2 + alpha3) / 3).toFixed(5);