Converting Lat lon to Mercator coordinate

The Mercator map projection is a special limiting case of the Lambert Conic Conformal map projection with the equator as the single standard parallel. All other parallels of latitude are straight lines and the meridians are also straight lines at right angles to the equator, equally spaced. It is the basis for the transverse and oblique forms of the projection. It is little used for land mapping purposes but is in almost universal use for navigation charts. As well as being conformal, it has the particular property that straight lines drawn on it are lines of constant bearing. Thus navigators may derive their course from the angle the straight course line makes with the meridians. ^[1.]

The formulas to derive projected Easting and Northing coordinates from spherical latitude φ and longitude λ are:

E = FE + R (λ – λₒ)

N = FN + R ln[tan(π/4 + φ/2)]   

where λ_O is the longitude of natural origin and FE and FN are false easting and false northing. In spherical Mercator those values are actually not used, so you can simplify the formula to

Pseudo code example, so this can be adapted to every programming language.

latitude    = 41.145556; // (φ)

longitude   = -73.995;   // (λ)

mapWidth    = 200;

mapHeight   = 100;

// get x value

x = (longitude+180)*(mapWidth/360)

// convert from degrees to radians

latRad = latitude*PI/180;

// get y value

mercN = ln(tan((PI/4)+(latRad/2)));

y     = (mapHeight/2)-(mapWidth*mercN/(2*PI));

References:

https://amp-reddit-com.cdn.ampproject.org/v/s/amp.reddit.com/r/educationalgifs/comments/5lhk8y/how_the_mercator_projection_distorts_the_poles/?usqp=mq331AQJCAEoAVgBgAEB&amp_js_v=0.  => Nice video on Mercator projection 

https://stackoverflow.com/questions/14329691/convert-latitude-longitude-point-to-a-pixels-x-y-on-mercator-projection