Conversion between models involves warping the RGB cube to the HSL cone, or back.

If you care, wikipedia has a good article on this.
It generally involves projecting the cube onto the HSV/HSL cone to get the HUE
Then looking at intensities to get lightness
And the difference between the minimal and maximum intensities to get the saturation.

Here is some code

function HSLtoRGB(hue, saturation, light){
    let r,g,b;

    let c = (1-Math.abs(2*light -1))*saturation;
    let h = hue/60;
    let x = c*(1-Math.abs(h %2 -1))
    let m = light - 1/2 * c ;

    if( h < 1) {
           r = c; g = x; b = 0;
    } else if (h < 2) {
           r = x; g = c; b = 0;
    } else if (h < 3) {
           r = 0; g = c; b = x;
    } else if (h < 4) {
           r = 0; g = x; b = c;
    } else if (h < 5) {
           r = x; g = 0; b = c;
    } else {
           r = c; g = 0; b = x;
    }

    r = Math.floor((m+r) * 255);
    g = Math.floor((m+g) * 255);
    b = Math.floor((m+b) * 255);
    return "rgb(" + r  + "," + g + "," + b + ")";
}

The demo is here