convert Hsl to rgb and hex

Question

I need a color converter to convert from hsl to rgb and hex value. I am going to do similar like this. I am using jquery and jquery ui range slider for this. Here is my code:

$(function() {
    $( "#hsl_hue_range" ).slider({
        min: 0,
        max: 100,
        value: 0,
        range: false,
        animate:"slow",
        orientation: "horizontal",
        slide: function( event, ui ) {
            var hsl_hue = ui.value;
        }
    });
});

$(function() {
    $( "#hsl_saturation_range" ).slider({
        min: 0,
        max: 100,
        value: 0,
        range: false,
        animate:"slow",
        orientation: "horizontal",
        slide: function( event, ui ) {
            var hsl_saturation = ui.value;
        }
    });
});

$(function() {
    $( "#hsl_light_range" ).slider({
        min: 0,
        max: 100,
        value: 0,
        range: false,
        animate:"slow",
        orientation: "horizontal",
        slide: function( event, ui ) {
            var hsl_light = ui.value;
        }
    });
});

I want the solution like this:

the input to converter can be given by the variables. like hsl_hue hsl_saturation hsl_light.

Is there any way to do this?
if no way, what can I do?

Answer 1

New approach (inspired by @Kamil-Kiełczewski solution)
Takes degree, percentage, percentage and returns css hex color:

function hslToHex(h, s, l) {
  l /= 100;
  const a = s * Math.min(l, 1 - l) / 100;
  const f = n => {
    const k = (n + h / 30) % 12;
    const color = l - a * Math.max(Math.min(k - 3, 9 - k, 1), -1);
    return Math.round(255 * color).toString(16).padStart(2, '0');   // convert to Hex and prefix "0" if needed
  };
  return `#${f(0)}${f(8)}${f(4)}`;
}

Example:

hslToHex(360, 100, 50)  // "#ff0000" -> red

Original version: (still OK, just longer)

Takes degree, percentage, percentage and returns css hex color:

function hslToHex(h, s, l) {
  h /= 360;
  s /= 100;
  l /= 100;
  let r, g, b;
  if (s === 0) {
    r = g = b = l; // achromatic
  } else {
    const hue2rgb = (p, q, t) => {
      if (t < 0) t += 1;
      if (t > 1) t -= 1;
      if (t < 1 / 6) return p + (q - p) * 6 * t;
      if (t < 1 / 2) return q;
      if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;
      return p;
    };
    const q = l < 0.5 ? l * (1 + s) : l + s - l * s;
    const p = 2 * l - q;
    r = hue2rgb(p, q, h + 1 / 3);
    g = hue2rgb(p, q, h);
    b = hue2rgb(p, q, h - 1 / 3);
  }
  const toHex = x => {
    const hex = Math.round(x * 255).toString(16);
    return hex.length === 1 ? '0' + hex : hex;
  };
  return `#${toHex(r)}${toHex(g)}${toHex(b)}`;
}

Example:

hslToHex(360, 100, 50)  // "#ff0000" -> red