# Luma: Apple & Perceived Brightness

Rec. 709 (ITU Recommendation BT.709) is the international standard for HDTV. The luma calculation from this standard provides a way to convert RGB color values into a perceived brightness value that closely matches human visual perception.

Human eyes are more sensitive to green light than red and to red light than blue. Rec. 709 luma coefficients account for this by weighting each color channel differently. The weighted sum produces a single brightness value that represents how bright a color appears to the human eye.

	variable	range	weight
Red	`R`	0-255	21.26%
Green	`G`	0-255	71.52%
Blue	`B`	0-255	7.22%
Luma	`Y`	0-255

# Luma Formula

Y = ( 0.2126 × R ) + ( 0.7152 × G ) + ( 0.0722 × B )

# JavaScript Implementation

function selectThemeWithLuma(bgColor) {
  // remove leading #
  let hex = bgColor.replace(/^#/, '');

  // parse RGB components from hex
  const r = parseInt(hex.substring(0, 2), 16);
  const g = parseInt(hex.substring(2, 4), 16);
  const b = parseInt(hex.substring(4, 6), 16);

  // calculate Rec. 709 Luma using standard coefficients
  const Y = 0.2126 * r + 0.7152 * g + 0.0722 * b;

  // threshold at midpoint: 127.5
  // Y ≤ 127.5 = dark background, use light text
  // Y > 127.5 = light background, use dark text
  return Y <= 127.5;
}

# Key Characteristics

# No Gamma Correction

Unlike relative luminance in W3C Accessibility Guidelines, the ITU calculation of luma applies coefficients directly to gamma-corrected RGB values for simplicty (no complex gamma correction) and efficency (fewer operations per calculation).

Feature	Rec. 709 Luma	WCAG relative luminance
RGB Coefficients	0.2126, 0.7152, 0.0722	0.2126, 0.7152, 0.0722
Gamma Correction	No	Yes: complex formula
Output Range	0-255	0-1
Threshold	127.5	0.179
Use Case	Perceived Brightness	Accessibility Contrast Ratios

# Output Range

minimum: 0 → luma value for black #000000
maximum: 255 → luma value for white #FFFFFF
midpoint: 127.5

# Threshold Decision

Using the midpoint as the threshold:

colors with luma ≤ 127.5 are considered dark → use light/white text
colors with luma > 127.5 are considered light → use dark/black text

# Example Colors

Color	Hex	R	G	B	Y	Theme
Black	`#000000`	0	0	0	0.00	Dark
Navy	`#000080`	0	0	128	9.24	Dark
Red	`#FF0000`	255	0	0	54.21	Dark
Green	`#00FF00`	0	255	0	182.38	Light
Blue	`#0000FF`	0	0	255	18.41	Dark
Yellow	`#FFFF00`	255	255	0	236.59	Light
Gray	`#808080`	128	128	128	128.00	Light
White	`#FFFFFF`	255	255	255	255.00	Light