Relative Luminance Calculator
Calculate the relative luminance of any color (0 = absolute black, 1 = absolute white) using the WCAG 2.x linearization formula, essential for contrast ratio and accessibility compliance checks.
Relative luminance
0.1831
Color: #1A73E8 — rgb(26, 115, 232)
Linearized channels
WCAG contrast ratios
Luminance breakdown
Quick answer
Relative luminance is a perceptual measure of a color's brightness, ranging from 0 (pure black) to 1 (pure white), as defined by WCAG 2.x and the IEC 61966-2-1 sRGB standard. To calculate it, each 8-bit RGB channel is divided by 255, gamma-corrected to linear light, and then combined using the weighted sum L = 0.2126R + 0.7152G + 0.0722B. The weights reflect human eye sensitivity: green contributes most to perceived brightness, red contributes moderately, and blue contributes least. Relative luminance is the foundation for computing the WCAG contrast ratio between two colors, which must be at least 4.5:1 for normal text (AA) and 7:1 for enhanced (AAA) compliance.
Formula & method
C_sRGB = C_8bit / 255
- C_8bit — Raw channel value (0–255)
- C_sRGB — Normalized channel value (0–1)
Step 1: Normalize each 8-bit channel (0–255) to a 0–1 floating-point value.
C_linear = C_sRGB / 12.92 if C_sRGB ≤ 0.04045, else ((C_sRGB + 0.055) / 1.055)^2.4
- C_sRGB — Normalized channel value (0–1)
- C_linear — Linearized channel value (0–1), representing physical light intensity
Step 2: Apply the sRGB gamma linearization (inverse gamma) to each normalized channel.
L = 0.2126 × R_linear + 0.7152 × G_linear + 0.0722 × B_linear
- L — Relative luminance (0 = black, 1 = white)
- R_linear — Linearized red channel
- G_linear — Linearized green channel
- B_linear — Linearized blue channel
Step 3: Compute relative luminance using ITU-R BT.709 luma coefficients. These weights reflect human eye cone sensitivity.
Examples
- Input
- R=255, G=255, B=255
- Result
- Relative luminance = 1.0000
- Why
- Each channel normalizes to 1.0. After linearization (1.0 > 0.04045): ((1.0 + 0.055) / 1.055)^2.4 = 1.0. L = 0.2126×1.0 + 0.7152×1.0 + 0.0722×1.0 = 1.0000. Pure white has the maximum luminance of 1.
- Input
- R=0, G=0, B=0
- Result
- Relative luminance = 0.0000
- Why
- Each channel normalizes to 0.0. Since 0 ≤ 0.04045, linearization gives 0 / 12.92 = 0 for all channels. L = 0.2126×0 + 0.7152×0 + 0.0722×0 = 0.0000. Pure black has the minimum luminance of 0.
- Input
- R=255, G=0, B=0
- Result
- Relative luminance = 0.2126
- Why
- R normalizes to 1.0, linearizes to 1.0. G and B normalize and linearize to 0. L = 0.2126×1.0 + 0.7152×0 + 0.0722×0 = 0.2126. Red's luminance exactly equals the red coefficient, demonstrating that green dominates perceived brightness.
- Input
- R=128, G=128, B=128
- Result
- Relative luminance ≈ 0.2160
- Why
- Each channel: 128/255 = 0.5020. Since 0.5020 > 0.04045: ((0.5020+0.055)/1.055)^2.4 = (0.5280)^2.4 ≈ 0.2160. L = (0.2126+0.7152+0.0722)×0.2160 = 1.0×0.2160 ≈ 0.2160. Note that #808080 is not perceptually 50% gray in luminance terms due to gamma encoding.
Frequently asked questions
What is relative luminance and why does it matter for accessibility?
Relative luminance is a WCAG-defined measure of a color's perceived brightness on a scale of 0 (black) to 1 (white). It matters because WCAG contrast ratios — required for accessible text — are computed directly from the luminance values of the foreground and background colors. Without correct luminance values, you cannot verify AA (4.5:1) or AAA (7:1) compliance.
How is relative luminance different from lightness (HSL)?
HSL lightness is a simple average-based approximation that does not account for human eye sensitivity to different wavelengths. Relative luminance uses ITU-R BT.709 coefficients (0.2126 R, 0.7152 G, 0.0722 B) that reflect how much each color channel contributes to perceived brightness. #FF0000 (red) has an HSL lightness of 50% but a relative luminance of only 0.2126.
What does the gamma linearization step do?
Digital images use gamma encoding (sRGB) so that more bit values are allocated to dark shades where human perception is most sensitive. Before computing luminance, you must undo this encoding (linearize) so that the values represent actual light intensity. Values ≤ 0.04045 are in a near-linear region and use simple division; higher values use the power function with exponent 2.4.
How do I calculate the WCAG contrast ratio using luminance?
Once you have the relative luminance of both colors, the contrast ratio is (L1 + 0.05) / (L2 + 0.05), where L1 is the lighter luminance and L2 is the darker. Adding 0.05 accounts for ambient light in a typical screen environment. For example, white (L=1.0) against black (L=0.0) gives (1.05) / (0.05) = 21:1, the maximum possible ratio.
Can I input a hex color code instead of separate RGB values?
Yes. A hex code like #1A2B3C maps directly to RGB: R=0x1A=26, G=0x2B=43, B=0x3C=60. You can split any 6-digit hex into three 2-digit hex pairs and convert each to decimal. This calculator accepts a hex field and converts it automatically, or you can enter the R, G, B values directly.
Why does green contribute so much more than blue to luminance?
The human eye has three types of cone cells. The L-cones (long wavelength, sensitive to red) and M-cones (medium, sensitive to green) are far more numerous and sensitive than S-cones (short, sensitive to blue). The BT.709 coefficients — 0.2126 R, 0.7152 G, 0.0722 B — encode this physiological reality. Blue contributes only about 7% of perceived brightness even at full intensity.
Sources & references
- https://www.w3.org/TR/WCAG21/#dfn-relative-luminance
- https://www.w3.org/TR/WCAG21/#contrast-minimum
- https://www.itu.int/rec/R-REC-BT.709/en
External references open in a new tab. We are independent and not affiliated with these organizations.
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Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
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