sRGB

sRGB defines the chromaticities of the red, green, and blue primaries, the colors where one of the three channels is nonzero and the other two are zero. The gamut of chromaticities that can be represented in sRGB is the color triangle defined by these primaries. As with any RGB color space, for non-negative values of R, G, and B it is not possible to represent colors outside this triangle, which is well inside the range of colors visible to a human with normal trichromatic vision.

The primaries come from HDTV (ITU-R BT.709), which are somewhat different from those for older color TV systems (ITU-R BT.601). These values were chosen to reflect the approximate color of consumer CRT phosphors at the time of its design. Since flat-panel displays at the time were generally designed to emulate CRT characteristics, the values also reflected prevailing practice for other display devices as well.[1]

Plot of the sRGB intensities (red), and this function's slope in log-log space (blue), which is the instantaneous gamma. Below a compressed value of 0.04045 or a linear intensity of 0.00313, the curve is linear so the gamma is 1. Behind the red curve is a dashed black curve showing an exact gamma = 2.2 power law.

On an sRGB display, each solid bar should look as bright as the surrounding striped dither. (Note: must be viewed at original, 100% size)

The IEC specification indicates a reference display with a nominal gamma of 2.2 similar to the gamma response of CRT displays (a more accurate value is 2.3[4]). The ability to directly display sRGB images on a CRT without any lookup greatly helped sRGB's adoption. Gamma also conveniently places more numbers near the black, reducing visible quantization artifacts.

The standard further defines a nonlinear electro-optical transfer function (EOTF), which exactly defines the conversion from image data to output intensity. This curve is a slight tweaking of x^2.2.[5] A linear section is near zero, in order to avoid an infinite or zero slope that an exponential has, this is spliced to a curved section designed so the overall function is very close. In order to do this a formula using a higher exponent (2.4 in this case) is necessary. The instantaneous gamma (the slope when plotted on a log:log scale) varies from 1 in the linear section to 2.4 at maximum intensity, with a median value being close to 2.2.

In practice a pure x^2.2 may be used with sRGB data with very little difference, this is referred to as "simple sRGB" by Adobe, and also what happens when it is displayed unchanged on a CRT.

A straight line that passes through (0,0) is ${\displaystyle y={\frac {x}{\Phi }}}$, and a gamma curve that passes through (1,1) is ${\displaystyle y=\left({\frac {x+A}{1+A}}\right)^{\Gamma }}$

If these are joined at the point (X,X/Φ) then:

${\displaystyle {\frac {X}{\Phi }}=\left({\frac {X+A}{1+A}}\right)^{\Gamma }}$

To avoid a kink where the two segments meet, the derivatives must be equal at this point:

${\displaystyle {\frac {1}{\Phi }}=\Gamma \left({\frac {X+A}{1+A}}\right)^{\Gamma -1}\left({\frac {1}{1+A}}\right)}$

We now have two equations. If we take the two unknowns to be X and Φ then we can solve to give

${\displaystyle X={\frac {A}{\Gamma -1}},\Phi ={\frac {(1+A)^{\Gamma }(\Gamma -1)^{\Gamma -1}}{(A^{\Gamma -1})(\Gamma ^{\Gamma })}}}$

The values A = 0.055 and Γ = 2.4 were chosen so the curve closely resembled the gamma-2.2 curve. This gives X ≈ 0.0392857, Φ ≈ 12.9232102. These values, rounded to X = 0.03928, Φ = 12.92321 sometimes describe sRGB conversion.[6]

Draft publications by sRGB's creators further rounded Φ = 12.92,[2] resulting in a small discontinuity in the curve. Some authors adopted these incorrect values, in part because the draft paper was freely available and the official IEC standard is behind a paywall.[7] For the standard, the rounded value of Φ was kept and X was recomputed as 0.04045 to make the curve continuous, resulting in a slope discontinuity from 1/12.92 below the intersection to 1/12.70 above.

CIE 1931 xy chromaticity diagram showing the gamut of the sRGB color space (the triangle). The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers (labeled in blue). This image is drawn using sRGB, so colors outside the triangle cannot be accurately colored and have been interpolated. The D65 white point is shown in the center, and the Planckian locus is shown with color temperatures labeled in kelvins. D65 is not an ideal 6504-kelvin black body because it is based on atmospheric filtered daylight.

The sRGB specification assumes a dimly lit encoding (creation) environment with an ambient correlated color temperature (CCT) of 5003 K. This differs from the CCT of the illuminant (D65). Using D50 for both would have made the white point of most photographic paper appear excessively blue.[8][9] The other parameters, such as the luminance level, are representative of a typical CRT monitor.

For optimal results, the ICC recommends using the encoding viewing environment (i.e., dim, diffuse lighting) rather than the less-stringent typical viewing environment.[2]

The sRGB component values ${\displaystyle R_{\mathrm {srgb} }}$, ${\displaystyle G_{\mathrm {srgb} }}$, ${\displaystyle B_{\mathrm {srgb} }}$ are in the range 0 to 1. When represented digitally as 8-bit numbers, these color component values are in the range of 0 to 255, and should be divided (in a floating point representation) by 255 to convert to the range of 0 to 1.

${\displaystyle C_{\mathrm {linear} }={\begin{cases}{\dfrac {C_{\mathrm {srgb} }}{12.92}},&C_{\mathrm {srgb} }\leq 0.04045\\[5mu]\left({\dfrac {C_{\mathrm {srgb} }+0.055}{1.055}}\right)^{\!2.4},&C_{\mathrm {srgb} }>0.04045\end{cases}}}$

where ${\displaystyle C}$ is ${\displaystyle R}$, ${\displaystyle G}$, or ${\displaystyle B}$.

These gamma-expanded values (sometimes called "linear values" or "linear-light values") are multiplied by a matrix to obtain CIE XYZ (the matrix has infinite precision, any change in its values or adding not zeroes is not allowed):

${\displaystyle {\begin{bmatrix}X_{D65}\\Y_{D65}\\Z_{D65}\end{bmatrix}}={\begin{bmatrix}0.4124&0.3576&0.1805\\0.2126&0.7152&0.0722\\0.0193&0.1192&0.9505\end{bmatrix}}{\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}}$

This is actually the matrix for BT.709 primaries, not just for sRGB, the second row corresponds to the BT.709-2 luma coefficients (BT.709-1 had a typo in these coefficients).

The CIE XYZ values must be scaled so that the Y of D65 ("white") is 1.0 (X = 0.9505, Y = 1.0000, Z = 1.0890). This is usually true but some color spaces use 100 or other values (such as in CIELAB, when using specified white points).

The first step in the calculation of sRGB from CIE XYZ is a linear transformation, which may be carried out by a matrix multiplication. (The numerical values below match those in the official sRGB specification,[1][10] which corrected small rounding errors in the original publication[2] by sRGB's creators, and assume the 2° standard colorimetric observer for CIE XYZ.[2]) This matrix depends on the bitdepth.

${\displaystyle {\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}={\begin{bmatrix}+3.2406&-1.5372&-0.4986\\-0.9689&+1.8758&+0.0415\\+0.0557&-0.2040&+1.0570\end{bmatrix}}{\begin{bmatrix}X_{D65}\\Y_{D65}\\Z_{D65}\end{bmatrix}}}$

These linear RGB values are not the final result; gamma correction must still be applied. The following formula transforms the linear values into sRGB:

${\displaystyle C_{\text{sRGB}}={\begin{cases}12.92C_{\text{linear}},&C_{\text{linear}}\leq 0.0031308\\[5mu]1.055C_{\text{linear}}^{1/2.4}-0.055,&C_{\text{linear}}>0.0031308\end{cases}}}$

where ${\displaystyle C}$ is ${\displaystyle R}$, ${\displaystyle G}$, or ${\displaystyle B}$.

These gamma-compressed values (sometimes called "non-linear values") are usually clipped to the 0 to 1 range. This clipping can be done before or after the gamma calculation, or done as part of converting to 8 bits. If values in the range 0 to 255 are required, e.g. for video display or 8-bit graphics, the usual technique is to multiply by 255 and round to an integer.

• IEC 61966-2-1:1999 is the official specification of sRGB. It provides viewing environment, encoding, and colorimetric details.
• Amendment A1:2003 to IEC 61966-2-1:1999 describes an sYCC encoding for YCbCr color spaces, an extended-gamut RGB encoding, and a CIELAB transformation.
• sRGB, International Color Consortium
• The fourth working draft of IEC 61966-2-1 is available online, but is not the complete standard. It can be downloaded from www2.units.it.
• Archive copy of sRGB.com, now unavailable, containing much information on the design, principles, and use of sRGB