SRGB

By the 1970's most computers translated 8-bit digital data fairly linearly to a signal that was sent to a video monitor. However video monitors and TVs produced a brightness that was not linear with the input signal, roughly a power law with an exponent between 2 and 3. The exponent was commonly denoted with the letter $\backslash gamma$, hence the common name "gamma correction" for this function. This design has the fortunate benefit of displaying an image with much less visual artifacts, as it places the digital values closer together near black and further apart near white (where changes in brightness are less visible). This gamma varied according to CRT manufacturers, but was normalized in 1993 for use in HDTV systems, as the ITU BT.709 standard The BT.709 standard specified a decoding function with a linear section near zero, transitioning to a shifted power law with exponent 1/0.45 ≈ 2.22...

sRGB was created a few years later by Hewlett-Packard and Microsoft. It was meant to describe the decoding function of most CRT computer monitors used with Windows operating systems at the time, which was still different from that assumed by BT.709. The first draft of the standard was published in 1996. A fourth draft, still incomplete, is available online. Like the BT.709, the sRGB decoding function was defined as a linear section near zero that transitions to a shifted power law

Actually using the sRGB standard became important as computer graphics software started to calculate in linear light levels in the late 1990s,{{cn|date=March 2025}} and needed to use sRGB to convert from and to the common 8-bit image standards.

File:srgbnonlinearity.pngImages such as shown here became popular for adjusting a CRT monitor to correctly display sRGB.

Amendment 1 to IEC 61966-2-1:1999, approved in 2003, also defines a Yuv-style colorspace called sYCC and a conversion to more than 8 bits called {{nowrap|bg-sRGB}}. The scRGB standard also tries to extend sRGB to more bits.

File:SRGB gamma.svg

An sRGB image file contains {{mvar|R′G′B′}} values for each pixel. 0.0 is "black" while 1.0 is the intensity of a color primary needed by "white". These floating-point values are derived from the file data, for a typical 8-bit-per-channel image the bytes are divided by 255.0.

The mapping from these values to intensity is a non-linear transfer function which is the combination of a linear function at low brightness values and a displaced power law for the rest of the range. Linear intensities {{mvar|RGB}} are derived using (same for all channels):

:$R\; =\; \backslash begin\{cases\}$

R'/12.92, & R' \le 0.04045 \\[5mu]

\left(\frac{\displaystyle R' + 0.055}{\displaystyle 1.055}\right) ^{2.4}, & R' > 0.04045

\end{cases}

This function is quite close to $R\text{'}^\{2.2\}$. However, for low values near 0.04045 the difference is perceptible.

The inverse function as defined by IEC2003 is:

:$R\text{'}\; =\; \backslash begin\{cases\}$

12.92 R, & R \le 0.0031308 \\[5mu]

(1.055)R^{1/2.4} - 0.055, & R > 0.0031308

\end{cases}

If needed by the file format, values greater than 1.0 can be used (the results will also be greater than 1.0), and values less than 0.0 can be converted as {{math|-f(-x)}}.

These functions are similar to those of BT.709, but the values are noticeably different. Because of the rounding of the parameters, they have small discontinuities at the transition between the linear and non-linear part, on the order of 10⁻⁸, and they are not precise inverses of each other. These errors are too small to matter in practical situations.

In practice many pieces of software use different close-by values (see below), or ignore the linear section, or use a plain gamma 2.2 function. The change in the images is almost imperceptible, however it will make noticeable seams when differently-converted images are overlapped, and mismatched translations back and forth accumulate color shifts. Many operating systems and programs send 8-bit sRGB images directly to video memory and assume this produces the correct levels.

A shifted power law curve that passes through {{math|(1,1)}} is $y\; =\; \backslash left(\backslash frac\{x+C\}\{1+C\}\backslash right)^\backslash gamma$.

The first draft of the sRGB standard chose $\backslash gamma=\; 2.4$ and then computed $C=0.055$ so that the value at $x=0.4$ was near $x^\{2.2\}$.{{cn|reason=This is a guess, reason is not in citation|date=March 2025}}

A straight line that passes through {{math|(0,0)}}, is $y\; =\; x/A$. The transition from the linear section to the power law section should be continuous (without a sudden step) and smooth (without a sudden change of slope). To make it continuous when {{math|1=x=X}}, we must have

:$\backslash frac\{X\}\{A\}\; =\; \backslash left(\backslash frac\{X+C\}\{1+C\}\backslash right)^\backslash gamma$

To avoid a sudden change of slope where the two segments meet, the derivatives must also be equal at {{mvar|X}}:

:$\backslash frac\{1\}\{A\}\; =\; \backslash gamma\backslash left(\backslash frac\{X+C\}\{1+C\}\backslash right)^\{\backslash gamma-1\}\backslash left(\backslash frac\{1\}\{1+C\}\backslash right)$

Solving the two equations for {{mvar|X}} and {{mvar|A}} we get

:$X\; =\; \backslash frac\{C\}\{\backslash gamma-1\}\backslash ;\backslash ;\backslash ;\backslash ;\backslash ;\; A\; =\; \backslash frac\{(1+C)^\backslash gamma(\backslash gamma-1)^\{\backslash gamma-1\}\}\{(C^\{\backslash gamma-1\})(\backslash gamma^\backslash gamma)\}$

This produces $X\; \backslash approx\; 0.0392857...$ and $A\; \backslash approx\; 12.9232102...$. These values, rounded to $X\; =\; 0.03928$ and $A\; =\; 12.92321$ are still incorrectly given in some publications.

However, the sRGB draft standard rounded $A$ to $12.92$, resulting in a small discontinuity in the curve.

The first official version of the standard was defined and published by the IEC in 1999. In this version, the rounded value of $A=12.92$ was retained, but the breakpoint $X$ was redefined as $0.04045$ to make the curve approximately continuous. With these values, there is still a discontinuity in the slope, from $1/12.92$ just below the intersection to $1/12.70$ just above it. The final standard also corrected some small rounding errors present in the draft.

The sRGB standard 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, which are set such that the range of colors inside the triangle is well within the range of colors visible to a human with normal trichromatic vision. As with any RGB color space, for non-negative values of {{mvar|R}}, {{mvar|G}}, and {{mvar|B}} it is not possible to represent colors outside this triangle.

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.

The sRGB standard specifies also the colors and relative intensities of the three primaries {{mvar|R}}, {{mvar|G}}, and {{mvar|B}}, by defining the mapping between these values (in linear brightness scale, before the gamma encoding) and the CIE XYZ perceptual color coordinates. This mapping is the same specified by the BT.709 standard; in matrix notation,

:$$

\begin{bmatrix} X \\ Y \\ Z \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 \\ G \\ B \end{bmatrix}

These coefficients should be considered exact and assume the 2° standard colorimetric observer for CIE XYZ. In particular, the second row of this matrix specifies the computation of the BT.709-2 luma (brightness) value from the linear {{mvar|R}}, {{mvar|G}}, and {{mvar|B}} values. (BT.709-1 had a typo in these coefficients.)

The inverse conversion, from from CIE XYZ to (linear) {{mvar|RGB}}, can be obtained by inverting the matrix above to a suitable numerical accuracy. The 1999 standard provides the matrix

:$$

\begin{bmatrix} R \\ G \\ B \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 \\ Y \\ Z \end{bmatrix}

which is not the exact inverse of the sRGB to XYZ transformation, but was expected to be accurate enough for 8-bit encoded samples (with $M=255$).

The 1999 IEC standard was amended in 2003. The sRGB to CIE XYZ matrix was retained, but the inverse transformation above was replaced by a more accurate version, with seven decimal fraction digits. It provides the matrix

:$$

\begin{bmatrix} R \\ G \\ B \end{bmatrix}

= \begin{bmatrix}

+3.2406255 & -1.5372080 & -0.4986286 \\

-0.9689307 & +1.8757561 & +0.0415175 \\

+0.0557101 & -0.2040211 & +1.0569959

\end{bmatrix}

\begin{bmatrix} X \\ Y \\ Z \end{bmatrix}

.

which is claimed to be sufficiently accurate for 16-bit samples.

For these formulas, the X, Y, and Z 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).

File:Cie Chart with sRGB gamut by spigget.png 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:

The assumed ambient CCT differs from that of the BT.709 standard illuminant (D65), which is still retained for the screen white point. Using D50 for both would have made the white point of most photographic paper appear excessively blue. 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.

Most file formats that use sRGB store 8-bit integers. Usually these are converted from 8 bits by dividing by 255.0, and converted to 8 bits by multiplying by 255 and rounding. However some software converts to 8 bits by multiplying by 256 and rounding down. Higher-quality software often uses dithering when writing so that color banding is hidden.

Annex G of the 2003 amendment of the sRGB standard describes an alternative encoding of color values, called bg-sRGB, that is recommended when the number of bits per channel is 10 or more. In this case 0.0 is mapped to a black point {{mvar|K}} and 1.0 is mapped to a white point {{mvar|W}}, with all other values interpreted linearly. For 10 bits {{math|1=K = 384}} and {{math|1=W = 894}} is specified, and for larger numbers {{mvar|N}} of bits:

:$K\; =\; 3\backslash times\; 2^\{N-3\}\backslash quad\backslash quad\; W\; =\; K\; +\; 255\backslash times\; 2^\{N-9\}$

The 12-bit scRGB format does something similar, with {{math|1=K = 1024}} and {{math|1=W = 2304}}.

Allowing numbers greater than 1.0 allows high dynamic range images, and negative numbers allows colors outside the gamut triangle.

File:CIE1931xy gamut comparison.svg xy chromaticity diagram]]

Due to the standardization of sRGB on the Internet, on computers, and on printers, many low- to medium-end consumer digital cameras and scanners use sRGB as the default (or only available) working color space.Even if uncalibrated, it is likely they match sRGB more closely than any other popular color space If the color space of an image is unknown and encoded with 8 bits in each channel, the sRGB encoding can be assumed. Due to programmers misunderstanding the meaning of "gamma" some image files that claim they contain a gamma of 1.0 should also be assumed to be sRGB.{{cn|reason=Absolutely true for early .png files|date=March 2025}}

As the sRGB gamut mostly meets or exceeds the gamut of a low-end inkjet printer, an sRGB image is often regarded as satisfactory for home printing. The sRGB color space is sometimes avoided by high-end print publishing professionals because its color gamut is not big enough, especially in the blue-green colors, to include all the colors that can be reproduced in CMYK printing. Images intended for professional printing via a fully color-managed workflow (e.g. prepress output) sometimes use another color space such as Adobe RGB (1998), which accommodates a wider gamut and CMYK color space like Fogra39.

The two dominant programming interfaces for 3D graphics, OpenGL and Direct3D, have both incorporated support for the sRGB gamma curve. OpenGL supports textures with sRGB gamma encoded color components (first introduced with EXT_texture_sRGB extension, added to the core in OpenGL 2.1) and rendering into sRGB gamma encoded framebuffers (first introduced with EXT_framebuffer_sRGB extension, added to the core in OpenGL 3.0). Correct mipmapping and interpolation of sRGB gamma textures has direct hardware support in texturing units of most modern GPUs (for example nVidia GeForce 8 performs conversion from 8-bit texture to linear values before interpolating those values), and does not have any performance penalty.

A lookup table may be used to efficiently convert sRGB to other color spaces.{{Citation needed|date=December 2024}} The International Color Consortium (ICC) has published color profiles for this purpose, which are widely used. There are several variants, including ICCmax, version 4, and version 2.

Version 4 is generally recommended, but version 2 is still commonly used and is the most compatible with other software including browsers.{{Cite web |title=Is your system ICC Version 4 ready? |url=https://www.color.org/version4html.xalter |access-date=2024-12-21 |website=www.color.org}} However, inconsistencies have been pointed out between those ICC profiles and the IEC sRGB standard. In particular, version 2 of the ICC profile specification does not implement the piecewise parametric curve encoding ("para") as specified by the IEC sRGB standard,{{Cite web |title=Android lock screen bug and ICC profiles |url=https://color.org/security/android_bug.xalter |access-date=2024-12-25 |website=color.org}} and has to implement the sRGB transfer function using a one-dimensional lookup table. Some implementations approximate the transfer function as 2.2 gamma, with no linear portion, called "simplified sRGB".{{Cite web |last=Developers |first=Colour |date=2019-10-25 |title=sRGB EOTF: Pure Gamma 2.2 Function or Piece-Wise Function? |url=https://www.colour-science.org/posts/srgb-eotf-pure-gamma-22-or-piece-wise-function/ |access-date=2024-12-25 |website=Colour Science |language=en}}

{{notelist}}

{{cite web|author1=Michael Stokes|author2=Matthew Anderson|author3=Srinivasan Chandrasekar|author4=Ricardo Motta|date=November 5, 1996|title=A Standard Default Color Space for the Internet – sRGB, Version 1.10|url=https://www.w3.org/Graphics/Color/sRGB.html|url-status=live|archive-url=https://web.archive.org/web/20230703221707/https://www.w3.org/Graphics/Color/sRGB.html |archive-date=Jul 3, 2023 |access-date=|website=}}

[https://web.archive.org/web/20141225172302/http://www2.units.it/ipl/students_area/imm2/files/Colore1/sRGB.pdf fourth working draft (4WD) for 2CD of IEC 61966-2-1], (archived). Still not the complete standard.

{{cite web|title=IEC 61966-2-1:1999|url=https://webstore.iec.ch/publication/6169|website=IEC Webstore|publisher=International Electrotechnical Commission|access-date=3 March 2017}}. The first official specification of sRGB.

{{cite web |url=https://webstore.iec.ch/publication/6168 |title=IEC 61966-2-1:1999 Multimedia systems and equipment – Colour measurement and management – Part 2-1: Colour management – Default RGB colour space – sRGB: Amendment 1 |date=2003 |publisher=International Electrotechnical Commission}} Replaces the version IEC 61966-2-1:1999, introducing the sYCC encoding for YCbCr color spaces, an extended-gamut RGB encoding bg-sRGB, and a CIELAB transformation.

{{cite book |title=Digital Video and HDTV: Algorithms and Interfaces |author=Charles A. Poynton |publisher=Morgan Kaufmann |year=2003 |isbn=1-55860-792-7 |url=https://books.google.com/books?id=ra1lcAwgvq4C&q=rec+709+smpte&pg=RA1-PA239}}

{{cite book|author1=Phil Green|url=https://books.google.com/books?id=tn09voxr6agC&q=srgb+0.03928+date:0-2002&pg=PA350|title=Colour Engineering: Achieving Device Independent Colour|author2=Lindsay W. MacDonald|publisher=John Wiley and Sons|year=2002|isbn=0-471-48688-4|name-list-style=amp}}

Jason Summers (2012): "[https://entropymine.com/imageworsener/srgbformula/ A close look at the sRGB formula]". Online document at entropymine.com. Accessed on 2014-12-17 ([https://web.archive.org/web/20240926160131/https://entropymine.com/imageworsener/srgbformula/ archived])

Daniele Siragusano (2020): "[https://www.youtube.com/watch?v=NzhUzeNUBuM Colour Online: sRGB... We Need To Talk]".

YouTube video of talk (2020-07-17, 57 min) discussing mismatch between sRGB and actual monitor transfer functions. Posted in channel @FilmLight. Accessed on 2024-12-17.

{{cite book|author=Jon Y. Hardeberg|url=https://books.google.com/books?id=e2umTIdI2u4C&q=srgb+0.00304+date:0-2002&pg=PA40|title=Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches|publisher=Universal-Publishers.com|year=2001|isbn=1-58112-135-0}}

{{cite report|last=Roberts|first=A.|title=BBC RD 1991/6 Methods of Measuring and Calculating Display Transfer Characteristics|url=https://downloads.bbc.co.uk/rd/pubs/reports/1991-06.pdf|publisher=BBC|pages=1}}

NumFocus Colour Science (2015): "[https://www.colour-science.org/posts/the-importance-of-terminology-and-srgb-uncertainty/ The Importance of Terminology and sRGB Uncertainty]". Online document at www.colour-science.org, dated 2015-12-05. Accessed on 2024-12-17 ([https://web.archive.org/web/20241218212521/https://www.colour-science.org/posts/the-importance-of-terminology-and-srgb-uncertainty/ archived]).

{{Cite web|url=https://www.itu.int/rec/R-REC-BT.709|title=BT.709 : Parameter values for the HDTV standards for production and international programme exchange|website=www.itu.net|date=n.d.|access-date=2021-04-19}}

{{cite web |title=EXT_texture_sRGB |date=24 January 2007 |url=https://www.khronos.org/registry/OpenGL/extensions/EXT/EXT_texture_sRGB.txt |access-date=12 May 2020}}

{{cite web |title=EXT_framebuffer_sRGB |date=17 September 2010 |url=https://www.khronos.org/registry/OpenGL/extensions/EXT/EXT_framebuffer_sRGB.txt |access-date=12 May 2020}}

{{cite web |title=GPU Gems 3: Chapter 24. The Importance of Being Linear, section 24.4.1 |publisher=NVIDIA Corporation |url=https://developer.nvidia.com/gpugems/gpugems3/part-iv-image-effects/chapter-24-importance-being-linear |access-date=3 March 2017}}

[https://web.archive.org/web/20030124233043/http://www.srgb.com/ sRGB.com Notes on design and use of sRGB] (archived) by HP.

Image Engineering GmbH (2012): "[https://www.image-engineering.de/library/technotes/714-color-spaces-rec-709-vs-srgb Color spaces - REC.709 vs. sRGB] Online document at www.image-engineering.de. Includes a graph comparing two transfer functions. Accessed on 2024-12-17.

International Color Consortium (undated): "[https://color.org/srgbprofiles.xalter sRGB profiles]". Summary page at color.org. Accessed on 2014-12-17 (archiving failed).

International Color Consortium (undated): "[https://www.color.org/chardata/rgb/srgb.xalter sRGB]" Summary page at color.org. Accessed on 2014-12-17 (archiving failed).

International Color Consortium (2015): "[https://www.color.org/sRGB.pdf How to interpret the sRGB color space (specified in IEC 61966-2-1) for ICC profiles]". Online document at www.color.org. Accessed on 2024-12-17 ([https://web.archive.org/web/20241209023511/https://color.org/chardata/rgb/sRGB.pdf archived])

[http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html Conversion matrices for RGB vs. XYZ conversion] by Bruce Justin Lindbloom

{{cite book |last=Rodney |first=Andrew |url=https://books.google.com/books?id=jFl-3v9sSEUC&q=%22My+suggestion+is+to+calibrate+to+a+D65+white+point.%22&pg=PA121 |title=Color Management for Photographers |publisher=Focal Press |year=2005 |isbn=978-0-240-80649-5 |page=121 |quote=}}

{{Cite web |title=Why Calibrate Monitor to D65 When Light Booth is D50 |url=https://www.xrite.com/service-support/why_calibrate_monitor_to_d65_when_light_booth_is_d50 |access-date=2022-09-11 |website=X-Rite |language=en}}

[https://ninedegreesbelow.com/photography/srgb-profile-comparison.html Will the Real sRGB Profile Please Stand Up?] by Elle Stone. Analyzes the inconsistency among sRGB ICC profiles

• [https://www.shadertoy.com/view/7sjBWD Test that shows whether your display is pure 2.2 gamma or sRGB (~2.2 gamma)] on Shadertoy

{{Color space}}

Category:1996 introductions

Category:Color space

Category:Film and video technology