I’m looking for some kind of formula or algorithm to determine the brightness of a color given the RGB values. I know it can’t be as simple as adding the RGB values together and having higher sums be brighter, but I’m kind of at a loss as to where to start.

The “Accepted” is Incorrect and Incomplete

The only answers that are accurate are the @jive-dadson and @EddingtonsMonkey answers, and in support @nils-pipenbrinck. The other answers (including the accepted) are linking to or citing sources that are either wrong, irrelevant, obsolete, or broken.

Briefly:

• sRGB must be LINEARIZED before applying the coefficients.
• Luminance (L or Y) is linear as is light.
• Perceived lightness (L*) is nonlinear as is human perception.
• HSV and HSL are not even remotely accurate in terms of perception.
• The IEC standard for sRGB specifies a threshold of 0.04045 it is NOT 0.03928 (that was from an obsolete early draft).
• The be useful (i.e. relative to perception), Euclidian distances require a perceptually uniform Cartesian vector space such as CIELAB. sRGB is not one.

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What follows is a correct and complete answer:

Because this thread appears highly in search engines, I am adding this answer to clarify the various misconceptions on the subject.

Luminance is a linear measure of light, spectrally weighted for normal vision but not adjusted for the non-linear perception of lightness. It can be a relative measure, Y as in CIEXYZ, or as L, an absolute measure in cd/m² (not to be confused with L*).

Perceived lightness is used by some vision models such as CIELAB, here L* (Lstar) is a value of perceptual lightness, and is non-linear to approximate the human vision non-linear response curve.

Brightness is a perceptual attribute, it does not have a “physical” measure. However some color appearance models do have a value, usualy denoted as “Q” for perceived brightness, which is different than perceived lightness.

Luma (Y´ prime) is a gamma encoded, weighted signal used in some video encodings (Y´I´Q´). It is not to be confused with linear luminance.

Gamma or transfer curve (TRC) is a curve that is often similar to the perceptual curve, and is commonly applied to image data for storage or broadcast to reduce perceived noise and/or improve data utilization (and related reasons).

To determine perceived lightness, first convert gamma encoded R´G´B´ image values to linear luminance (L or Y ) and then to non-linear perceived lightness (L*)

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TO FIND LUMINANCE:

…Because apparently it was lost somewhere…

Step One:

Convert all sRGB 8 bit integer values to decimal 0.0-1.0

  vR = sR / 255;
  vG = sG / 255;
  vB = sB / 255;

Step Two:

Convert a gamma encoded RGB to a linear value. sRGB (computer standard) for instance requires a power curve of approximately V^2.2, though the “accurate” transform is:

Where V´ is the gamma-encoded R, G, or B channel of sRGB.
Pseudocode:

function sRGBtoLin(colorChannel) {
        // Send this function a decimal sRGB gamma encoded color value
        // between 0.0 and 1.0, and it returns a linearized value.

    if ( colorChannel <= 0.04045 ) {
            return colorChannel / 12.92;
        } else {
            return pow((( colorChannel + 0.055)/1.055),2.4);
        }
    }

Step Three:

To find Luminance (Y) apply the standard coefficients for sRGB:

Pseudocode using above functions:

Y = (0.2126 * sRGBtoLin(vR) + 0.7152 * sRGBtoLin(vG) + 0.0722 * sRGBtoLin(vB))

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TO FIND PERCEIVED LIGHTNESS:

Step Four:

Take luminance Y from above, and transform to L*

Pseudocode:

function YtoLstar(Y) {
        // Send this function a luminance value between 0.0 and 1.0,
        // and it returns L* which is "perceptual lightness"

    if ( Y <= (216/24389) {       // The CIE standard states 0.008856 but 216/24389 is the intent for 0.008856451679036
            return Y * (24389/27);  // The CIE standard states 903.3, but 24389/27 is the intent, making 903.296296296296296
        } else {
            return pow(Y,(1/3)) * 116 - 16;
        }
    }

L* is a value from 0 (black) to 100 (white) where 50 is the perceptual “middle grey”. L* = 50 is the equivalent of Y = 18.4, or in other words an 18% grey card, representing the middle of a photographic exposure (Ansel Adams zone V).

References:

IEC 61966-2-1:1999 Standard
Wikipedia sRGB
Wikipedia CIELAB
Wikipedia CIEXYZ
Charles Poynton’s Gamma FAQ