W3C has the following:http://www.w3.org/WAI/ER/WD-AERT/#color-contrast

If you're only doing black or white text, use the color brightness calculation above. If it is below 125, use white text. If it is 125 or above, use black text.

edit 1: bias towards black text. :)

edit 2: The formula to use is ((Red value * 299) + (Green value * 587) + (Blue value * 114)) / 1000.

Here is a Swift (3) extension to perform this check.

This extension works with greyscale colors. However, if you are creating all your colors with the RGB initializer and not using the built in colors such as UIColor.black and UIColor.white, then possibly you can remove the additional checks.

extension UIColor {    // Check if the color is light or dark, as defined by the injected lightness threshold.    // Some people report that 0.7 is best. I suggest to find out for yourself.    // A nil value is returned if the lightness couldn't be determined.    func isLight(threshold: Float = 0.5) -> Bool? {        let originalCGColor = self.cgColor        // Now we need to convert it to the RGB colorspace. UIColor.white / UIColor.black are greyscale and not RGB.        // If you don't do this then you will crash when accessing components index 2 below when evaluating greyscale colors.        let RGBCGColor = originalCGColor.converted(to: CGColorSpaceCreateDeviceRGB(), intent: .defaultIntent, options: nil)        guard let components = RGBCGColor?.components else {            return nil        }        guard components.count >= 3 else {            return nil        }        let brightness = Float(((components[0] * 299) + (components[1] * 587) + (components[2] * 114)) / 1000)        return (brightness > threshold)    }}

Tests:

func testItWorks() {    XCTAssertTrue(UIColor.yellow.isLight()!, "Yellow is LIGHT")    XCTAssertFalse(UIColor.black.isLight()!, "Black is DARK")    XCTAssertTrue(UIColor.white.isLight()!, "White is LIGHT")    XCTAssertFalse(UIColor.red.isLight()!, "Red is DARK")}

Note: Updated to Swift 3 12/7/18

Swift3

extension UIColor {    var isLight: Bool {        var white: CGFloat = 0        getWhite(&white, alpha: nil)        return white > 0.5    }}// Usageif color.isLight {    label.textColor = UIColor.black} else {    label.textColor = UIColor.white}