The conversion from RGB to CMYK is dependent on the physical device/process being used to lay down the CMYK ink. These are represented in software as Color Profiles. ICC and ICM color profiles of physical devices determine the resulting colors.

If you are not concerned with true representation on a physical device then use the direct conversion formulas in other posts.

If, however, you are concerned with this aspect, then you need to use a either the Windows Color Management APIs or something like LittleCMS to do the color conversions for you (as they apply the proper color profile during the conversion).

Check out this link: http://www.codeproject.com/KB/applications/xcmyk.aspx. It gives this formula.

Black   = minimum(1-Red,1-Green,1-Blue)
Cyan    = (1-Red-Black)/(1-Black)
Magenta = (1-Green-Black)/(1-Black)
Yellow  = (1-Blue-Black)/(1-Black) 

If you want good result, you need to apply a color profile. In .NET, you can do it like that (assuming the the original CMYK components are in the range between 0 and 255):

float[] colorValues = new float[4];
colorValues[0] = c / 255f;
colorValues[1] = m / 255f;
colorValues[2] = y / 255f;
colorValues[3] = k / 255f;

System.Windows.Media.Color color = Color.FromValues(colorValues,
    new Uri(@"C:UsersmeDocumentsISOcoated_v2_300_eci.icc"));
System.Drawing.Color rgbColor = System.Drawing.Color.FromArgb(color.R, color.G, color.B);

Note that two different Color classes from two different namespaces are used. And you probably need to add the PresentationCore DLL as a reference.

The required color profile can be downloaded from the downloads section of eci.org. It s part of a bigger ZIP file containing several profiles. They explicitly recommend to use the ISO Coated v2 300% (ECI) profile.

If you need to convert a complete image from CMYK to RGB, there are special classes for this in the same namespace.

My complete example for C# conversion between CMYK <-> HEX:

public class ColorConverter
{
    public static string CMYKtoHex(decimal[] cmyk)
    {
        if (cmyk.Length != 4) return null;

        var r = (int)(255 * (1 - cmyk[0]) * (1 - cmyk[3]));
        var g = (int)(255 * (1 - cmyk[1]) * (1 - cmyk[3]));
        var b = (int)(255 * (1 - cmyk[2]) * (1 - cmyk[3]));

        var hex = "#" + r.ToString("X2") + g.ToString("X2") + b.ToString("X2");
        return hex;
    }

    public static decimal[] HexToCMYK(string hex)
    {
        decimal computedC = 0;
        decimal computedM = 0;
        decimal computedY = 0;
        decimal computedK = 0;

        hex = (hex[0] ==  # ) ? hex.Substring(1, 6) : hex;

        if (hex.Length != 6)
        {
            return null;
        }

        decimal r = int.Parse(hex.Substring(0, 2), System.Globalization.NumberStyles.HexNumber);
        decimal g = int.Parse(hex.Substring(2, 2), System.Globalization.NumberStyles.HexNumber);
        decimal b = int.Parse(hex.Substring(4, 2), System.Globalization.NumberStyles.HexNumber);

        // BLACK
        if (r == 0 && g == 0 && b == 0)
        {
            computedK = 1;
            return new[] { 0, 0, 0, computedK };
        }

        computedC = 1 - (r / 255);
        computedM = 1 - (g / 255);
        computedY = 1 - (b / 255);

        var minCMY = Math.Min(computedC, Math.Min(computedM, computedY));

        computedC = (computedC - minCMY) / (1 - minCMY);
        computedM = (computedM - minCMY) / (1 - minCMY);
        computedY = (computedY - minCMY) / (1 - minCMY);
        computedK = minCMY;

        return new[] { computedC, computedM, computedY, computedK };
    }
 }

I agree with the previous answers, but I want to say that:

if ( K == 1 ) 
{ 
   C = 0
   M = 0
   Y = 0
} 

It can be if r = g = b = 0.

I think photoshop uses profile based conversions. Have a look at the documentation for the color options. If it is the case you won t be able to match this behavior with simple formula based solutions.

I have found LCMS to be very handy, simple and efficient for this kind of task.I don t known if there is any .net binding for it...

For convert RGB to CMYK you can use ColorHelper library.

using ColorHelper;
RGB rgb = new RGB(220, 234, 174);
CMYK cmyk = ColorConverter.RgbToCmyk(rgb);

Conversion algorithm in this library:

public static CMYK RgbToCmyk(RGB rgb)
{
    double modifiedR, modifiedG, modifiedB, c, m, y, k;

    modifiedR = rgb.R / 255.0;
    modifiedG = rgb.G / 255.0;
    modifiedB = rgb.B / 255.0;

    k = 1 - new List<double>() { modifiedR, modifiedG, modifiedB }.Max();
    c = (1 - modifiedR - k) / (1 - k);
    m = (1 - modifiedG - k) / (1 - k);
    y = (1 - modifiedB - k) / (1 - k);

    return new CMYK(
        (byte)Math.Round(c * 100),
        (byte)Math.Round(m * 100),
        (byte)Math.Round(y * 100),
        (byte)Math.Round(k * 100));
}

Link - https://github.com/iamartyom/ColorHelper/blob/master/ColorHelper/Converter/ColorConverter.cs