I like Calculations for several reasons. I can use it for masking and I can use it for black and white conversions. By using it for black and white conversions, I have an incredible amount of control over the final look of the image. I also have the ability to create a new document from the results, thus preserving my original. Let's take a look.
The main reason that I convert to black and white is to facilitate printing on a laser printer. If I know that a detective or attorney will be printing my images in this way, I'd rather tune the images accordingly than leave things up to chance. I want to have good separation and a lot of contrast to my images as many government machines are older and don't have the ability to output a subtle range of tones.
Normally, I use this process late in my work flow. I want to get my image corrected and content sharpened first. I will make the conversion right before I interpolate. In order to make sure that all of my adjustments are applied before I process this image with calculations, I will want to flatten the image (Layers Palette fly-out menu). Note: Make sure that you save your intermediate version, preserving all of your layers before you flatten and begin with Calculations.
First look at the Source 1 and Source 2 drop-down menus. They should both display the name of the image that we are working on. Having found your two channels with the most colour and detail, we are going to choose this in the Source 1/2 Channel drop-down menus (red and green). Then we're going to blend these two channels using Photoshop's standard Blending Modes (just like you'd blend two layers together Multiply makes them blend darker, Screen makes them lighter, etc.). For our conversion, Overlay or Soft Light will give us the most contrast. Soft Light works best for this image as it gives us the contrast that we need, but isn't as harsh as Overlay.
Finally, choose New Document as the result. This will create a new document from the combination of the Soft Light blended channels.
The new image will show up as an Alpha channel in Multichannel mode. Not to worry. Alpha channels store selections as grayscale images, which is what we want. Multichannel mode images contain 256 levels of gray in each channel and are useful for specialized printing, in our case ... the single Alpha channel. Now simply convert the image to grayscale, Image>Mode>Grayscale.
Now, I'll interpolate and add a final touch of sharpening. Then, my image will be ready for the laser printer.