Calculating RC values for time

I am trying to figure out how to adjust the momentary time for this relay configuration. The test suggests differing capacitance values to adjust time, but I don't know a formula for doing so. I tried this calculator to figure it out, but when I enter the numbers shown in the diagram, I don't get 1/2 second, I get 10 seconds! Obviously I am missing something. I am using 7.62 as the instantaneous voltage in the calculator (63.5% of 12V) - is this wrong? Can someone share a formula, offer a better calculator, or simply explain what I am mising here?

Update. I see now how I arrived at ten seconds - that is the discharge time. So the "Constant to Momentary" relay configuration is not really constant - the circuit would never reset if it were. And if you use the suggested values for a 1/2 second pulse, you cannot repeat the pulse until you wait for 10 seconds to elapse. For example, if you triggered the relay, then tried to trigger it again three seconds later, you would simply reset the 10 second timeout and now it would be a total of 13 seconds before the relay could be triggered again. Not the end of the world for my application, but I wish I had figured this out before I started. :-\