Convert ac voltage rms to dc voltage?

The dc voltage of a rectified ac voltage will be the peak value of the ac voltage less the forward voltage drop of the diode.

The rms voltage of a sinusoidal ac voltage is sqrt(peak) / 2, but you also have to consider if the ac voltage is balanced around zero.

For a normal US house voltage of 117VAC, the peak voltage is about 165V, or 330V peak to peak. Your dc voltage is then around 164V.

Run that rectified voltage through a capacitor, and you will still have 164V peak value, but the voltage over time will dip because the capacitor will discharge during diode off time, and recharge when it turns back on.

A given value of a.c. rms voltage is exactly equivalent to the corresponding value of d.c. voltage. For example, 120 V (rms) is exactly equivalent to 120 V d.c. This is why the alternative name for 'rms voltage' is 'effective voltage'. This is based on the fact that a current of, say, 10 A (rms) will do exactly the same amount of work as a d.c. current of 10 A. And, of course, voltage and current are proportional.