Agree on soil test first. Even with clay as mine, it may take several years of silt for it to really become functional which mine did require. My main problem even with clay and all was that it's cut into the side of a hill where the dam outer perimeter was some 10' below spillway. At 1/2# per foot of elevation, that's only 5 psi of water pressure against the soil, but it doesn't take much to work it's way through it.
On volume, you said 13 acres in your place. What you need to know is the size of the watershed then multiply by the anticipated rainfall to get an acre-feet number. Apply that to your acre-feet or whatever measurement reference you choose for pond size and you will have the answer to your question. Course like we have had this past winter and spring, I got lots of rain, but it was spaced out and slow in falling and all soaked in....pond got only what fell on it. Ground has to get saturated and then rain must fall at a rate that will produce runoff and then the acre-ft of watershed can apply......per my experience here over the last 35 years.
HTH,
Mark