I suspect that the calculation is correct
if you are indeed using a variable cap designed for the broadcast band. I have one small commercial loop that has a 9" coil and is wound with 28 turns of something like #26 enamel coated wire, closely spaced.... Pix 1.
I have constructed several loops, such as the 2 foot (diagonal) loop in Pix 2.
It has 18 turns of # 22 wire, spaced about one wire diameter. It has a 1 turn coil in the the in the center, between the other turns, for pickup. The pickup coil is helpful, as connecting a radio directly to the tuned loop reduces its "Q" and causes the tuning to become rather broad and reduces the improvement provided by the loop.
It may be that your environment is noisy from computers, lamp dimmers tv sets, battery chargers and other common household items that produce interference, and pretty much render the loop useless, as it picks up more noise as well as additional signal. Get away from the house and see if the loop works better. For most AM DXing, I use an outdoor loop (about 4 1/2 foot diag. 8 turns #14 wire) located about 75 feet from the house. It can barely be seen from the "radio room"... hint: the cross arm is directly behind a hummingbird feeder in the "woods". Pix 3.... Unfortunately, there are a couple of "solar dryers" located very close to the loop, which mess up the sharpness of the directionality somewhat, but it still beats using something indoors.
I added a close up pix of the outdoor loop... the 1 turn pick up loop can
almost be seen at about 2/3 the diagonal of the main loop. I experimented with several different sizes for the pick-up coil and chose a configuration that yielded decent signal strength without reducing the "Q" too much. Many times, mostly in the summer, I will park my Icom on the small table in front of the loop, and operate it from a 12V lawnmower battery, to further reduce interference from sources in the house. I have an additional capacitor mounted in a box below the loop, to tune below the broadcast band. Last winter, I nailed several Long wave stations from Russia! These were on 153,189 and 279 kHz.
jr