Oh, like a "how many jellybeans are in the jar" contest. I will offer a guess based upon my jellybean jar success, but only if you have counted the bees and if there is a prize. In other words: no idea. The only way I know how to estimate is based on 300 bees in a mite test. J
A full standard 9-11/16ths inch brood box with 10 frames packed with bees should be about 30,000 bees, so 3,000 to a frame, 1,500 to a side, but this is often an over-estimate because the are more spread out than when the whole box is packed tight.
So put the swarm in a box of frames and fudge your estimate on the light side, numerically. I will often give a SWAG at about 1,000 bees per frame side if the population is low, even less if the frame is not entirely covered.
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