The exact length is not crucial. Typical receivers have antennas ranging between 36" and one meter long.

Some single-conversion receivers, like GWS receivers, have 18"-20" antennas, and the instructions with some of these tell you to cut the antenna if you're having severe interference problems. A warning, though: DON'T CUT YOUR ANTENNA UNLESS THE INSTRUCTIONS RECOMMEND IT. What's happening is the receiver is getting TOO MUCH signal, and is being swamped. Cutting the antenna reduces the intensity of the signal the receiver is receiving.