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If I have a neo magnet with a Br of 12,300 Gauss, should I be able to measure 12,300 Gauss on its surface?

No. The Br value is measured under closed circuit conditions. A closed circuit magnet is not of much use. In practice, you will measure a field that is less than 12,300 Gauss close to the surface of the magnet. The actual measurement will depend on whether the magnet has any steel attached to it, how far away from the surface you make the measurement, and the size of the magnet (assuming that the measurement is being made at room temperature). For example, a 1” diameter Grade 35 Neo magnet that is 1/4“long, will measure approximately 2,500 Gauss 1/16” away from the surface, and 2,200 Gauss 1/8” away from the surface.