Why is the golf hole the size it is, exactly 4.25 inches in diameter?

In 1829 The Royal Musselburgh Golf Club invented the first known hole-cutter which had a diameter of 4.25 inches.

More about the size of the golf hole.

This particular hole-cutter is still in existence and on display at the club. It had become the accepted norm at clubs in that part of Scotland. No one knows why it exactly measures 4.25 inches

In 1891 the Royal and Ancient Golf Club of St Andrews (R&A), at the time golf's sole governing body, issued a new rule that the hole size should be standard on golf courses around the world at 4.25 inches.