A hand is equal to 4 inches, with fractions of a hand measured in terms of quarters of a hand. Fractions of a hand are written in what at first appears to be decimal form, but this is not the case. For example, 14.3 hands is equal to 14 hands and 3 inches. The "0.3" translates to 3 inches. With this essential knowledge you can proceed easily to convert to centimeters.
Converting the height in hands of your horse to inches is simple. Use the formula (4 x WH) + FH to obtain the height in inches, where WH is the number of whole hands and FH the fraction of hands left over. So a horse measuring 14.3 hands is 59 inches tall -- 14 x 4 = 56 and 56 + 3 = 59.
One inch is equal to 2.54 cm. To calculate the height of your horse in centimeters multiply its height in inches by 2.54. Therefore, a horse that stands 59 inches tall is 149.9 cm.
If you're uncomfortable with making this calculation yourself, use one of the many online conversion tools and tables available on numerous equestrian websites. Note that the charts break the hand fractions into quarters, as in 13.0, 13.1, 13.2 and 13.3.