According to the shoe size chart from GrivetOutdoors.com, a size 37 in UK shoes is equivalent to a size 4.5 in the US and has a length of 9.25 inches or 23.5 centimeters. Similarly, the conversion chart from Health and Care shows that a size 37 in UK shoes is equivalent to a size 4.5 in the US and a size 6.5 in the EU. The shoe size table from Sioux Shop also confirms that a size 37 in UK shoes is equivalent to a size 4.5 in the US and has a length of 23.5 centimeters. Therefore, a size 37 in UK shoes is equivalent to a size 4.5 in the US and has a length of 9.25 inches or 23.5 centimeters.