1:24 also called half scale for dolls houses is a ratio used to define the relationship between the actual size of an object and its reduced or scale size.The term "half scale" is not a true indicator of the scale, half scale is actually 1:2, rather than 1:24. In the case of 1:24 scale dolls house builders refer to it as "half scale" due to it being one half of the "regular" dolls house scale of 1:12.
Like all scales, the first section of the ratio (1), or the size measured on the model, is equivalent to the second section of the ratio, or 24 times that amount or twenty-four of the same measure on the original. In other words, one inch in the model represents twenty-four inches (two feet) in the original. As these measurements are 1/2 the size of a regular dolls house scale of 1:12, dolls house collectors often refer to this as "half" scale. In metric measurements 1 cm in the model represents 24 cm in the original. The first part of the ratio, "1" refers to the number of units or measurements that are equivalent to 24 of the same units or measurements in full size.
For a 1:24 scale dolls house, the 3 1/4 inch doors in scale, would compare to full size doors which are 3 1/4 x 24 inches large - if you are reporting the dolls house size in inches the ratio is worked out in the same units) 90 inches or 90/12 = 7 1/2 feet. An adult male figure or doll in this scale is usually between 2 1/2 and 3 inches tall, or the equivalent of 5ft 6in. to 6 feet tall.
1:24 scale, a reduction of the popular 1:12 scale in dolls houses was a very easy scale to use when inches were commonly divided into twelfths on most rulers. With modern imperial rulers being divided into 1/16ths instead of 12ths it is not quite as convenient to use, although rulers in 12ths are still available. It is not as useful a scale if you are working in metric measurements, as the ratios are not as easy to switch mentally. One centimetre is equivalent to twenty-four centimetres, but as 24 centimetres doesn't translate easily to any common segment of metric measure, the scale is slightly more difficult to mentally compute.
One twenty-fourth scale, 1:24 is common for dolls houses, plastic and some larger scale die cast car models, some toy dolls houses (Playmobil and other brands) and items designed to fit in with Garden or G scale railroads.
Printable sheets of scale figures, including some in 1:24 scale can be found here as a downloadable pdf file and are useful as a reference check for scales. There is also a ruler marked in 12ths on a dividing page for a six ring organizer for miniature collectors.