Forty feet, three ways
A 40 ft prototype car is 480 inches. Divide by 87.1 and you get 5.51 in, or 139.98 mm. Divide by 87 instead and you get 5.52 in, 140.14 mm. The two answers differ by 0.16 mm over the whole car, which is less than the thickness of a coat of paint and about a fifth of the width of a scribed line. Nobody is going to see it.
The reason the field is there anyway is that the error is proportional to the length, and layouts are not made of single cars. The drift works out at 0.004 mm per prototype foot, so an 85 ft locomotive comes out 0.34 mm different, which is still nothing. A 20 ft run of layout stands for 1,742 prototype feet at this ratio, and there the same drift is 7 mm. Whether that matters depends entirely on whether the parts have to meet something else that was drawn to the other number.
The square and the cube are where the surprises are
Length divides by the ratio. Area divides by the ratio squared, so at 1 to 87.1 one square foot of prototype wall is 0.019 square inches of model. Volume and weight divide by the cube, which at 1 to 87.1 is 660,776. One prototype cubic foot of coal comes to 0.0026 cubic inches of model load.
Run that backwards and it explains the thing that catches people moving between scales. Going from 1 to 87 to 1 to 48 is a factor of 1.81 on every length. On resin in the vat, on filler, on the weight the shelf carries, it is 1.81 cubed, which is 5.97. A build that took one bottle takes six. That is the single most useful thing the cube law does for a modeller, and it has nothing to do with converting a dimension.
The detail check is the honest half
A 4 in grab iron on the prototype is 1.17 mm at 1 to 87.1. Set against a 0.15 mm finest feature, the detail is 7.8 times the tool. That is a comfortable ratio and it is why HO grab irons exist as printed parts at all. Halve the scale to 1 to 160 and the same grab iron is 0.64 mm, only 4.2 times the tool, and it starts mattering which axis the part is printed in.
The page will not tell you whether the part comes out. A layer height is not a feature size, resins vary, and a fine detail standing proud prints differently from the same detail sunk in. What the number does is tell you which side of the line you are on before you spend an evening on it.
Where the ratio comes from
The field defaults to a number, and the number is a placeholder. Scales are defined by standards bodies and societies, several of them, and they disagree. The same track gauge is modelled at different ratios in different countries, several common scales are quoted both rounded and unrounded depending on who is publishing, and manufacturers pick whichever they like. Take the ratio from whatever you are actually building to and put that in the field.
Questions people ask
How do I convert a prototype dimension to model size?
Divide by the scale ratio, after putting both in the same unit. A 40 ft car is 480 inches; at 1 to 87.1 that is 5.51 in or 139.98 mm. Going the other way, multiply: a 5.51 in model part at 1 to 87.1 stands for 40 prototype feet. The page does the unit handling and gives the answer in inches, millimetres and thousandths at the same time.
Does it matter whether I use 1 to 87 or 1 to 87.1?
Over a single car, no. The difference is 0.16 mm on a 40 ft body, thinner than a coat of paint. It matters when the error accumulates across a long measurement or when your part has to meet something drawn to the other number. The second ratio field gives you the difference in millimetres for the actual length you are working on, so you can decide rather than guess.
Why does a bigger scale need so much more material?
Because volume goes as the cube of the ratio. Moving from 1 to 87 up to 1 to 48 is 1.81 times on every length, but 1.81 cubed on volume, which is 5.97. Resin, filler, ballast and the weight on the shelf all follow the cube. Paint and decal area follows the square, so it goes up 3.29 times over the same step, not 5.97.
What scale ratio should I put in?
The one published by whoever defines the scale you build to, or printed on the drawing for the parts you buy. This page does not supply it, deliberately. Scale names are used at different ratios in different countries and by different manufacturers, and several are quoted both rounded and exact, so a number carried in from memory is the most common source of a part that does not fit.
Can it tell me if a detail will print or cut?
No, and it does not try. It compares the model size of a prototype detail against the finest feature you told it your tools make, and reports the ratio between them. Whether a feature at that ratio survives depends on the material, the orientation, the cleanup and how the detail sits on the part, and none of that is arithmetic.