What scale tells you
A scale of 1:76 means a length on the prototype is divided by 76 to obtain the equivalent model length. A one-metre object would therefore be about 13.16 millimetres long in the model. Use the same unit on both sides of the calculation. A model’s quoted scale relates to size; it does not automatically tell you the track spacing or whether every dimension is a perfect reduction.
What gauge tells you
Gauge is the distance between the inner faces of the running rails. For a three-foot prototype, the full-size distance is 914.4 millimetres. At 1:76 the mathematically scaled gauge is about 12.03 millimetres. That is a conversion, not a recommendation for a proprietary track system. Actual model standards and readily available equipment can involve compromises. Check the intended track gauge of each vehicle you buy.
Avoid the island shortcut
A model inspired by the Isle of Man need not be a precise reproduction, but label your intention honestly. Do not assume ordinary OO track accurately represents three-foot Manx track simply because both are railway models. Equally, choosing a narrow-gauge product by name alone does not establish the correct prototype gauge. Keep three fields on your planning sheet: prototype gauge, model scale and actual model track gauge.
Use the calculator as a checking tool
Enter a known prototype gauge and a positive scale denominator. The output helps you understand the dimensional relationship and compare it with available model track. It cannot establish wheel standards, coupler compatibility, clearances or minimum curve radius. For a first project, settle those practical questions through the manufacturers’ documentation before buying a mixture of equipment. If you choose a deliberate compromise, note it in your model description; a clearly explained interpretation is more useful than a claim of accuracy it cannot support.