Lego scale

Around the time of the Lego Town Plan sets, Lego produced window and door pieces, along with sets of small buildings to go on the Town Plan baseboards, and a range of small plastic cars, nominally scaled at 1:87 (the same scale as the H0 model railway scale used across Continental Europe).

How close are the 1960s buildings to the scale of the cars?

A standard Lego brick is 9.6mm high

Standard UK doorways are 78 inches Imperial standard (1981 mm) or 2040mm metric standard.

If we assume that a doorway is two metres high for convenience, then a 1960s Lego door at three bricks high (3×9.6mm = 28.8mm), would come out as having a scale of about ~1:71. But this doesn't take into account that the Lego doorway includes the frame height, and also a step. Subtracting slightly more than one stud height then gives the internal doorway height as being more like 27mm. Scale is then 1:75.55', or 1:76 - 00 gauge scale!

Alternatively, we might want to calculate the internal room height as being three bricks (28.8mm). If the average internal height of a "modern" (~1950s) UK ground floor room is 2.4 metres, then translating this to three bricks gives a scale of 1:83(.33') This is decently close to 1:87 scale of H0.

If we take the older UK average room height of 2.2 metres, the scale comes out as 1:76(.38), which is back to UK 00-gauge scale.

Coincidence?

This may be a happy accident, but given that the Lego dimensions (including the wierd height-width ratio) were taken from the dimensions of the Hilary Page Kiddicraft bricks, and Page seems to have created the size of his bricks from scratch, and put an awful lot of time into designing them, it's possible that Page might have deliberately designed the bricks to allow houses with three-brick-high rooms to correspond to the size of 00-gauge model railways that were becoming popular in Britain (especially since it was something of a tradition for building sets to try to match model railway scales: Lotts Bricks buildings were often designed to scale with with gauge 0 model railways).

Building for 00 and H0 gauge

Given that Lego buildings are not expected to be micrometer-precise, it'd seem that the 1960s doors and windows allow a reasonable match to 00-gauge or H0 gauge model railways, if we allow three bricks as the internal room height, and also put in single-plate floors, or add one plate height per floor if a building has no internal structure. This gives a default storey height of three-bricks-and-one-plate, or 9.6mm +9.6mm +9.6mm +3.2mm = 32mm.

Building for N-gauge

If N gauge is supposed to be scaled somewhere between 1∶148 and 1∶160, then its pretty much half the size of 00/H0 (half of 00 would be 1:152, half of H0 would be 1:74). If our 00-scale Lego building storeys are three-bricks-and-a-plate high, and three plates equal one brick, then Lego 00-gauge buildings would be ten plates per storey, and N gauge would be five plates per storey (or one-brick-and-two-plates). For building with large windows, one could use brick-size windows, sitting on two rows of plates.