Three pieces of roof arithmetic
Slates by gauge
Every number here comes from your own measurements
A slate roof is set out from one figure, the gauge: the distance from one batten to the next, which is also how much of each slate shows. It follows from the slate's length and the headlap, and from it come the number of courses, the slates and battens a slope takes, and where the nail holes go. The three calculations on this page do that arithmetic with the numbers you give them.
Measure from drawings, from the loft, or from the street with a sensible guess; never from the roof itself, which is a job for someone on a scaffold with edge protection. The answers describe a plain rectangle of slope. Cutting round a stack, a dormer or a valley, the verges, breakage and the slate maker's own figures all change a real order, and the fixing specification for your roof's exposure, worked out to BS 5534, decides the nails and hooks.
The gauge is half of what is left when the headlap is taken off the slate's length, because two thicknesses of slate lie over every point of the roof. With a 500 by 250 millimetre slate and a 75 millimetre headlap that is 212.5 millimetres, and a square metre takes one million divided by the gauge times the width: about 18.8 slates. The holing gauge puts the nail holes a little above the gauge plus the headlap, measured from the tail, so each nail sits clear of the slate it covers.
The pitch is the angle whose rise over run you entered; the rafter is the hypotenuse of the same triangle, and the slope's true area is its plan area divided by the cosine of the pitch. That rafter length is close to the slope length the gauge calculation above asks for. The lowest pitch a particular slate or tile may be laid at is given in its maker's data, and it is one of the things a survey checks before a covering is changed.
BS 6229 sets the minimum finished fall of a flat roof at 1 in 80 and recommends designing at 1 in 40, because building tolerances and the deflection of the deck under load eat into a fall that started exactly at the minimum. A four-metre roof designed at 1 in 40 drops 100 millimetres from the wall to the outlet. The drawing above is stretched upward nine times so a fall that small can be seen at all.