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Roofs of Wood Green, London N22

Natural slates fixed with copper nails running down to a lead valley, beaded with rain in low evening light.

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.

Slates by gauge

Gauge212.5 mm Courses, eaves to ridge22 Slates in a course20, with half slates at the verges in every other course Slates to the square metre18.8 Slates for this slope440 by course count Battensabout 108 m Holing gauge, from the tail296 to 303 mm
ridgeeaves5 m wide, 4.6 m eaves to ridge

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.

Pitch and true area

A slope is bigger than its plan. Give the rise and the run of one slope, from drawings or measured inside the loft, and the width of the slope along the eaves.

Pitch31.6° Rafter length4.58 m Plan area of the slope19.5 m² True area of the slope22.9 m² Both slopes, if they match45.8 m²

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.

Flat-roof fall

Depth along the fall from drawings, or measured on the ceiling below; the drop from a level line inside, or from drawings.

1 in 67 Steeper than the 1 in 80 minimum finished fall, flatter than the 1 in 40 BS 6229 recommends designing at. For 1 in 40 over 4 m, design for a drop of 100 mm; 1 in 80 needs at least 50 mm once finished.
The flat roof in section, drawn at the fall you enteredthe fall is drawn nine times steeper than it is

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.