Roof pitch calculator

What this answers

A roof pitch is written in three ways: as an angle in degrees, as a percentage, and as a ratio such as 1 : 2 or “6 in 12”. They are one number — rise divided by run — in different clothes. This page converts between them, and if you give the width of the building it also works out the ridge height and the length of a rafter.

The three notations

• Degrees — the angle from horizontal. 45° is as much up as across.
• Percent — the rise per 100 of run. 100% is 45°, and 50% is a rise of 1 over a run of 2.
• Ratio — rise to run in any one unit. 1 : 2 and 6 : 12 are the same roof. The page also gives the North American form, the rise for every 12 of run.

The conversion goes through the tangent: percent = 100 · tan(angle). The tangent is rise over run in a right triangle.

The rafter

For a symmetric gable roof the rafter is the long side of a right triangle whose short sides are the rise and half the building’s width (plus the overhang, if the roof reaches past the wall):

The same factor, 1 / cos(angle), is how much larger the roof surface is than the ground under it — see roof area from pitch.

Worked example

A building 8 m wide with a pitch of 30°, and no overhang:

• half the width is 4 m
• the rise is 4 · tan 30° = 2.31 m
• the rafter is 4 / cos 30° = 4.62 m
• the pitch is 57.7%, a ratio of 1 : 1.73, and 6.93 in 12

What is not included

• Joints and cuts. The rafter length is straight along the slope, with nothing added for the cut at the foot or the ridge.
• Other roof shapes. The page assumes one pitch on both sides.
• What pitch you may use. Which pitch a roofing material can be laid at is for its maker and the building rules where you are. This page does not say.

Common questions