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Roof Pitch Calculator

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A roof is a triangle that costs money to get wrong. This calculator converts a pitch between the four ways it is written — 6/12, 26.57°, 50%, 1:2 — and then does the two things that follow from it: how long the rafters are, and how much surface the roof actually has. The second is where material orders go wrong, because a sloping roof always covers more area than the ground beneath it.

Roof shape

Two rectangular planes meeting at a ridge. The run is half the span.

The trade form: 6 means 6 units of rise for every 12 along.

/12
Common pitches:
m

Wall face to wall face

m
m

Horizontal projection. 0 for none

%

10% suits a simple roof

How to use the roof pitch calculator

  1. 1Pick the roof shape. A gable splits the span into two runs, a shed roof runs the full span in one slope, and a hip roof adds diagonal rafters.
  2. 2Say how the pitch is given to you — rise per 12, degrees, percent or a ratio — and enter it. The common pitch buttons fill it in for you.
  3. 3Enter the span across the walls and the length along the ridge.
  4. 4Add the eaves overhang if the roof projects past the wall, measured as horizontal projection per side, and set a waste allowance for materials.
  5. 5Press Calculate roof. The pitch appears in all four notations, with rafter lengths and both the footprint and the true sloping area underneath.

Examples

A common residential pitch, converted

Input
6/12 pitch
Result
26.57° · 50% slope · ratio 1 : 2 · slope factor 1.1180

The 50% is the giveaway that pitch is not proportional to angle: half the rise of a 12/12 roof is not half of 45°.

What the slope costs in materials

Input
12 m × 8 m gable roof at 6/12, 0.5 m overhang, 10% waste
Result
Roof area about 128.4 m² against a footprint of 114.8 m² — order for roughly 141 m²

The roof is 11.8% larger than the ground it covers, before any waste allowance. Ordering against the footprint would leave the job short.

The steepest common pitch

Input
12/12 pitch, any building
Result
Exactly 45°, 100% slope, slope factor 1.4142

Forty-one per cent more surface than the footprint. At this pitch the difference is impossible to absorb in a waste allowance.

About the roof pitch calculator

Four ways to say the same slope

Roof pitch is written differently by different trades, and every one of them is in daily use. Carpenters in the US and much of India say rise in twelve — a 6/12 roof rises six units for every twelve along. Drawings and inclinometers give degrees. Civil and drainage work uses percent, which is simply rise ÷ run × 100. And a ratio like 1:2 means one up for two along, though it is worth checking which way round a given drawing means it.

They all describe the same geometry, and the conversions between them are trigonometric rather than arithmetic. The tangent of the roof angle is the rise divided by the run, so 6/12 gives a tangent of 0.5 and an angle of 26.57°, while the percent form is that same tangent expressed out of a hundred. Once you have any one of the four, the other three follow — which is what the top half of this calculator does.

The practical value is in translation. A supplier quoting a minimum pitch in degrees, a drawing marked 1:3, a builder talking about a four-twelve and a spec sheet giving 33% can all be describing roofs that are or are not compatible, and the only way to know is to put them in the same notation.

The slope factor, and the delivery that comes up short

Every pitched roof covers more surface than the ground beneath it, and the multiplier is 1 ÷ cos θ. It is the single most useful number on this page, because it is the one that turns a measurement anyone can take — the building's footprint — into the figure a supplier needs.

The size of the effect is easy to underestimate. At 4/12 it is 5.4%, which sounds negligible and is roughly half a standard waste allowance, so ordering against the footprint appears to work until the last few squares. At 8/12 it is 20%. At 12/12 it is 41.4%, and no waste allowance absorbs that: a job ordered on plan area is missing two fifths of its covering, and the shortfall is discovered on the roof rather than in the office.

The same factor applies to everything laid on the slope — underlayment, battens, insulation between rafters — and not to anything measured on plan, such as the ceiling below. Overhangs also count: eaves add to the covered area on all four sides, which is why this calculator asks for the projection rather than assuming the roof stops at the wall. What it does not model is complexity. Dormers, valleys, chimneys and roof windows all add cutting and waste beyond what a plain plane needs, and on a complicated roof the allowance should rise accordingly.

Frequently asked questions

Why is a 6/12 roof 26.57° and not 30°?
Because the relationship is an arctangent, not a proportion. The pitch is a ratio of rise to run, and turning a ratio into an angle means asking which angle has that tangent — 6 ÷ 12 is 0.5, and arctan 0.5 is 26.565°. The consequence is that the two scales do not track each other: 12/12 is exactly 45°, but 6/12 is not 22.5° and 24/12 is not 90°. Converting by halving or doubling is the commonest pitch error there is.
What is the slope factor and why does it matter?
It is 1 ÷ cos of the roof angle, and it is what turns a footprint area into a real roof area. At 4/12 it is 1.054, so the roof has 5.4% more surface than the ground it covers; at 12/12 it is 1.414 and the roof has 41% more. Order shingles, membrane or battens against the building's plan area and you are short by exactly that percentage — which on a shallow roof hides inside a waste allowance and on a steep one very much does not.
Does a hip roof need more material than a gable?
Not at the same pitch over the same footprint — the surface area is identical, because the four planes of a hip are the two planes of a gable cut up and rearranged. What a hip roof does add is cutting: every hip rafter meets the common rafters at a compound angle, the coverings need trimming along each hip, and waste allowances are usually set higher for that reason. It also removes the two gable walls, which is a saving elsewhere in the build.
Do the rafter lengths include the cuts?
No. The figures are measured along the top edge of the rafter, from the outside face of the wall to the centre of the ridge, with the overhang version continuing to the end of the eaves. A carpenter still deducts half the ridge board's thickness, sets out the birdsmouth where the rafter sits on the wall plate, and marks the plumb cut at the tail. Those are shop decisions that depend on the timber and the detailing, so this gives the geometry and no more.
Can I use this to size the rafters?
No, and this is the important limit on the page. Everything here is geometry — lengths, angles and areas. What size timber a rafter needs, at what spacing, in what grade, and what snow and wind loads it must carry are structural engineering questions governed by local building codes and by the specific building. Take the geometry from here and the sizing from a code table or an engineer.

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