Roof Pitch Calculator

One slope, four ways of writing it

A roof slope is a single fact about a building, and the trades that meet on it each write that fact down differently. The framer writes a ratio — so much rise for every twelve of run, because twelve is the number stamped on a framing square. The architect writes an angle, because a drawing is dimensioned in degrees. The surveyor writes a percent, because that is how every other fall on the site is written. The estimator wants none of those: he wants the slope factor, which turns the footprint he can measure into the surface he has to buy.

All four come out of the same two measurements. Rise over run gives the ratio; its arctangent gives the angle; the ratio times a hundred gives the grade; and the hypotenuse of the same triangle over its run gives the factor. The sheet opens on the pitch most people picture when they hear the word: 6 inches up for 12 across, which is 6 in 12, 26.5651 degrees, 50 percent and a factor of 1.118034. Four numbers, one roof.

The conversion runs in every direction, which is the point of the mode selector above. Give the sheet 22.5 degrees and it solves the rise back out — tangent of the angle times twelve — and prints 4.9706 in 12, 41.4214 percent, factor 1.082392. Give it 50 percent and it comes back as 6 in 12 exactly; give it 45 degrees and you get the one pitch anybody can check in their head, 12 in 12 at 100 percent. Whatever the mode, the same four lines are printed, so you can hand the angle to the architect and the ratio to the framer without converting anything twice.

The edges behave too. A pitch of 0.25 in 12 is 1.1935 degrees, 2.0833 percent and a factor of 1.000217: a surface that is, for buying purposes, its own footprint. A rise of zero gives a slope factor of exactly 1 and a drawing with no angle arc. A negative rise is read as a fall and named as one, never silently flipped.

Measuring a pitch you cannot climb

Most of the roofs anyone needs a pitch for cannot be walked, and do not need to be. The measurement is a ratio, so it can be taken anywhere the roof line is visible: at the gable end from a ladder, along a rake board, in the attic, or off the eave with a level.

That last one is the method the fourth mode is built for. Hold a level against the roof line with its bubble centred, mark where its far end sits, and measure straight down from that mark to the roof. The drop is the rise; the length of the level is the run. The sheet keeps the run as an editable field rather than locking it at twelve because levels are not twelve inches long: a two-foot level reads the drop over 24 inches, and 12 inches of drop over that run is 6 in 12, not twelve in twelve. Get the run wrong and the pitch is wrong by exactly that factor.

Rafters in an attic give the same ratio over whatever length you can reach: 18 inches up over 36 across is 6 in 12. Awkward pairs work as readily as tidy ones — 9 over 20 is 5.4 in 12 and 24.2277 degrees — and a pitch landing between the usual whole numbers is not a mistake. Old roofs settle.

Assumption. The rise and the run are read over the same line, in the same unit. The sheet cannot tell a true horizontal from a nearly-horizontal one: centre the bubble.

What the slope factor is actually for

Of the four figures, the slope factor is the one that spends money. A footprint is measured flat, but shingles, underlayment and sheathing are bought by the sloped surface, which is always larger. The factor is the ratio between the two, and it is pure geometry: the hypotenuse of the rise-and-run triangle divided by its run. Nothing published, nothing proprietary, nothing that needs a citation.

At 6 in 12 the factor is 1.118034, so a thousand square feet of footprint carries 1,118 square feet of roof; at 4 in 12, 1,054. At 12 in 12 — the 45-degree roof — it is 1.414214, and the surface is 41 percent larger than the ground it covers. Miss the factor on a steep roof and the order is short by more than four squares.

Multiplying by it is where this sheet stops and the material takeoff begins. Squares, shingle bundles, underlayment rolls, ridge cap and starter are the work of the roofing calculator, which uses this exact factor on up to four roof sections and reads every yield off a named manufacturer sheet. A-104 converts the slope; A-102 buys the roof.

From pitch to rafter, and where that stops

Type a building span and a second block appears, because the pitch and the span together fix the two lengths a framer asks for first. A common rafter runs over half the span, so a 24-foot building gives a half run of 12 ft. The overhang is added to that half run before the slope is applied, and it is measured horizontally, not along the rafter line. A twelve inch overhang on that span makes the run 13 ft, the ridge height 6 ft and the common rafter 14 ft 6 7/16 in, against 13 ft 5 in without the tail.

The lengths come out in feet and inches to the sixteenth, reduced the way a tape is read: a 30-foot span at 4 in 12 with no overhang gives a ridge of 5 ft and a rafter of 15 ft 9 3/4 in, not nine twelfths of anything; 28 feet at eight in 12 with a two-foot tail gives 9 ft 4 in and 19 ft 2 3/4 in. The ridge height is measured from the top of the wall plate, and it is the figure that tells you whether a dormer or a second storey clears.

A rafter is a diagonal, so it is always longer than the run it covers: the slope factor applies to a line exactly as it applies to an area. That is why the overhang is typed as a horizontal distance rather than as a length of tail — the sheet stretches it for you.

That is deliberately the end of it. This sheet prints a rafter line length and stops: no rafter count, no spacing, no birdsmouth, no plumb cut, no deduction for the ridge board’s thickness, no hip and no valley. Those are a framing takeoff rather than a slope conversion, and a conversion tool that guesses at member counts is how a cut list ends up wrong. The span block assumes one symmetric roof with a single pitch on both sides.

What this sheet will not print

There is a family of figures that roof pitch pages hand out freely and that you will not find here: the shallowest slope a given roofing material may be laid on, the line below which a roof is treated as low-slope, the point at which a crew stops walking one. Each is a requirement set by a building code or by a manufacturer, and a requirement carries a jurisdiction and a revision date. Reprinted stripped of both, it becomes the kind of number that gets a roof rejected at inspection.

So the rule here is simple: this sheet does the trigonometry and sends you to the document. What a slope is allowed to be, and what may be laid on it, lives on your own drawings, in the instructions for the product you are buying, and in the code your jurisdiction has adopted. Read it there. Everything above is arithmetic on two numbers you measured yourself, which is why this page cites nothing.

Pitch         P  =  rise x 12 / run
Angle         A  =  atan( rise / run )        degrees
Grade         G  =  rise / run x 100          percent
Slope factor  F  =  sqrt( rise^2 + run^2 ) / run
From angle    rise =  tan(A) x 12
From grade    rise =  G / 100 x 12
Half run      h  =  span / 2
Run + eave    R  =  h + overhang
Ridge height  H  =  h x rise / run
Common rafter L  =  R x F

Frequently asked

How to calculate for roof pitch?

Measure how far the roof climbs, measure the horizontal distance it climbs over, and divide one by the other. The US convention writes that ratio over twelve: 6 inches of rise over 12 of run is 6 in 12, 26.5651°, a 50 % grade. The two measurements need not be twelve inches apart: 18 over 36 is the same roof, 6 in 12.

What is a 4/12 roof pitch formula?

Four inches of rise for every twelve of run. The angle is atan(4 ÷ 12) = 18.4349°, the grade is 4 ÷ 12 × 100 = 33.3333 %, and the slope factor is √(4² + 12²) ÷ 12 = 1.054093. That last one is the figure a shingle order needs: every square foot of footprint under a 4/12 carries 1.0541 square feet of roof.

What pitch is a 22.5 degree roof?

Solve it backwards: rise = tan(22.5°) × 12 = 4.9706 in 12, a touch under five in twelve. Its grade is 41.4214 % and its slope factor 1.082392. For reference, 30° is 6.9282 in 12 and 45° is exactly 12 in 12.

What does a 4/12 pitch roof look like?

Like the triangle drawn above, at 18.43° off horizontal — shallow enough to read as a low roof from the street, steep enough that the eye sees a slope. Switch the sheet to 4 in 12 and the drawing is redrawn to scale with that angle marked. A 12 in 12 stands at 45° for comparison, a 3 in 12 at 14.04°.

How many degrees is a 7 pitch roof?

30.2564° — atan(7 ÷ 12). Its grade is 58.3333 % and its slope factor 1.157704, so a footprint of a thousand square feet carries 1,158 square feet of roof surface above it.

What is a 25% roof slope?

The roof rises a quarter of what it runs, which is 3 in 12 and 14.0362°. Grade and pitch are the same measurement in different clothes: a 50 % grade comes back as exactly 6 in 12. Percent is how a surveyor writes a slope; rise in twelve is how a framing square reads one.

Limits of this sheet

A-104 converts one slope and measures nothing else: no material, no price, no member count, and no constant of its own. Switch to metric and the angle, the grade and the factor do not move, because none of them has a unit; only the headline changes, to degrees, since “rise in twelve” is an inch convention that does not survive translation.

Sheet A-104 prepared by TakeoffMetric Editorial; no author, credential or field measurement is claimed.