Roof Pitch Calculator

What Is Roof Pitch?

Every sloped roof is a right triangle in disguise. The horizontal leg is the run, the vertical leg is the rise, and the sloping face you can see is the hypotenuse, which is also the rafter line. Pitch is the relationship between the first two legs, and almost everything else about the roof follows from that one proportion: which coverings are legal on it, how much material it swallows, and whether anyone can stand on it.

Rise, Run, and the X-in-12 Notation

Rise is how far the roof climbs vertically. Run is how far it travels horizontally to do it, measured on the level rather than along the slope. Both belong to a single roof plane, taken from the eave toward the ridge, never across a valley or over a dormer.

American roofing fixes the run at 12 and quotes the rise against it, which compresses the whole vocabulary of the trade into one number: a 4:12, a 7:12, a 12:12. The 12 is arbitrary but universal, so a framer can say “it's an eight” and every other trade on site knows the plane sits at 33.7 degrees without measuring anything.

You do not have to measure a 12-inch run to get there. Rise divided by run, multiplied by 12, converts any honest pair into the standard notation: 14 inches of rise over a 24-inch run is 7.00 in 12.

Pitch, Slope, Degrees, Percent

Four descriptions of one quantity are in circulation. The X-in-12 ratio is what roofers and building codes use. Degrees is what architects, solar designers and anyone setting a miter saw use. Percent slope, which is rise divided by run times 100, is what surveyors and drainage engineers use, so a 6:12 roof is a 50% slope. The fourth is the angle's tangent, the bare decimal 0.5, which is what the trigonometry underneath is actually handling.

The model code settles the wording. In the roof-assemblies chapter cited at the foot of this page, “slope” appears 87 times and “pitch” three, and where “pitch” does appear it carries the identical meaning: “3:12 pitch to < 4:12”. An older carpentry usage made pitch the rise over the full span instead of the run, so a 6:12 roof on a 24-foot span was quarter pitch. That survives only in old framing tables. For anything specified, permitted or bought today, pitch means rise per 12 of run.

What This Calculator Returns

The panel prints one line: the words Roof Pitch Angle, then the degrees to one decimal. Enter 8 and 12 and it reads Roof Pitch Angle: 33.7°. Nothing appears beneath it — no ratio, no rafter length, no area.

The input side is equally spare, because the angle depends on the ratio alone. The tool never needs to know how big the roof is or which tape you used. Everything the panel leaves out is worked through in the sections below.

Turning an angle into an order is a separate job: the footprint has to be scaled up by the slope, divided into squares and padded for waste, which is the work done by the Roof Shingle Calculator.

How Do You Calculate Roof Pitch?

The arithmetic is one division and one inverse trigonometric function. Getting an honest rise and run off a real roof is the part that goes wrong, which is why measuring gets as much room here as the math.

The Roof Pitch Formula, Written Out

Divide the rise by the run, then take the arctangent of the result. Arctangent — the inverse tangent, written arctan or tan⁻¹ — is the function that answers the question “what angle has this ratio between its opposite and adjacent sides?” It is the exact inverse of the tangent, and it is the only piece of trigonometry a roof needs.

Formula

angle in degrees = arctan(rise ÷ run) × 180 ÷ π

rise per 12 of run = (rise ÷ run) × 12
percent slope      = (rise ÷ run) × 100

The first line is what the calculator evaluates. The second is the one it does not do for you, and it is the number your supplier will ask for. The third is the same ratio wearing a surveyor's hat.

How to Measure Rise and Run

Three ways to get the pair, all producing the same ratio:

• On the roof: lay a level on the slope, hold it horizontal, and mark a run along it. Twelve inches works; twenty-four inches is steadier. Measure straight down from the mark to the roof surface, perpendicular to the level. That drop is the rise.
• In the attic: press the level against the underside of a rafter instead of the shingles. Identical geometry, no ladder, and nothing to slip on.
• Gable to ridge: measure the horizontal distance from the outside wall in to a point below the ridge, and the vertical height from the ceiling joist up to the underside of the ridge board. A 60-inch rise over a 120-inch run returns 26.6°, the same answer 6 and 12 give.

Both figures must be in the same unit and taken on one roof plane. A run measured along the slope rather than on the level reads long, and the pitch that comes back is too shallow.

Step by Step

• Choose one roof plane and take the run on the level — say 24 inches.
• Measure the rise: the vertical drop from the free end of the level down to the roof — say 14 inches.
• Leave Measurement Unit on Inches. The selector does not change the answer, so it only has to match your own notes.
• Type 14 into Vertical Height (Rise) and 24 into Horizontal Distance (Run).
• Press Calculate. The readout shows Roof Pitch Angle: 30.3°.
• For the trade ratio, do the division yourself: 14 ÷ 24 × 12 = 7.00, so this is a 7-in-12 roof.

Both fields open empty, so nothing is computed until you press the button, and the panel does not update again while you type. Change a figure and press Calculate a second time.

Worked Example: an 8-in-12 Roof

A level held out 12 inches from the roof face drops 8 inches to meet the shingles. Rise 8, run 12, unit inches.

Rise 8 in, run 12 in

Roof Pitch Angle: 33.7°

The same roof is a 66.7% slope to a drainage engineer, and its sloping face measures 1.202 times the ground it covers. It sits above the federal 4-in-12 dividing line, so for work-safety purposes it is a steep roof rather than a low-slope one.

Worked Example: a 24-Inch Level and a 14-Inch Drop

Longer levels give steadier numbers because the same slip of the tape covers a smaller share of the reading. Held out 24 inches, this roof drops 14.

Rise 14 in, run 24 in

Roof Pitch Angle: 30.3°

Rise divided by run times 12 turns that into 7.00 in 12, and typing 7 and 12 into the same form returns Roof Pitch Angle: 30.3° once more. Only the ratio was ever in play.

Worked Example: 40 cm Over 100 cm

Metric measurements need no conversion first. A 100 cm run with a 40 cm drop goes in as 40 and 100.

Rise 40 cm, run 100 cm

Roof Pitch Angle: 21.8°

Switching Measurement Unit to Centimeters returns that same 21.8°, because the tool divides both entries by 2.54 and a ratio is untouched by dividing both of its sides by the same number. In American notation this plane is 4.80 in 12: legal for asphalt shingles, and just past the 4-in-12 mark where the double-underlayment requirement stops.

Roof Pitch Chart: Ratio, Degrees and Percent

Every slope you are likely to meet, with the angle this calculator returns for it. The multiplier column is the length of the sloping face per unit of run, so one figure scales both rafter length and surface area.

Read the multiplier as a price tag. A 40 by 30 foot gable covers 1,200 square feet of ground; at 6:12 the roof surface is 1,341.6 square feet, at 8:12 it is 1,442.2, and at 12:12 it is 1,697.1. Framing, sheathing, underlayment and covering all scale with that surface figure, never with the footprint.

Rafter length uses the same column. A 15-foot horizontal run at 8:12 needs a rafter of 15 × 1.202, which is 18.03 feet before any overhang, and the ridge sits 10.00 feet above the wall plate. Up to about 3:12 the multiplier is within 3.1% of 1.000, which is why low-slope estimating can ignore it and steep-roof estimating cannot.

Converting Degrees Back to a Ratio

Drawings arrive in degrees; suppliers and framers work in twelfths. Going back the other way is the tangent, not the arctangent.

Formula

rise per 12 of run = tan(angle) × 12

Of those eight, only 45° lands on a whole twelfth. A drawing calling for 30° gets built as a 7:12, which this calculator returns as 30.3°: about a quarter of a degree steeper than drawn, and small enough to vanish under the covering.

How to Read Your Result

A rise of 6 against a run of 12 produces the single line Roof Pitch Angle: 26.6°, and that is the entire output. What the number means depends on which threshold you are standing near.

Where the Category Lines Fall

One threshold governs safety. Federal construction rules define a low-slope roof as “a roof having a slope less than or equal to 4 in 12 (vertical to horizontal)” and a steep roof as one “having a slope greater than 4 in 12”. In degrees the line sits at 18.4°, and it carries real weight above 6 feet: roofing work on a low-slope roof may be protected by a warning line paired with a safety monitoring system, or by a safety monitor alone where the roof is 50 feet or less in width, while a steep roof permits only guardrails with toeboards, safety nets or a personal fall arrest system.

A second threshold governs water. Below roughly 2:12, which is 9.5°, runoff is slow enough that wind-driven rain can travel back up under overlapping pieces, which is why every shingle and tile in the next table has its code minimum at or above that line. What the code still allows below it are built-up roofs, metal panels with folded or sealed seams, and mineral-surfaced roll roofing down to 1:12.

Steeper than that and the limit stops being geometry. Roofers set roof jacks, staging or a lift once a plane is no longer safe to stand on, and where that point falls depends on the covering, the weather and the crew. The calculator returns 63.4° for a 24-in-12 mansard face without comment; what it costs to work on that face is no part of the number.

Minimum Slope by Roofing Material

Model code sets a floor for every covering. The slopes below are quoted from Chapter 9 of the 2012 Seattle Residential Code, the edition of the model text adopted and published by the City of Seattle; each angle is what this calculator returns for that slope.

Three rows repay a second look. Asphalt shingles are permitted from 2:12, but from 2:12 up to 4:12 the code calls for double underlayment, so a roof between 9.5° and 18.4° costs more to prepare than a steeper one does. Clay and concrete tile carry the same double-underlayment requirement from 2 1/2 : 12 to 4:12. Standing-seam metal ties built-up roofing for the shallowest slope on the list, both at 1/4 : 12, because a folded seam gives water no lap to climb.

Codes are adopted locally and revised on a cycle, and coal-tar built-up roofing is allowed shallower still, down to 1/8 in 12 or 0.6°. Treat the table as the shape of the rule, then confirm the edition your jurisdiction actually enforces before ordering.

When a Field Is Blank, Zero or Negative

A blank field and a typed zero take different paths. Press Calculate with Vertical Height (Rise) left empty and nothing is computed at all: the amber “Check your inputs” panel appears with the line “Enter a value for Vertical Height.” Leave both boxes empty and it names both, as “Enter a value for: Vertical Height, Horizontal Distance.” The message drops the parenthetical from each label, which is why it reads Vertical Height rather than Vertical Height (Rise). Neither field is exempt from that check, so an empty box is never read as a zero.

A zero or a negative number is a different case, because something was actually entered. Those clear the empty-field check, reach the formula and are refused there, and the panel then shows a large 0° with the words Invalid input under it rather than the amber notice. Read that 0° as “the tool declined”, not as “your roof is flat”. Both boxes need a value above zero.

Each field declares a minimum of 0.1, but the form is not validated by the browser, so smaller entries pass straight through: a rise of 0.05 against a run of 12 returns Roof Pitch Angle: 0.2°. The two checks above are the only ones that bite: a value in both boxes, and both of them above zero.

Limits: When This Does Not Apply

One Plane at a Time

The calculation describes a single flat roof plane. Gambrels and mansards carry two different pitches by design, saltboxes are asymmetric, and on a hip roof the hip rafter itself runs at a shallower angle than either plane it separates. Measure and enter each plane on its own; a roof with more than one slope has no single pitch to report.

The Unit Selector Changes Nothing

Choosing Centimeters divides both entries by 2.54, and dividing both sides of a ratio by the same number leaves the ratio exactly where it started. A rise of 15 and a run of 30 return 26.6° under either setting. The control exists for your own bookkeeping, and it cannot rescue the mistake it looks like it should catch: a rise recorded in inches paired with a run recorded in centimeters is wrong under both settings.

An Angle Is Not a Code Check

Learning that a plane sits at 14.0° tells you it is a 3-in-12 and that asphalt shingles clear the minimum. It says nothing about whether the deck, underlayment, ice barrier, fastener pattern, exposure or wind rating satisfy the code where you live, and several of those vary with slope in their own right.

Pitch alone also settles nothing about load. Whether a structure can carry the snow that lands on it is a structural calculation against a design ground snow load, and steepness cuts both ways: a steeper plane sheds snow more readily and presents more area to the wind.

Where Your Measurement Error Goes

Precision comes from a long run, not from the calculator. Read a 6-in-12 roof off a 12-inch level and a quarter-inch slip in the rise moves the answer between 25.6° and 27.5°, a spread of 1.91 degrees. Make the same quarter-inch error against a 24-inch level, where the nominal rise is 12 inches, and the spread narrows to 26.1° through 27.0°, or 0.95 degrees. Both spreads are the difference between the underlying angles rather than between the rounded readouts, and doubling the run halves the damage.

A level that is not truly level costs more than that. One degree of tilt over a 24-inch run displaces the mark by 0.42 inches, which reports a genuine 26.6° roof as 27.4°. Check the bubble before the tape.

What the Number Leaves Out

Rafter length, ridge height, roof area, overhang and the waste allowance on a material order all sit downstream of pitch, and none of them appear in the panel. The multiplier column in the chart above covers rafter length and roof area; ridge height is a separate step, the run times rise over 12, and overhang and waste depend on decisions the geometry cannot make for you.