Roof Pitch Explained: Rise Over Run, Angles, and Rafter Lengths

Roof pitch is the steepness of a roof, expressed as rise over run: the inches the roof rises for every 12 inches of horizontal run. A 6/12 pitch rises 6 inches per foot. The angle in degrees, the multiplier that converts horizontal area to roof area, and the rafter length all follow from that one ratio by right-triangle geometry. This guide covers the ratio, the angle, the multiplier, the rafter length with the ridge and eaves, and the material and code consequences of the pitch — the parts a pitch number alone does not state.

The ratio: rise over run, in inches per foot

Pitch is written as a fraction with 12 as the denominator: 4/12, 6/12, 8/12, 12/12. The numerator is the rise in inches over a 12-inch horizontal run. A 6/12 pitch rises 6 inches for every 12 inches horizontally — a slope of 0.5, or 1 in 2. The denominator is always 12 in US practice, because the run is measured in feet and the rise in inches per foot; the fraction is a slope stated in the units of the trade. A pitch of 12/12 rises 12 inches per foot, a 45° angle, and is the point where the roof is as steep as it is wide.

The same pitch can be stated as an angle, a slope, or a ratio, and the conversions are exact: angle = arctan(rise ÷ run), slope = rise ÷ run, and the fraction is the slope with run fixed at 12. A 4/12 pitch is 18.43°, a slope of 1/3. A 6/12 pitch is 26.57°, a slope of 1/2. A 12/12 pitch is 45°, a slope of 1. The angle is what a protractor or a level reads; the fraction is what the trade quotes; the slope is what the geometry uses. Confusing them — quoting 6/12 as 6° — is a 20° error, and it happens. The Roof Pitch Calculator reports all three forms side by side, so the conversion is visible rather than trusted.

Pitch is measured on the roof’s slope, not on its plan. The run is the horizontal distance from the eave to the ridge, not the distance along the roof surface, and the rise is the vertical distance from the eave line to the ridge. Measuring along the slope instead of horizontally overstates the run and understates the pitch, and the error grows with the pitch. For an existing roof, measure the rise and run inside the attic, where the rafters are visible and the horizontal is measurable, rather than on the outside, where the slope tempts the tape.

Angle, multiplier, and roof area

The multiplier converts horizontal area to roof surface area: multiplier = √(1 + (rise ÷ run)²), which is the hypotenuse of the rise-run triangle divided by the run. It is the secant of the pitch angle. At 3/12 the multiplier is 1.0308; at 6/12 it is 1.1180; at 12/12 it is 1.4142. A roof with 1,000 sq ft of footprint at 6/12 needs 1,118 sq ft of roofing material, before waste, hips, valleys, and ridges. The multiplier grows slowly at low pitches and fast at high ones: doubling the pitch from 6/12 to 12/12 raises the multiplier from 1.1180 to 1.4142, a 26% increase in material for the same footprint.

The table below gives the angle and multiplier for the common pitches. It is worth memorising the pattern, not the table: the angle is the arctangent, the multiplier is the secant, and both are determined by the ratio alone. A pitch between table entries — 5/12, 7/12 — falls between the neighbouring values, and the calculator interpolates exactly rather than by eye. The multiplier is also the factor for the rafter length: the rafter is the hypotenuse, and its length is the run times the multiplier, which is the next section’s subject.

Roof area for ordering is the footprint area times the multiplier, plus waste and the allowances for hips, valleys, ridges, and starter courses. Waste is commonly 10–15% for a simple gable roof and more for a cut-up roof with many valleys. The multiplier gives the neat area; the order quantity is the neat area plus waste, and the waste percentage is set by the roof’s complexity, not by the calculator. A roof whose multiplier was computed from the wrong pitch is ordered wrong by the multiplier’s error, which is why the pitch measurement comes first and the order second.

Angles are arctan(rise ÷ 12); multipliers are √(1 + (rise ÷ 12)²).

Rafters, materials, and code

Rafter length is the hypotenuse: rafter = √(run² + rise²), which is run × multiplier. A 20 ft run at 6/12: rise 10 ft, rafter √(400 + 100) = √500 = 22.36 ft, before allowances. At 12/12: rise 20 ft, rafter √(400 + 400) = 28.28 ft. The allowances are the ridge — half the ridge board’s thickness, where the rafter meets it — and the eaves overhang, the tail beyond the wall, which is added to the rafter length and cut to the fascia. The calculator reports the theoretical length; the cutting length is the theoretical length plus the allowances, and the allowances are set by the framing, not by the pitch.

Pitch decides the roofing material. Asphalt shingles generally require 4/12 or steeper, with special underlayment between 2/12 and 4/12; below 2/12, low-slope membranes — modified bitumen, TPO, EPDM — are used, because shingles cannot shed water reliably on a near-flat slope. Metal roofing spans a wider range, with standing-seam profiles usable at low pitches and through-fastened profiles needing more. Tile and slate need steep pitches and the structure to carry their weight. The pitch is a material constraint before it is an aesthetic choice, and a material chosen for a pitch it cannot serve will leak however well it is installed.

Pitch also decides behaviour. Steeper roofs shed snow and rain faster, reducing the load and the leak risk, but they catch more wind, increasing uplift, and they are harder and more dangerous to walk on — above about 8/12, walking without staging is unsafe. Shallower roofs hold snow, increasing the structural load, and need the structure designed for it. Local code sets minimum pitches for materials, snow-load requirements, and wind-uplift resistance, and the code governs where this guide generalises. A pitch chosen for looks that violates the material’s minimum or the snow load is not a design; it is a future repair.

Worked gable: a 30 by 40 foot roof at 6/12

A gable roof on a 30 ft by 40 ft footprint, at 6/12 pitch. The footprint area is 1,200 sq ft. The multiplier at 6/12 is 1.1180, so the neat roof area is 1,200 × 1.1180 = 1,341.64 sq ft, before waste. At 10% waste for a simple gable, the order quantity is about 1,476 sq ft of roofing. The ridge runs the 40 ft length, and the run — half the 30 ft span — is 15 ft, so the rise is 15 × 6/12 = 7.5 ft, and the rafter length is 15 × 1.1180 = 16.77 ft, before the ridge and eaves allowances. The rafters are cut from 18 ft stock, with the overhang tail included in the cut.

The same roof at 12/12 shows the pitch’s cost. The multiplier is 1.4142, so the neat area is 1,200 × 1.4142 = 1,697.04 sq ft — 355 sq ft more roofing, 26% more, for the same footprint — and the rafter length is 15 × 1.4142 = 21.21 ft, needing 22 ft stock. The rise is 15 ft, the ridge stands 15 ft above the eave line, and the roof’s volume — the attic — is far larger, which is usable space or wasted heat depending on the design. The pitch is not only a slope; it is a quantity of material, a length of timber, and a volume of air, and the steeper roof buys all three at once.

The waste allowance deserves its own decision. A simple gable with few penetrations wastes 10%; a roof with hips, valleys, dormers, and skylights wastes 15% or more, because every valley and hip cuts shingles to angles that discard the offcuts. The order should also include the ridge cap, the starter course, the underlayment, and the flashing — none of which are in the neat area, and all of which are in the cost. A roofing estimate that quotes the neat area as the order quantity is short by the waste and the accessories, and the shortfall is discovered on the roof, where the remedy is a second delivery at a second delivery charge.

Measuring an existing roof, from inside and outside

The attic is the best place to measure. The rafters are visible, the horizontal is measurable with a level, and the rise and run can be taped directly: mark a level line 12 inches horizontally from a point on the rafter, measure the vertical distance from that line to the rafter, and the result is the rise per foot — the pitch numerator. Measure in two or three places, because rafters vary and old roofs settle, and take the consistent reading. The ridge board, the collar ties, and the ceiling joists give reference lines, and the measurement should be checked against the roof’s age and style: a 1950s bungalow is unlikely to be 12/12, and a reading that says so should be re-measured.

From outside, measure the eave-to-ridge horizontal distance and the ridge height, with a tape and a level, from the ground where the roof is low and from a ladder where it is safe — never by walking a steep roof to measure it. A smartphone inclinometer, held against the roof slope or against a straight board laid on it, reads the angle directly, and the pitch follows from the angle: a 26.57° reading is 6/12, a 45° reading is 12/12. The inclinometer’s accuracy is a degree or so, which is a pitch error of about 1/12 at moderate pitches — good enough to choose the material and order the roofing, and not good enough to cut rafters, which need the tape measurement from inside.

The measurement should be recorded with the method: “6/12, measured in the attic, 12-inch run, three readings consistent.” A pitch recorded without its method cannot be checked, and a pitch that cannot be checked will be re-measured by the next person who needs it — the roofer, the estimator, the building inspector — at the cost of another visit. The record belongs with the house’s documents, beside the roofing material, the installation date, and the warranty, because the next roof will need the same figure, and the next owner will need it too.

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