Roof Pitch Calculator

Formula

Pitch from Rise and Run

roof pitch = rise ÷ run
x in 12 = (rise ÷ run) × 12

Roof Pitch in Degrees

angle = arctan(rise ÷ run). The angle is measured from the horizontal.

Roof Slope Percentage

slope (%) = (rise ÷ run) × 100. See the percentage calculator for general percent conversions, or the percentage difference calculator to compare two pitches expressed as percents.

Rafter Line Length

rafter length = √(rise² + run²). This is the mathematical sloped length and excludes overhang, ridge board adjustment, birdsmouth cuts, and other framing allowances.

Roof Pitch Multiplier (also called Roof Pitch Factor)

multiplier = √(1 + (rise ÷ run)²). The roof pitch multiplier, also known as the roof pitch factor, is the ratio of sloped length to horizontal run, or equivalently the ratio of sloped area to horizontal projected area for a plane of constant pitch. This calculator does not compute roof area on its own — measure the horizontal footprint with the square footage calculator and multiply by this factor for a sloped-area estimate.

Variable definitions

• Rise: Vertical change from the wall plate to the ridge over the given horizontal run.
• Run: Horizontal distance the roof plane covers (not the sloped length).
• Decimal slope: Rise divided by run, expressed as an unscaled decimal (for example 0.5).
• X:12 pitch: Traditional roofing shorthand: rise per 12 units of horizontal run.
• Angle: Roof pitch expressed as an angle from horizontal, equal to arctan(rise ÷ run).
• Slope percentage: Decimal slope multiplied by 100, expressed as a percent.
• Rafter line length: Sloped length from wall plate to ridge, equal to √(rise² + run²).
• Pitch multiplier: Ratio of sloped length to horizontal run, equal to √(1 + slope²).

Step-by-step calculation

1. Confirm that rise and run use the same measurement unit.
2. Divide rise by run to get the decimal slope.
3. Multiply the decimal slope by 12 to get the x:12 pitch.
4. Multiply the decimal slope by 100 to get the slope percentage.
5. Take the arctangent of the decimal slope to get the angle in degrees.
6. Apply the Pythagorean theorem to rise and run for the rafter line length.
7. Compute the pitch multiplier as the square root of (1 plus slope squared).

Worked example

Known values: roof pitch 6:12 and run 15 ft.

• Decimal slope: 6 ÷ 12 = 0.5
• Rise: 15 × 0.5 = 7.5 ft
• Angle: arctan(0.5) = 26.57°
• Slope percentage: 0.5 × 100 = 50%
• Rafter line length: √(7.5² + 15²) ≈ 16.77 ft
• Pitch multiplier: √(1 + 0.5²) ≈ 1.1180

A 6:12 roof rises 6 units for every 12 units of horizontal run. Over a 15 ft run the rise is 7.5 ft and the rafter line length is about 16.77 ft before framing allowances.

How to use this calculator

1. Pick what you want to calculate: roof pitch, rise, or run.
2. Select a pitch format (x in 12, degrees, or percent) if a pitch is required.
3. Choose one measurement unit for rise, run, and the rafter length.
4. Enter the known values. Results update as you type.
5. Use Copy, Share, or Reset in the actions bar below the result card.

Changing the unit after a valid calculation converts the rise, run, and rafter length to the new unit rather than only relabeling them. The x:12 ratio, angle, percentage, and multiplier are unit independent.

Common mistakes

• Measuring along the sloped roof surface instead of the horizontal run.
• Mixing feet and inches, or metric and imperial units, without converting.
• Entering an angle in degrees where an x:12 ratio is expected.
• Typing 50 instead of 0.50 in a decimal-slope formula outside this calculator.
• Confusing the full building span with the run of a single roof plane.
• Using rafter line length as a finished cut length.
• Assuming a pitch alone determines code compliance or material suitability.
• Rounding intermediate values too early and losing accuracy.

Roof Pitch Chart (x:12, Degrees, Slope %, Multiplier)

This roof pitch chart doubles as a roof slope chart. Every value is computed with the same formulas the calculator uses, so the table cannot drift out of sync with the tool.

Roof Pitch Categories (Flat, Low, Conventional, Steep)

Roofs are commonly grouped into four pitch ranges. Category boundaries are conventions, not code — always check manufacturer instructions and local building codes for the materials and climate on your project.

• Flat roofs — roughly 0.5:12 to 2:12 (about 2.4° to 9.5°). Not truly flat; a small slope is needed for drainage.
• Low-slope roofs — about 2:12 to 4:12 (about 9.5° to 18.4°). Often require special underlayment or membranes.
• Conventional roofs — about 4:12 to 9:12 (about 18.4° to 36.9°). The most common residential range and generally the easiest to work on.
• Steep-slope roofs — 9:12 and above (about 36.9° and higher, up to about 21:12 in extreme designs). May need extra fasteners and safety equipment.

How to Measure Roof Rise and Run

Run is the horizontal distance the roof covers, not the length along the sloped surface. Rise is the vertical change over that horizontal distance. A common field method is to hold a level so that 12 inches of it are horizontal and measure the vertical gap from the roof surface down to the end of the level. Measurements can also come from architectural drawings or from accessible framing inside an attic. Do not climb onto a roof where doing so is unsafe. When you report a pitch or rafter length to a supplier, use the rounding calculator to keep the number of decimals consistent with the measurement precision.

Roof Pitch vs. Roof Slope

This calculator follows the common roofing convention of expressing pitch as vertical rise per 12 units of horizontal run. The terms roof pitch and roof slope are commonly used interchangeably in everyday roofing work. Some technical references distinguish slope as rise over run and pitch as rise over the full roof span, but all calculator outputs on this page use rise over run.

Frequently asked questions