How to Calculate Roof Pitch from Rise and Run

1. Understanding the Core Concept: What is Roof Pitch?

In North American residential framing, roof pitch quantifies how steeply a roof slope rises vertically for every 12 inches of horizontal run. It is conventionally recorded in the standard ratio format X:12 (or X/12), where:

X (Rise): The vertical distance gained in inches.
12 (Run): A fixed standard benchmark of 12 inches (one linear foot) of horizontal distance.

For example, a 5:12 pitch roof ascends 5 vertical inches for every 12 horizontal inches traversed.

2. The Universal Mathematical Formula

Because rise and run form the perpendicular legs of a right triangle, finding the standard 12-inch pitch ratio is a straightforward proportion:

Pitch (X:12) = (Total Vertical Rise ÷ Total Horizontal Run) × 12

Note: Rise and run must be measured in the identical unit of measurement (inches or feet).

If your measurements are in decimal feet, either convert both numbers to inches first (feet × 12) or execute the division directly, since dividing feet by feet cancels out the dimension units.

3. Step-by-Step Calculation Procedure

Measure Total Horizontal Run: For a standard gable roof with a central ridge board, horizontal run equals half the total building span (excluding eave overhangs). If a shed is 24 feet wide, the run is 12 feet (144 inches).
Measure Total Vertical Rise: Measure from the top horizontal wall framing plate vertically to the apex intersection of the rafter centerlines at the ridge.
Convert to Common Units: If your rise is 6 feet and run is 12 feet, convert both to inches (72 inches and 144 inches) or maintain both in feet.
Divide Rise by Run: 72 ÷ 144 = 0.50.
Multiply by 12: 0.50 × 12 = 6. Your roof pitch is exactly 6:12.

4. Worked Real-World Examples

Example A: Residential Ranch Addition

A builder measures a vertical rise of 35 inches across a horizontal run of 105 inches:

Rise / Run = 35 / 105 = 0.3333

Pitch = 0.3333 × 12 = 4.0

→ Pitch: 4:12 (18.43°)

Example B: Steep Detached Garage

A garage gable rises 7 feet 6 inches (90 inches) over a horizontal run of 11 feet 3 inches (135 inches):

Rise / Run = 90 / 135 = 0.6667

Pitch = 0.6667 × 12 = 8.0

→ Pitch: 8:12 (33.69°)

5. Common Calculation Mistakes to Avoid

Confusing Span with Run: The total building span is the distance between outer exterior walls. On a symmetrical gable roof, horizontal run is only half of the span (Run = Span ÷ 2).
Including Eave Overhangs in Rise/Run: The framing triangle is calculated between the wall plate line and ridge apex. Do not include exterior soffit tails in the primary run calculation unless calculating overhang tail length specifically.
Mixing Units: Never divide rise in inches by run in feet without converting first. Dividing 36 inches by 9 feet gives 4, but 36 inches is 3 feet, so (3/9) × 12 = 4:12.