Roof Pitch Calculator

Roof pitch defines the steepness of a roof, usually expressed as the vertical rise over a 12-inch horizontal run (e.g., 4/12). The underlying mathematical relationships combine basic geometry and trigonometric functions. Using the fundamental Pythagorean theorem, the relationship between the horizontal run, vertical rise, and sloping rafter length is expressed as rafter^2 = rise^2 + run^2. Furthermore, the pitch ratio is determined by dividing the rise by the run, which is also equal to the tangent of the roof angle: pitch = rise / run = tan(angle). Multiplying this decimal pitch by 12 yields the standard pitch number used in North American construction.

Imagine you are planning a shed roof with a horizontal run of 12 feet (144 inches) and a vertical rise of 5 feet (60 inches). To find the pitch, divide the rise by the run: 60 / 144 = 0.4167. Multiply this by 12 to get the standard pitch expression: 0.4167 * 12 = 5, giving you a 5/12 roof pitch. To find the exact rafter length, apply the Pythagorean theorem: rafter^2 = 60^2 + 144^2 = 3600 + 20736 = 24336. Taking the square root gives a rafter length of 156 inches, or 13 feet. Finally, the angle can be calculated using the inverse tangent of the pitch: arctan(5/12), which equals approximately 22.6 degrees.

Always measure the horizontal run using a precise level to ensure your baseline is perfectly horizontal before calculating angles. When working on existing structures, place a 12-inch level flat against the roof surface, hold a tape measure vertically from the end of the level down to the roof deck, and read the rise directly in inches. Keep local climate in mind: regions with heavy snowfall require steeper pitches to prevent structural overload, whereas arid regions can utilize lower slopes effectively.