Roof Pitch

Converting Between Roof Pitch, Angle, and Slope

Roof pitch is the ratio of a roof’s vertical rise to its horizontal run, expressed as an X-in-12 notation, an angle in degrees, or a slope percentage. Enter a measured rise and run — or an angle read straight off a level or digital angle finder — and this calculator converts it into all three notations at once, so you can hand a contractor whichever one they ask for.

This is the reverse of the site’s Roofing Calculator — that calculator takes pitch as a known INPUT to work out how much roofing material a slope needs; this one solves for the pitch itself, before you know it.

The Formula

Every notation is the same underlying rise/run ratio, just scaled or converted differently:

$$\vC{\text{Ratio}} = \frac{\vA{\text{Rise}}}{\vB{\text{Run}}}$$ $$\text{Pitch (X-in-12)} = \vC{\text{Ratio}} \times 12$$ $$\vE{\text{Angle}} = \arctan(\vC{\text{Ratio}})$$ $$\text{Slope \%} = \vC{\text{Ratio}} \times 100$$

When you start from a measured angle instead, the same relationship runs backwards: $\vC{\text{Ratio}} = \tan(\vE{\text{Angle}})$, and every other figure follows from there.

Worked Example

A roof measuring 6 inches of rise over 12 inches of run:

1. Ratio: $\dfrac{\vA{6}}{\vB{12}} = \vC{0.5}$.
2. Pitch: $\vC{0.5} \times 12 = 6\text{-in-12}$.
3. Angle: $\arctan(\vC{0.5}) \approx \vE{26.57}°$.
4. Slope: $\vC{0.5} \times 100 = 50\%$.

And for a 45° angle read off a level:

1. Ratio: $\tan(\vE{45°}) = \vC{1}$.
2. Pitch: $\vC{1} \times 12 = 12\text{-in-12}$.
3. Slope: $\vC{1} \times 100 = 100\%$.

Key Factors to Consider

• A roof’s pitch determines which roofing materials are actually suitable for it. Very low-slope roofs generally require membrane or built-up roofing rather than standard asphalt shingles, since shingles rely on a steep enough slope to shed water effectively rather than letting it pool — checking a material manufacturer’s own minimum-slope requirement against a measured pitch is worth doing before choosing a roofing material.
• Steeper roofs shed rain, snow, and debris more effectively, but come with real construction and safety tradeoffs. A higher pitch generally drains water and snow faster, but is also more difficult and often more expensive to work on safely, and typically uses more roofing material for the same footprint than a lower-pitch roof would.
• X-in-12 notation is a U.S. roofing-industry convention specifically because 12 inches is a standard framing reference length, not an arbitrary choice. A “6-in-12” pitch means the roof rises 6 inches for every 12 inches (1 foot) of horizontal run — this convention is distinct from, though mathematically related to, the angle-in-degrees and slope-percentage notations this calculator also provides.
• Measuring rise and run accurately matters more than which notation you ultimately convert to. Since every notation this calculator produces derives from the same underlying rise/run ratio, a small measurement error in either rise or run propagates identically into the pitch, angle, and slope percentage results alike.

Common Mistakes

• Confusing which number is the rise and which is the run. In “6-in-12,” the 6 is always the rise and the 12 is always the run — reversing them describes a completely different, much steeper or shallower roof.
• Measuring rise and run along the roof’s sloped surface instead of true horizontal and vertical distances. Run must be measured horizontally and rise vertically — measuring along the angled roof surface itself produces a distorted ratio.
• Assuming pitch and angle scale together linearly. Because the relationship involves a tangent function, doubling the pitch (say, 6-in-12 to 12-in-12) does not double the angle in degrees — the angle grows faster at first and then more slowly as pitch increases.

Useful to Know

• Already know your roof’s pitch and need to estimate materials instead? Roofing Calculator calculates the sloped surface area and shingle count from a footprint and pitch.
• Sizing siding for the same building? Siding Calculator estimates the material needed to cover exterior wall area.
• Planning gutters to match your roof’s drainage needs? Gutter Size & Length Calculator sizes gutters and downspouts from roof area and rainfall intensity.