Roof Pitch Calculator
Roof slope gets written three different ways on site — as a rise-in-12 ratio, as a degree angle, or as a percent grade — and framers, engineers and civil drawings each tend to favour a different one. Type a number into any field below and the other two update immediately.
That slope is 20.8:12, 60.0°, and 173.2% grade — three names for the same line.
How Rise-in-12 Notation Works
Rise-in-12 is a carpenter's shorthand, not a separate unit of measurement. It states how many inches a rafter climbs for every 12 inches it runs horizontally — nothing more than the tangent of the slope angle, scaled so the run is always 12. The number 12 is not arbitrary: a standard framing square has a 12-inch body, so a carpenter lays the square against the rafter, reads the rise off the tongue at the 12-inch mark, and has the pitch with no arithmetic and no protractor.
That convention is why pitch is almost always spoken as "seven-twelve" or "seven in twelve" rather than as an angle. A 7:12 roof rises 7 inches for every 12 inches of run: 7 ÷ 12 = 0.583, and atan(0.583) = 30.3°. Steeper roofs carry a bigger first number; a gambrel lower rafter at 60° reads 20.8:12 on the same square, because tan(60°) × 12 = 20.78.
Percent grade follows the identical logic at a different scale: instead of dividing rise by a 12-inch run, it divides rise by a 100-unit run and reports the result as a percentage. A 12:12 roof (45°) is exactly 100% grade, because 12 ÷ 12 = 1.00. All three notations — ratio, degrees, percent — describe the same physical slope; converting between them is just changing which run length the rise gets compared against, or applying the tangent function directly.
Reference
Pitch Conversion Table, 2:12 to 24:12
Every row is solved with the same tangent relationship as the converter above, from a nearly flat 2:12 roof through a very steep 24:12. Gambrel lower pitches typically fall between 16:12 and 24:12 (55°–67.5°); upper pitches typically fall between 3:12 and 7:12 (14°–30°).
| Rise-in-12 | Degrees | Percent grade |
|---|---|---|
| 2:12 | 9.5° | 16.7% |
| 4:12 | 18.4° | 33.3% |
| 6:12 | 26.6° | 50.0% |
| 8:12 | 33.7° | 66.7% |
| 10:12 | 39.8° | 83.3% |
| 12:12 | 45.0° | 100.0% |
| 14:12 | 49.4° | 116.7% |
| 16:12 | 53.1° | 133.3% |
| 18:12 | 56.3° | 150.0% |
| 20:12 | 59.0° | 166.7% |
| 22:12 | 61.4° | 183.3% |
| 24:12 | 63.4° | 200.0% |
Notice the relationship is not linear: doubling the rise-in-12 ratio from 12:12 to 24:12 only takes the angle from 45.0° to 63.4°, not to 90°. Percent grade, by contrast, scales exactly with the ratio — 24:12 is exactly double 12:12's percent grade, 200% against 100% — because percent grade is a direct multiple of the rise/run ratio while degrees are not.
The Conversion Formulas
All three conversions reduce to one value — the tangent of the slope angle — read at a different scale, or inverted to solve for the angle itself.
- θ
- Slope angle, measured in degrees from horizontal.
- X
- Rise-in-12 ratio — the rise, in inches, over a 12-inch run.
- P
- Percent grade — the rise over a 100-unit run, as a percentage.
Ratio to degrees, and back
θ = atan(X ÷ 12)
X = tan(θ) × 12
Example: X = 20.8 → θ = atan(20.8 ÷ 12) = 60.0°. Reversed: θ = 60.0° → tan(60.0°) × 12 = 20.8.
Percent grade to degrees, and back
θ = atan(P ÷ 100)
P = tan(θ) × 100
Example: θ = 15.0° → tan(15.0°) × 100 = 26.8%. Reversed: P = 26.8% → atan(26.8 ÷ 100) = 15.0°.
Ratio to percent, directly
P = (X ÷ 12) × 100
Skips degrees entirely. Example: X = 12.0 → (12.0 ÷ 12) × 100 = 100%.
Every gambrel roof carries two independent slopes, so every one of these formulas gets applied twice per roof — once for the lower pitch, once for the upper pitch — never combined into a single average.
Why Gambrel Roofs Run Two Different Pitches
A gable roof has one slope per side and one pitch to convert. A gambrel breaks each side at a horizontal line called the knuckle, giving it a steep lower section and a shallow upper section — two separate slopes that each get their own rise-in-12, degree and percent-grade figures. This calculator treats them as two completely independent conversions; nothing here assumes the two pitches are related to each other.
On the traditional barn version of the roof, the two pitches are related, but only because of how the shape is drawn, not because of anything in the pitch math itself. The half-circle method lays the knuckle and ridge on a semicircle struck from the centre of the span, which forces the upper pitch to sit exactly 45° below the lower one. Under that method, a 60° lower pitch (20.8:12) always pairs with a 15° upper pitch (3.2:12), and a 67.5° lower pitch — the traditional barn figure — pairs with a 22.5° upper pitch, converting to 29.0:12 over 5.0:12.
Under the alternative two-pitch method, described on the gambrel roof calculator home page, the upper pitch is chosen independently of the lower one — a 60° lower slope can pair with anything from a very shallow 3° up to just under the lower angle itself. Either way, converting each pitch to rise-in-12, degrees or percent grade works exactly as shown above: solve the lower pitch, then solve the upper pitch, treating them as two separate inputs to the same formula.
Worked Example: Converting a 60° Lower Pitch
Sixty degrees is the lower-pitch figure used throughout this site's worked examples, paired with a 15° upper pitch under the half-circle construction. Here is the conversion for both, step by step.
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Read the lower pitch off the framing square
Hold a framing square against the lower rafter with the 12-inch mark on the body against the rafter edge. Read the rise on the tongue where it crosses the edge — that number, over 12, is the rise-in-12 figure.
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Convert it to degrees
Type the rise-in-12 figure into the ratio field above. A reading of 20.8 on the tongue converts to 60.0°, which is the lower pitch this site uses as its working example throughout.
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Convert the upper pitch the same way
The upper pitch is a separate slope with its own rise-in-12 reading. A 3.2 reading converts to 15.0° — the shallow slope from the knuckle to the ridge.
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Check the percentage grade if the job calls for it
Site and civil work often specifies slope as a percentage rather than degrees or a ratio. The same 60.0° lower pitch is 173.2% grade; the 15.0° upper pitch is 26.8%.
With both pitches converted, the next step is usually rafter length — the rafter length calculator takes the same θ and φ figures and turns them into cut lengths for a given span, and the framing guide covers the knuckle joint where the two rafters meet.
Roof Pitch Questions
What does "8 in 12" mean on a roof?
An "8 in 12" roof rises 8 inches vertically for every 12 inches of horizontal run. That is a ratio, not a fraction of degrees — dividing 8 by 12 and taking the arctangent gives the actual slope angle, 33.7°. Rise-in-12 became standard because a framing square already has 12-inch markings on its body, so a carpenter reads the pitch directly off the tool with no separate protractor.
How do I convert roof pitch to degrees?
Divide the rise by 12, then take the arctangent of that number. For a 6:12 pitch, 6 ÷ 12 = 0.5, and atan(0.5) = 26.6°. The converter above does this instantly for any ratio, and the table further down lists it pre-solved from 2:12 through 24:12.
What is the difference between roof pitch and percent slope?
Pitch (rise-in-12) and percent slope are the same ratio at different scales. Pitch scales rise to a 12-unit run; percent slope scales it to a 100-unit run. A 12:12 pitch (45°) is 100% grade because 12 ÷ 12 = 1.00 = 100%. A 6:12 pitch is 50% grade. Civil and drainage work almost always uses percent; residential and barn framing almost always uses rise-in-12.
Why do gambrel roofs have two different pitches?
A gambrel breaks each roof side into a steep lower section and a shallow upper section, meeting at a horizontal line called the knuckle. The steep lower pitch — commonly 55° to 70° — keeps the walls close to vertical and buys standing headroom near the eaves; the shallow upper pitch — commonly 15° to 30° — closes off the roof without wasting height. Each pitch converts to rise-in-12, degrees or percent independently using the exact same formulas on this page; nothing about having two pitches changes the conversion math, only which angle you are converting. See how the two pitches relate to each other when they are built from a single lower-pitch input.
What rise-in-12 is a 60 degree roof?
A 60° slope is 20.8:12 — tan(60°) × 12 = 20.78, rounded to 20.8. As a percentage grade that same slope is 173.2%. Sixty degrees is the lower pitch this site uses as its default worked example, paired with a 15° upper pitch under the half-circle construction described on the angle calculator and the home page.