Roof Pitch Calculator

You’re standing in the driveway with a tape measure because the roofing supplier asked a simple question: “What pitch is it?” You’re replacing shingles, ordering underlayment, or framing a new gable, and the answer affects everything from material quantities to safety planning. A roof pitch calculator helps translate what you can measure (or what you already know, like the angle) into the numbers builders actually use: roof pitch (like 6/12), angle in degrees, rise, run, rafter length, and ridge height.

What Is a Roof Pitch Calculator?

A pitch calculator typically supports multiple ways to start: - You know the angle (degrees) and want pitch. - You measured rise and run directly (in the same units) and want pitch/angle. - You know the pitch and the building’s roof span and want rafter length and ridge height.

Context fact: roof steepness changes how you work and what you install. OSHA treats roofs with slopes greater than 4:12 as “steep roofs” for fall-protection planning (see OSHA 29 CFR 1926 Subpart M, “Fall Protection,” a primary reference for residential roofing safety). That’s not just paperwork—steeper roofs often require different staging, harness use, and material handling.

The Formula (Pitch, Angle, Slope %, Rafter Length)

Key relationships, written the way builders use them:

- Rise (inches per 12 inches) = 12 × (rise/run) - Angle (degrees) = arctan(rise_in / 12) × (180/π) - Slope % = (rise_in / 12) × 100 - Run (ft) = span / 2 - Ridge height (ft) = run × (rise_in / 12) - Rafter length (ft) = √(run² + ridge_height²)

If you start from angle instead of rise/run: - Rise_in (inches per 12) = tan(angle_deg × π/180) × 12

If you start from measured rise and run (any consistent units): - Rise_in (inches per 12) = (rise_val / run_val) × 12

Plain-English walkthrough: 1. Convert whatever you know (angle, or rise/run ratio) into “inches of rise per 12 inches of run” because that’s the standard pitch label. 2. Convert pitch to an angle using arctangent (or the other way using tangent). 3. Use half the span as the run for one side of a gable roof. 4. Multiply run by the rise/run ratio to get ridge height. 5. Use the Pythagorean theorem to get rafter length.

Industry note: framing lumber is typically laid out in feet and inches, and common rafter layout uses “rise per foot of run.” That’s why 12 inches is the reference run.

Step-by-Step Worked Examples (Real Numbers)

1) Convert angle to rise per 12: - Rise_in = tan(30°) × 12 - tan(30°) ≈ 0.57735 - Rise_in ≈ 0.57735 × 12 = 6.928 in

Pitch label ≈ 6.93/12 (often rounded to the nearest 1/4" in practice: 7/12 is a common field label).

2) Slope percent: - Slope % = (6.928 / 12) × 100 ≈ 57.7%

3) Run is half the span: - Run = 24/2 = 12 ft

4) Ridge height: - Ridge height = 12 × (6.928/12) = 6.928 ft

5) Rafter length: - Rafter = √(12² + 6.928²) - = √(144 + 48.00) ≈ √192.00 ≈ 13.86 ft

So a 30° roof over a 24 ft span is about 6.93/12, ~57.7% slope, ~6.93 ft ridge height, and ~13.86 ft rafter length (before overhangs and ridge details).

### Example 2: You measured rise and run directly (rise 18", run 36"), span 20 ft Given: rise = 18 in, run = 36 in, span = 20 ft 1) Convert measured rise/run to rise per 12: - Rise_in = (18/36) × 12 = 0.5 × 12 = 6 in Pitch = 6/12

2) Angle: - Angle = arctan(6/12) × (180/π) - = arctan(0.5) × 57.2958 - arctan(0.5) ≈ 0.46365 rad - Angle ≈ 0.46365 × 57.2958 = 26.57°

3) Run: - Run = 20/2 = 10 ft

4) Ridge height: - Ridge height = 10 × (6/12) = 5 ft

5) Rafter length: - Rafter = √(10² + 5²) = √125 = 11.18 ft

This is a classic 6/12 pitch roof: about 26.6°, 50% slope, 5 ft ridge height over a 20 ft span, and ~11.18 ft rafters (again, not counting overhangs).

### Example 3: You know pitch is 4/12 and span is 30 ft (common “walkable” slope) Given: Rise_in = 4 in per 12, span = 30 ft 1) Angle: - Angle = arctan(4/12) × 57.2958 - arctan(0.3333) ≈ 0.32175 rad - Angle ≈ 18.43°

2) Slope percent: - Slope % = (4/12) × 100 = 33.3%

3) Run: - Run = 30/2 = 15 ft

4) Ridge height: - Ridge height = 15 × (4/12) = 5 ft

5) Rafter length: - Rafter = √(15² + 5²) = √(225 + 25) = √250 = 15.81 ft

Practical context: many crews consider around 4/12 to be near the upper end of “comfortable to walk” without special footing, but safety requirements depend on site conditions. OSHA’s fall protection rules still apply based on height and exposure, not just pitch.

Common Mistakes to Avoid (and a Pro Tip)

Common Mistake #2: Using full span as run. For a symmetrical gable roof, the run is half the span. Using the full span doubles ridge height and inflates rafter length.

Common Mistake #3: Confusing pitch (X/12) with slope percent. A 6/12 roof is 50% slope, not 6%. Percent slope is (rise/run)×100, and pitch is rise per 12 inches.

Common Mistake #4: Forgetting overhangs and ridge/seat cuts. The calculated rafter length is the “theoretical” length from wall line to ridge line. Real cut length changes with birdsmouth seat cut, ridge board thickness, and eave overhang.

Pro Tip: If ordering materials, measure or confirm the actual roof area separately. Pitch helps convert horizontal “footprint” area into roof surface area, but valleys, dormers, and overhangs can add significant square footage. Also note common roof sheathing is 4×8 ft (32 sq ft) panels—knowing pitch helps anticipate handling difficulty and waste on steeper roofs.

Code/source note: OSHA’s residential fall protection requirements are detailed in 29 CFR 1926 Subpart M (U.S. Department of Labor, .gov). Always follow local building codes for structural sizing and fastening; pitch alone doesn’t size rafters.

When to Use a Roof Pitch Calculator vs. Doing It Manually

Manual calculation is fine when you’re already comfortable with right-triangle math and only need one value (like angle from a known pitch). A calculator is most helpful when switching between input types (angle vs rise/run), rounding to typical field-friendly increments, and producing all related outputs consistently in one pass.

rise_in (in/12) = tan(angle_deg × π/180) × 12

Roof pitch is just a way to express the steepness of a roof as “rise per 12 inches of run.” The calculator supports three equivalent ways to describe the same slope: you can enter the pitch directly as rise over run (like 6/12), you can enter the roof angle in degrees, or you can enter a rise and run pair that isn’t necessarily based on 12 inches. Internally, everything is converted to a standardized pitch rise_in, meaning “inches of rise for every 12 inches of horizontal run.”

If you choose Angle, the reasoning comes from right-triangle trigonometry. For a roof cross-section, the horizontal run and vertical rise form the legs of a right triangle, and the roof surface is the hypotenuse. By definition, tan(angle) = rise/run. If we define run as 12 inches (one “foot” of run in pitch notation), then rise_in = tan(angle) × 12. That’s why the calculator computes rise_in = tan(angle_deg × π/180) × 12, converting degrees to radians because standard math functions use radians.

If you choose Rise/Run, the same tan relationship applies but you provide the ratio directly: rise/run = rise_val/run_val. To convert that ratio to “per 12 inches,” multiply by 12: rise_in = (rise_val/run_val) × 12. If you already entered a conventional pitch like 6 over 12, then rise_in = (6/12)×12 = 6, which matches the familiar label 6/12.

Once rise_in is known, the calculator derives other outputs. The angle is reconstructed as angle_deg = atan(rise_in/12) × 180/π. The slope percent is slope_pct = (rise_in/12) × 100, because percent grade is rise divided by run, times 100. For rafter length and ridge height, the calculator uses the roof span (the full building width from eave to eave). The horizontal run for one side is run = span/2. Ridge height is the vertical rise over that run: ridge_height_ft = run × (rise_in/12). The rafter length is the hypotenuse of the right triangle: rafter_ft = √(run² + ridge_height_ft²).

Example 1 (Angle input). Suppose angle_deg = 30° and roof span = 24 ft. First compute pitch rise per 12: rise_in = tan(30°)×12 = 0.577350…×12 = 6.9282 in. The pitch label rounds to the nearest 1/4 inch: 6.9282 rounds to 7.00, so pitch ≈ 7/12. Now compute slope percent: slope_pct = (6.9282/12)×100 = 57.735%. Run is half the span: run = 24/2 = 12 ft. Ridge height: ridge_height_ft = 12×(6.9282/12) = 6.9282 ft. Rafter length: rafter_ft = √(12² + 6.9282²) = √(144 + 48.000…) = √192.000… = 13.8564 ft.

Example 2 (Rise/Run input not based on 12). Suppose rise_val = 300 mm, run_val = 1000 mm, and roof span = 8 m. First get the ratio: rise/run = 300/1000 = 0.3. Convert to rise per 12 inches: rise_in = 0.3×12 = 3.6 in, so pitch ≈ 3.5/12 (rounded to nearest 1/4). Angle: angle_deg = atan(3.6/12)×180/π = atan(0.3)×57.2958 = 16.699° (about 16.70°). Slope percent: slope_pct = 0.3×100 = 30.0%. Now use span in feet or meters consistently. Using meters: run = span/2 = 8/2 = 4 m. Ridge height = run×(rise/run) = 4×0.3 = 1.2 m. Rafter length = √(4² + 1.2²) = √(16 + 1.44) = √17.44 = 4.176 m. If you want feet, use 1 m = 3.28084 ft: run = 4 m = 13.123 ft, ridge height = 1.2 m = 3.937 ft, rafter = 4.176 m = 13.701 ft.

For unit conversions, the key is that pitch is traditionally “inches per 12 inches,” but it’s dimensionless as a ratio. If you work in metric, you can keep rise and run in the same metric units (mm, cm, or m), compute the ratio rise/run, and everything (angle, percent slope, ridge height, rafter length) follows without ever converting to inches. Only the pitch label in “x/12” is inherently imperial; it’s just another way of expressing the same ratio.

Edge cases and limitations matter. Run_val cannot be zero, and span should be positive; otherwise the geometry breaks. Extremely steep angles near 90° make tan(angle) blow up, producing unrealistic rise_in. The rafter length here is the “theoretical” length from the outside wall line to the ridge along the roof plane; it does not include overhangs, ridge board thickness, heel cuts, or allowances for birdsmouth and fascia details. Variations include using actual run (from plate to ridge) instead of span/2 when the ridge is offset, and using different rises on each side for asymmetrical roofs; in those cases you compute each side’s run and pitch separately with the same right-triangle method.

• University of Kentucky (UKnowledge) — Roof Framing / Rafter Layout (Rise-Run and Pitch Concepts)
• American Wood Council (AWC) — National Design Specification (NDS) for Wood Construction (Roof/Rafter Design Context)
• International Code Council (ICC) — International Residential Code (IRC) (Roof Construction Requirements; Pitch-Related Provisions in Code)
• ASTM International — Standards and Publications (Construction Standards Referenced in Roofing/Building Practice)
• International Code Council