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Roof Pitch Converter

Enter angle (°), slope (%), or pitch (rise/12) — get the other representations and the area correction factor instantly.

Input Mode

Result

Pick an input mode and enter a value.

What this tool does

The roof pitch converter instantly converts between three pitch notations — degrees (°), slope percentage (%), and x/12 rise — in either direction. Enter any one value and the other two, the area correction factor (sec θ), and the pitch category (flat / low / medium / steep / extreme slope) are displayed immediately. It resolves the notation mismatches that arise when architects, framers, and roofers each use a different convention on the same project.

Who uses this

  • Drawing conversion: translate a drawing's '26.6°' into the framer's 6/12 or the roofer's 50% in one step
  • Material takeoff: use sec θ to convert projected floor area to actual roof area for shingle or tile quantities
  • On-site communication: resolve notation conflicts between designers (degrees), carpenters (x/12), and waterproofers (percentage)
  • Roofing material selection: confirm pitch category (low-slope vs. steep-slope) to choose the correct material and installation method
  • Light-frame education: understand the relationship between angle, slope ratio, and rise-per-foot

How to use (2 steps)

  1. 1Select the notation you already know: 'Angle (°)' for drawing or inclinometer readings, 'Slope (%)' for Korean construction drawings and civil engineering documents, or 'x/12 Rise' for North American light-frame notation.
  2. 2Enter the value. The other two notations, area correction factor (sec θ), and pitch category appear instantly. Categories: flat (< 10°), low slope (10–30°), medium slope (30–45°), steep slope (45–60°), extreme slope (≥ 60°).

Formula & basis

Angle (°) → slope % and x/12: Slope (%) = tan(θ) × 100 x/12 rise = tan(θ) × 12 Area correction factor (sec θ) = 1 / cos(θ) Slope (%) → angle and x/12: θ = atan(slope / 100) x/12 = (slope / 100) × 12 x/12 rise → angle and slope: θ = atan(rise / 12) Slope (%) = (rise / 12) × 100 Pitch categories (Korean practice / AIK): Flat : θ < 10° Low slope : 10° ≤ θ < 30° Medium slope: 30° ≤ θ < 45° Steep slope : 45° ≤ θ < 60° Extreme : θ ≥ 60° Key reference values: 4/12 ≈ 18.4° ≈ 33.3% (sec 1.054) 5/12 ≈ 22.6° ≈ 41.7% (sec 1.083) 6/12 = 26.6° = 50.0% (sec 1.118) 8/12 ≈ 33.7° ≈ 66.7% (sec 1.202) 12/12 = 45.0° = 100.0% (sec 1.414)

Worked examples

Example 1: Drawing shows '26.6°' — convert to construction notations

θ = 26.6°. Slope = tan(26.6°)×100 = 50.0%. x/12 = tan(26.6°)×12 = 6.0 → 6/12. sec θ = 1/cos(26.6°) = 1.118. Category: low slope. 100 m² projected → 111.8 m² actual roof area.

Example 2: Korean drawing '45%' — convert to degrees and x/12

Slope 45% → θ = atan(0.45) = 24.2°. x/12 = 0.45×12 = 5.4/12. sec θ = 1.098. Category: low slope. Sometimes written as '4.5-sun' in traditional Korean notation.

Example 3: 8/12 steep roof — area correction

8/12 rise → θ = atan(8/12) = 33.7°. Slope = 66.7%. sec θ = 1.202. Category: medium slope. Roofing material requirement is 20.2% greater than the projected area; specialized safety equipment is recommended at this pitch.

Frequently asked questions

How does Korean 'sun (寸)' notation differ from x/12?

Korean 'x-sun' means x units of rise per 10 units of run (ratio x/10). North American x/12 means x inches of rise per 12 inches of run. Example: Korean 5-sun = 50% slope = atan(0.5) = 26.6° = 6.0/12. The 'Slope (%)' input mode in this calculator is equivalent to the x/10 Korean notation.

Why does pitch category matter for roofing materials?

Each pitch range requires different waterproofing: below 10° (flat) needs membrane waterproofing (asphalt, urethane coating); 10–30° (low slope) suits TPO, metal standing seam, or fixed-panel systems; above 30° (medium/steep) drains fast enough for shingles, tiles, or metal panels.

Why is the area correction factor always greater than 1?

At 0° the factor is sec(0°) = 1/cos(0°) = 1 (flat roof = projected area). As the angle increases, cos θ decreases so sec θ grows above 1. A factor of 1.118 at 26.6° means the sloped surface is 11.8% larger than what you see from directly above.

What happens if I enter 0°?

0° is a perfectly flat roof: slope 0%, x/12 = 0, sec θ = 1.000, category 'flat'. In practice even 'flat' roofs need a minimum 1–2% slope for drainage.

Are pitches steeper than 45° used in residential construction?

Not commonly in Korea. Slopes above 45° (steep) appear mainly in European chalet-style or religious buildings. Above 60° (extreme), safe installation requires specialist equipment and rigging — it is rarely seen in standard residential work.

Cautions

  • •This tool covers pitch notation conversion and area correction factor only. Structural load, rafter sizing, and span limits require separate tools.
  • •The x/12 rise input accepts values from 0 to 60 (angles up to 89.99°). Near-vertical values produce very large area correction factors and have no practical meaning in standard construction.
  • •The area correction factor assumes a flat inclined plane. Curved surfaces (domes, barrel vaults) require a different approach.
  • •Pitch categories follow Korean architectural practice and AIK guidelines; classification thresholds may differ by country or application.

Last reviewed: 2026-06-17

Roof Pitch Converter | Workmate