6:12 GEOMETRY CHECK

6:12 Pitch Roof Calculator

A 6:12 roof rises 6 units for every 12 horizontal units of run. Enter the horizontal run to check the matching rise, geometric diagonal, 26.565° angle, and 1.118 slope factor.

Calculate a matching 6:12 triangle

RESULT

Matching dimensions

Rise6run ÷ 2
Geometric diagonal13.416same length unit
Angle26.565°from horizontal
Slope factor1.118diagonal ÷ run
Original right triangle showing a 6-unit rise, 12-unit horizontal run, 26.565-degree angle, and 13.416-unit diagonal.
At 6:12, the rise is half the horizontal run; the diagonal is a separate geometric result.

Start with the ratio, not the angle

A 6:12 label reduces to 1:2: the vertical rise is half the horizontal run. For a 20-unit run, the matching rise is 20 ÷ 2 = 10 units. Check back with (10 ÷ 20) × 12 = 6.

The angle comes from atan(rise ÷ run). For 6:12, that is atan(6 ÷ 12) ≈ 26.565°. Right-triangle trigonometry defines tangent from the opposite and adjacent sides.1

Original three-step diagram showing a 20-unit horizontal run, 10-unit rise, and reverse calculation that confirms a 6 to 12 pitch.
Preserve the measured pair so someone else can repeat the calculation.

Check the geometric diagonal separately

The diagonal is √(rise² + run²). With 6 and 12, that is √(6² + 12²) = √180 ≈ 13.416. The Pythagorean theorem relates the legs of a right triangle to its hypotenuse.2 Dividing that diagonal by the run gives 13.416 ÷ 12 ≈ 1.118, the geometric slope factor.

Is a 6:12 roof a 45-degree roof?

No. A 6:12 ratio is 26.565° because its rise/run ratio is one-half. A 45° roof has equal rise and run, which is 12:12. Keep the ratio and the angle together when comparing documents that use different formats.

What this calculator does not decide

It converts a stated roof triangle. It does not set rafter cuts, ridge treatment, material suitability, drainage performance, safety precautions, local requirements, or a material order. Use the recorded geometry as one input to those separate project checks.

Sources

  1. OpenStax, “Right Triangle Trigonometry” — explains tangent using opposite and adjacent sides.
  2. OpenStax, “Right Triangle Trigonometry” — presents the Pythagorean theorem for a right triangle.

The diagrams and calculations are original geometry explanations, not construction drawings or project approvals.