Roof Pitch Calculator

Enter rise and run, an x:12 ratio, degrees, or percent slope. Get every equivalent plus a scaled roof triangle and a copyable geometry receipt.

Private by design: calculations stay in this browser tab. Your measurements are not added to the URL, history, storage, cookies, requests, or analytics.

By Wei Chieh Liao. Roof pitch geometry and rafter line length run in your browser.

Roof pitch formulas

Roof pitch starts with a right triangle. Let rise be its vertical leg and run be its horizontal leg. The slope is rise ÷ run. Multiply slope by 12 to express the result as an x:12 pitch, or by 100 to express it as a percentage.

The angle in degrees is arctan(rise ÷ run). The pitch multiplier is √(1 + slope²), and multiplying that value by the horizontal run gives the straight sloping line from the run's starting point to its end.

Worked example: a 6:12 pitch

For every 12 feet of horizontal run, a 6:12 roof rises 6 feet. Its slope is 6 ÷ 12 = 0.5, so it is a 50% slope. Arctan(0.5) gives an angle of about 26.57°.

The pitch multiplier is √(1 + 0.5²), or about 1.118. For a 12-foot run, the straight right-triangle hypotenuse is about 13.416 feet.

Choose the input mode that matches your measurement

Use Rise & run when both legs were measured from the same right triangle. Use x:12 ratio for common pitch notation, Degrees for an inclinometer reading, or Percent when a plan or specification gives percent slope. Every mode uses the horizontal run to calculate physical rise and line length.

The common-pitch buttons load a ratio and a 12-unit run so you can inspect a familiar example immediately. Feet and meters use the same dimensionless pitch math; keep rise and run in one consistent unit.

Run, span, and rafter length are different

Horizontal run is one side of the triangle. On a symmetrical gable roof, it is commonly half the full building span, but offset ridges, hips, valleys, and other roof forms require their own measurements. The result marked rafter line length is only the geometric hypotenuse for the entered run.

It does not add an eave overhang or subtract for ridge thickness, and it does not lay out birdsmouth seats, plumb cuts, hip or valley rafters, or field tolerances. Use the copied receipt as a geometry check, then apply the construction details from the project documents.

Geometry is not structural design

This calculator does not size rafters or evaluate span tables, loads, species and grade, connections, snow, wind, drainage, roof-covering limits, permits, or code compliance. Those decisions depend on the building, location, materials, and applicable requirements.

Roof work also involves fall hazards. The linked OSHA guidance covers fall protection in residential construction. Do not treat a pitch result or diagram as a safe-work plan.

Input and rounding rules

Numeric fields accept unsigned complete ASCII decimals with up to six fractional digits. Signs, commas, fractions, exponent notation, Unicode digits, leading dots, trailing dots, and unit suffixes are rejected. Rise and run must be greater than 0 and no more than 1,000,000. Ratio rise is limited to 120 per 12, degrees must be below 90, and percent slope is limited to 1,000.

The calculator retains full JavaScript floating-point precision through trigonometry and rounds only for display: degrees and percent to two decimal places, pitch multiplier to four, and lengths or x:12 rise to three. Use unrounded project measurements for final layout.

Frequently asked questions

What angle is a 6:12 roof pitch?

A 6:12 pitch rises 6 units for every 12 units of horizontal run. Its angle is about 26.57°, its slope is 50%, and its pitch multiplier is about 1.118.

How do I calculate roof pitch from rise and run?

Divide vertical rise by horizontal run. Multiply that slope by 12 to write an x:12 pitch, multiply it by 100 for percent slope, or take the arctangent to get degrees.

Is roof run the same as the full building width?

Usually no. For a symmetrical gable roof, run is the horizontal distance from one wall plate to the ridge, commonly half the full span. Measure the actual roof geometry for offset ridges and other roof shapes.

How is rafter line length calculated?

The calculator treats rise and run as the legs of a right triangle. The displayed line length is √(run² + rise²), before overhang, ridge reduction, birdsmouth details, or field cuts.

Can this calculator size rafters or tell me which roof material to use?

No. It calculates geometry only. It does not evaluate loads, spans, lumber grade, fasteners, snow or wind conditions, drainage requirements, roofing-product limits, permits, or building-code compliance.