Roof Pitch Calculator

What is roof pitch?

Roof pitch describes how quickly a roof rises as it moves horizontally. Builders, roofers, designers and manufacturers express the same slope in several forms: rise over run, an x:12 pitch, an angle in degrees, a decimal ratio or a percent slope.

The geometry is one right triangle. The vertical leg is the rise, the horizontal leg is the run, and the sloping leg is the roof or rafter line.

What does a 6:12 roof pitch mean?

A 6:12 roof rises 6 units for every 12 units of horizontal run. The units cancel as long as both rise and run use the same unit.

So 6:12, a 0.5 rise/run ratio, a 50% slope and an angle of about 26.6° all describe the same geometric steepness.

Roof pitch formula from rise and run

If you measured any rise R over any horizontal run H:

The standardized pitch is then x:12. For a rise of 3 ft over a horizontal run of 8 ft:

The equivalent roof pitch is 4.5:12.

Roof pitch angle formula

The roof angle is measured from horizontal. Use the inverse tangent of rise divided by run:

For a 4:12 roof:

Angle and x:12 pitch are simply different ways to report the same right-triangle slope.

Convert degrees to roof pitch

If the angle θ is already known:

A 30° roof therefore has a rise per 12 of about 6.928.

Convert percent slope to roof pitch

Percent slope is rise divided by run multiplied by 100:

Reverse the relationship by dividing the percentage by 100, then multiply by 12:

A 25% slope equals 3:12. A 100% slope equals 12:12, which is a 45° angle.

Pitch factor or roof slope multiplier

The pitch factor compares the sloping line to its horizontal projection:

For a 6:12 roof the slope ratio is 0.5, so:

A sloping roof line is therefore about 1.118 times its horizontal run at this pitch.

How to calculate straight rafter line length

Rise, run and the straight rafter line form a right triangle:

Because pitch factor already represents hypotenuse divided by run, the same calculation can be written:

This is geometric line length only. Actual framing member length can require additional allowances and layout details.

Run to ridge versus full building span

A common error is to use the full building width as the run of one roof side. On a simple symmetrical gable roof, the horizontal run from outside wall line toward the ridge is usually one-half of the relevant span:

That relationship does not automatically apply to shed roofs, unequal gables, offset ridges, hips or more complex geometry. Use the actual horizontal run represented by the roof plane you are calculating.

Optional overhang calculation

An eave overhang extends the roof horizontally beyond the wall line. For a roof plane that continues at the same pitch, add the horizontal overhang to the run before multiplying by the pitch factor:

The calculator treats entered overhang as a horizontal projection. If your measurement is already taken along the slope, do not enter it as a horizontal overhang.

Rafter length is not the same as cut length

The geometric slope line is a useful reference, but a carpenter may need to account for ridge thickness, birdsmouth geometry, tail details, fascia conditions, plumb cuts, seat cuts, bearing and stock selection.

Rise and run must use compatible units

For the slope ratio, rise and run must be expressed in the same unit before division. Six inches over twelve inches gives the same ratio as 0.5 ft over 1 ft.

That unit independence is why x:12 pitch is convenient: it normalizes the run to 12 units.

US customary and metric roof pitch

The x:12 notation is strongly associated with North American construction, but the underlying ratio is unitless and can be calculated from metric measurements too. Metric users may more commonly describe roof slope by degrees, a ratio or percent.

This calculator allows either US customary or metric project dimensions while still providing x:12 as a convenient converted reference.

Common roof pitch reference values

Roof pitch and roof area

For a simple roof plane with a horizontal projected area, the pitch factor converts projected area to sloped area:

This works directly only when the projected area corresponds to the same uniform roof slope. Complex roofs should be divided into individual planes, with hips, valleys, dormers, waste and product coverage handled separately.

If your goal is material quantity rather than slope conversion, use a dedicated roofing material takeoff based on the actual roof geometry.

Roof pitch and roofing materials

Roofing products have minimum-slope and installation requirements. Those requirements vary by material, product, system, jurisdiction and sometimes by underlayment or seam configuration. A mathematically valid pitch does not mean every roofing material is suitable for it.

Check the current product installation instructions and applicable local requirements for the roof you are working on. This calculator intentionally does not issue a universal “approved material” result.

Low-slope versus steep-slope terminology

Terms such as low slope and steep slope are used in roofing, but their practical meaning can depend on the standard, product and context. Do not use a generic internet category as a substitute for a manufacturer's stated minimum slope or local code provision.

The calculator therefore reports numerical geometry—pitch, degrees and percent—without turning those values into a universal compliance category.

Roof pitch and drainage

Slope affects how quickly water moves across a roof surface, but drainage performance is not determined by pitch alone. Roof geometry, drainage paths, membrane or covering type, detailing, debris, snow, gutters and local climate can all matter.

A steeper mathematical slope should not be used as a substitute for proper drainage design or product-specific installation requirements.

Roof pitch and structural design

Pitch influences geometry, member lengths and roof height, but it does not by itself determine structural capacity. Loads, spans, member species or section, connections, bracing, snow, wind and other factors can control design.

This calculator does not size rafters, trusses, beams, fasteners or connections.

Roof pitch and safe access

Roof work involves fall hazards at many slopes. A pitch calculator cannot decide that a roof is “safe to walk.” Surface material, moisture, footwear, edge conditions, fall protection, work task and applicable safety rules all matter.

How to measure roof pitch from an attic or rafter

When the framing is accessible, establish a truly horizontal run with a level, measure the vertical rise over that run, and keep both measurements in the same units. A 12-inch horizontal run is convenient because the measured rise directly becomes the familiar x:12 pitch.

Measurements taken on warped framing, finishes or uneven surfaces can introduce error. Use reliable reference lines and repeat the measurement when accuracy matters.

How to measure pitch without climbing onto the roof

Depending on the building, pitch may be measurable from an accessible attic, gable end, plans or framing rather than from the exterior roof surface. Digital angle tools can also provide an angle that this calculator converts to x:12 pitch.

The safest valid measurement method depends on the site. Do not create a fall exposure merely to obtain a number that can be measured from a safer location.

Worked example: 8 m wide symmetrical gable

Suppose a simple symmetrical gable has an 8 m span and a 30° roof angle. The horizontal run for one side is 4 m.

This is geometric roof-plane information, not a final rafter cut list.

Worked example: convert 7:12 pitch

For 7:12:

Common roof-pitch mistakes

• Using sloped distance as run. Run is horizontal.
• Using full gable span for one side. A symmetrical gable commonly uses half-span as the one-side run.
• Mixing units. Convert rise and run to compatible units before dividing.
• Confusing angle and percent slope. A 45° roof is 100% slope, not 45%.
• Assuming x:12 and degrees use the same number. 6:12 is about 26.6°, not 6°.
• Adding an along-slope overhang as if it were horizontal. Know how the overhang was measured.
• Treating geometric rafter length as final cut length. Framing details add other considerations.
• Assuming a pitch automatically approves a roofing material. Check product and local requirements.
• Assuming a numerical pitch tells you whether roof access is safe. It does not.

How to verify a roof pitch calculation

Use at least two equivalent forms. For example, a 6:12 pitch has ratio 0.5. Multiplying 0.5 by 100 gives 50%, while atan(0.5) gives about 26.565°. The pitch factor √1.25 is about 1.118.

If those conversions do not agree, check the inputs and whether the run was measured horizontally.

Frequently asked questions

Final note: roof pitch is a geometric relationship, so the most reliable workflow is to establish a true horizontal run, measure or enter the corresponding rise or angle, and convert that same slope consistently into x:12, degrees and percent. Use the pitch factor and rafter-line result for geometry only, then apply the actual product, framing, safety and local requirements separately.