Roof Pitch Calculator: Angle, Slope and Rafter Length

What roof pitch means

Roof pitch is how many inches a roof rises for every 12 inches it runs horizontally. A 6/12 pitch rises 6 inches in every 12, which is an angle of 26.57 degrees and a slope of 50 percent. The calculator above accepts any of those forms, converts between them, and works out rafter length, ridge height and roof area from the size of the building. Drag the handle on the drawing and every number changes with it.

The formula behind it is short: pitch = rise ÷ run × 12, and angle = arctan(rise ÷ run). Everything else, from the slope percentage to the rafter length, follows from that one ratio.

How to measure roof pitch

You only need two numbers, the rise and the run, and there are four practical ways to get them.

1. On the roof with a level and a tape. Hold a level horizontally with one end touching the roof, mark 12 inches along it, and measure straight down from that mark to the roof surface. That measurement is the rise in 12. Only do this on a roof you can stand on safely.
2. From inside the loft or attic. Do the same against the underside of a rafter: level 12 inches out from the rafter, measure up to it. The pitch of the rafters is the pitch of the roof.
3. With your phone. Choose measure with my phone in the calculator, lay the phone flat on a rafter or on the roof with its top edge pointing up the slope, and press Start. The phone reads the angle and the calculator converts it to a pitch. This works best on a rafter or a ladder rail laid on the slope; keep off steep or wet roofs.
4. From the size of the house. The rise is the height of the ridge above the top of the walls, and the run is half the width of the building for a gable roof (the full width for a shed roof). Enter both as rise and run.

Pitch, slope and angle: the same roof three ways

American roofers quote pitch as a rise in 12 (6/12, 8/12). British and European builders and most manufacturers quote the angle in degrees (35°, 40°). Engineers and drainage designers often use a percentage slope or a ratio. They all describe the same thing:

The full chart from 1/12 to 24/12 is under the calculator, and each row loads into the tool with one tap. To go the other way, from degrees to pitch, use rise in 12 = 12 × tan(angle). A 30° roof is 6.93/12, a 35° roof 8.40/12 and a 40° roof 10.07/12.

Roof pitch formulas

• Pitch (rise in 12) = rise ÷ run × 12
• Angle = arctan(rise ÷ run), converted to degrees
• Slope percentage = rise ÷ run × 100
• Pitch multiplier = √(1 + (rise ÷ run)²). Multiply any horizontal distance by it to get the length along the slope.
• Rafter length = run × pitch multiplier, plus the overhang × pitch multiplier

Common roof pitches

• Below 2/12: treated as a flat or low slope roof, finished with a membrane rather than shingles or tiles.
• 3/12 to 4/12: porches, ranch houses and many shed roofs. Shingles are allowed here, but 2/12 to 4/12 needs a double layer of underlayment.
• 4/12 to 9/12: the range most American houses fall in, with 6/12 the classic middle. Walkable for most roofers up to about 6/12.
• 9/12 to 12/12 and above: steep roofs such as A-frames and Tudor styles. Roofers work from roof jacks or harnesses, which adds labour cost.
• UK and Europe: pitched roofs are usually between about 30° and 45°, roughly 7/12 to 12/12, because tiles and slate need the steeper pitch to shed rain.

Minimum roof pitch by material

Every roof covering has a minimum slope below which water can be driven back under it. In the US the International Residential Code sets these minimums in section R905; manufacturers can require more.

In the UK the minimum is set by the tile or slate manufacturer and British Standard BS 5534 rather than a single code table. Interlocking concrete tiles can go down to around 12.5° to 22.5° depending on the product, plain clay or concrete tiles usually need about 35°, and natural slate roughly 20° to 30° depending on the slate size and how exposed the site is. Always check the product's own installation guide for your exposure zone.

Shed and lean-to roof pitch

A shed or lean-to roof has a single slope, so its run is the full width of the building, not half. Switch the calculator to Shed or lean-to and it measures the run across the whole span and shows how much higher the tall wall must be. For a 10 ft wide shed at 3/12, the high side sits 2 ft 6 in above the low wall.

Pick the pitch from the roof covering: at least 2/12 for shingles (better 4/12), 3/12 for lapped metal sheets, or a membrane on anything flatter. A steeper pitch sheds rain and leaves faster, which matters on sheds under trees.

Rafter length

For a gable roof the calculator takes the run as half the building width, minus half the thickness of the ridge board, because each rafter stops at the face of the ridge rather than its centre. It multiplies that run by the pitch multiplier for the rafter length from the wall plate to the ridge, then adds the overhang measured along the slope. The result is the sloping length; the plumb cut at the ridge, the birdsmouth at the wall and the tail cut are left to you, so buy stock a little longer than the figure and cut to fit. To size the rafters themselves, check the span with the joist span calculator.

Hip and valley rafters

On a hip roof the corner rafters run diagonally across the plan, so they are longer than the common rafters for the same pitch. Their multiplier is √(2 + (rise ÷ run)²) per unit of common run, instead of √(1 + (rise ÷ run)²). At 4/12 that is 1.453, at 6/12 exactly 1.5, at 8/12 1.563 and at 12/12 1.732. A hip rafter over 12 ft of common run on a 6/12 roof is therefore 18 ft long before the overhang and cuts, against 13 ft 5 in for the common rafters. Valley rafters, where two roof slopes meet in an internal corner, use the same multiplier.

The angle of a hip rafter is also shallower than the roof pitch, because it covers more horizontal distance for the same rise. That is why hip and valley rafters need their own plumb and seat cuts, marked from the diagonal rather than the common pitch.

Roof pitch and loft space

Pitch decides how much usable room there is under a roof. For a given building width, a steeper pitch lifts the ridge and gives more floor area with standing head height, which is why many older houses with 40° to 45° roofs convert easily while a 22° roof of the same width rarely does without a dormer. If you are thinking about using the space, check the height with the loft head height calculator and price the work with the loft conversion cost calculator, which covers dormers, hip to gable and mansard conversions.

Roof area and the pitch multiplier

A sloping roof has more surface than the floor it covers. Multiply the footprint, including the overhangs, by the pitch multiplier and you get the true roof area: a 42 by 26 ft footprint at 6/12 is 1,092 sq ft on plan but about 1,221 sq ft of roof, or 12.2 squares. Take that area into the roofing calculator with waste factor to order shingles or sheets, and the metal roofing screw calculator for fasteners.

What pitch means for cost and safety

Pitch changes the price of a roof more than most people expect. A steeper roof has more surface for the same house, and above about 7/12 to 8/12 roofers need roof jacks, harnesses and more time, which most contractors charge extra for. A very low pitch saves material but limits you to membranes or specific metal systems and drains more slowly, which matters in heavy rain and snow areas.

Worked examples

1. 24 ft wide gable house at 6/12

Building 24 ft wide and 40 ft long, 12 in overhang, 1.5 in ridge board. The pitch is 26.57° with a multiplier of 1.118. Each rafter is 13 ft 4 1/8 in from wall plate to ridge, 14 ft 5 5/8 in with the overhang, and the ridge sits 6 ft above the top of the walls. The roof area is about 1,221 sq ft, or 12.2 squares.

2. 10 ft wide shed at 3/12

Single slope across the full 10 ft, 6 in overhang. The angle is 14.04° with a multiplier of 1.031. The rafter is 10 ft 3 3/4 in, or 10 ft 9 7/8 in with the overhang, and the high wall must be 2 ft 6 in taller than the low one.

3. UK house at 35 degrees

Span 7.5 m, length 9 m, 300 mm overhang, 38 mm ridge board. 35° is a pitch of 8.40/12 with a multiplier of 1.221. Each rafter is about 4.555 m to the ridge or 4.921 m with the overhang, the ridge sits 2.626 m above the wall plate, and the roof area is about 94.9 m².

Sources

• International Code Council, International Residential Code 2021, section R905: minimum slopes for roof coverings.
• British Standard BS 5534, Slating and tiling for pitched roofs and vertical cladding, and tile manufacturers' installation guides: UK minimum pitches.
• Pitch, angle, slope and multiplier values calculated from right-angle trigonometry and checked against published rafter tables.

Last checked October 2026.