Roof Pitch Calculator — Angle, Rise, Run & Rafter Length
Any roof pitch in every form, with the rise, run, rafter length and cuts.
Your roof
Rafter and cuts
Common pitches: degrees, percent and multipliers
| Pitch | Angle | Percent | Multiplier | Hip / valley |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.003 | 1.417 |
| 2/12 | 9.46° | 16.7% | 1.014 | 1.424 |
| 3/12 | 14.04° | 25% | 1.031 | 1.436 |
| 4/12 | 18.43° | 33.3% | 1.054 | 1.453 |
| 5/12 | 22.62° | 41.7% | 1.083 | 1.474 |
| 6/12 | 26.57° | 50% | 1.118 | 1.500 |
| 7/12 | 30.26° | 58.3% | 1.158 | 1.530 |
| 8/12 | 33.69° | 66.7% | 1.202 | 1.563 |
| 9/12 | 36.87° | 75% | 1.250 | 1.601 |
| 10/12 | 39.81° | 83.3% | 1.302 | 1.641 |
| 11/12 | 42.51° | 91.7% | 1.357 | 1.685 |
| 12/12 | 45.00° | 100% | 1.414 | 1.732 |
| 14/12 | 49.40° | 116.7% | 1.537 | 1.833 |
| 16/12 | 53.13° | 133.3% | 1.667 | 1.944 |
| 18/12 | 56.31° | 150% | 1.803 | 2.062 |
| 21/12 | 60.26° | 175% | 2.016 | 2.250 |
| 24/12 | 63.43° | 200% | 2.236 | 2.449 |
Multiplier: sloped length per unit of run. Hip / valley: hip length per unit of common run on an equal-pitch roof.
About the Roof Pitch Calculator — Angle, Rise, Run & Rafter Length
Turn a roof pitch written one way into every other — x in 12 (the US "6/12"), a rise : run ratio, degrees and percent — and work out the roof triangle: the rise, the run, the common-rafter length with the eave overhang, the pitch multiplier, the hip or valley rafter and the angles for the plumb and seat cuts.
Tell it what you know: the pitch and the run (or the building span), the rise and the run, or the pitch and the rise. Work in feet and inches — results to the nearest 1/16 in — or in metres and millimetres. Everything is plain right-triangle trigonometry, shown under the result so you can check it.
How to use it
- Pick US (ft, in) or Metric (m, mm) and what you know: pitch and run, rise and run, or pitch and rise.
- Type the pitch in the unit you have —
6in 12,5:12or1:2.4as a ratio,30degrees or50percent — or tap a common pitch. - Enter the run of one rafter, or switch to span and give the building width for a gable (the run is half of it). Lengths such as
12' 6"or3.6 mwork. - Add the overhang (measured level, out from the wall) and the ridge board thickness (0 if there is none). Optionally give the rafter depth and the seat cut for the plumb-cut depth, a birdsmouth and the board length to buy.
- Read the pitch in every form, the rise, run and rafter lengths and the cut angles; copy the summary for the site.
Examples
6/12 = 26.57° = 50 % = 1 : 2, multiplier 1.118 · rise 6′ · line length 13′ 5″ − 13/16″ for the ridge + 1′ 1 7/16″ overhang = rafter 14′ 5 9/16″ · plumb cut 26.57° and seat cut 63.43° from square · plumb-cut depth 6 1/8″, 4 3/8″ left above the plate · board at least 14′ 8 5/16″ (buy 16 ft) · hip 18′ at 4.24 in 12
30° = 6.93 in 12 = 57.7 % = 1 : 1.732, multiplier 1.1547 · rise 2.078 m · rafter 4.157 m − 22 mm + 520 mm = 4.655 m
1.5 ÷ 4 = 0.375 → 4.5 in 12 = 20.56° = 37.5 % = 1 : 2.667, multiplier 1.068 · rafter 4.272 m
How it is worked out
With p = rise ÷ run: the angle is atan(p), the percent slope is 100 × p, "x in 12" is 12 × p and the ratio 1 : n has n = 1 ÷ p.
The pitch multiplier (slope factor) is √(1 + p²): any level distance times it gives the length along the slope. So the line length of a common rafter is run × multiplier, the overhang along the rafter is the level overhang × multiplier, and a roof's sloped area is its plan area × multiplier.
A rafter that meets a ridge board stops at the board's face, so it is shortened by half the board's thickness measured level: (thickness ÷ 2) × multiplier along the rafter.
On a hip roof with equal pitches the hip (or valley) runs diagonally across the plan, √2 times as far as a common rafter: its length is common run × √(2 + p²) and its pitch is p ÷ √2 — the same rise over 16.97 in of run instead of 12.
Cuts, the speed square and the birdsmouth
- Plumb cut (top of the rafter and a plumb tail): the line is vertical once the rafter is in place, which is the pitch angle away from a square cut — set a mitre saw to that angle, or pivot a speed square until the rise (6 for a 6/12 roof) on its common scale meets the rafter edge and mark along the pivot edge.
- Seat or level cut: square to the plumb line, 90° minus the pitch angle from a square cut.
- Plumb-cut depth: a board of depth d on edge is d ÷ cos(angle) tall measured plumb.
- Birdsmouth: a seat cut as long as the bearing on the wall plate gives a heel (plumb) cut of seat × p; what is left above the plate is the plumb depth minus the heel. Keep enough of the rafter above the seat for its span and loads — check notching rules in your building code.
- Board length: with plumb cuts at both ends the board is the rafter length plus d × tan(angle) long at least; buy the next stock length.
Pitch, slope and angle are the same thing
In the US and Canada a pitch is usually the inches of rise per 12 inches of run ("6 in 12", written 6/12 or 6:12). Elsewhere roofs are often given in degrees (UK, Europe, Australia) or as a ratio such as 1 : 3. A percent slope is the rise per 100 of run, so 6/12 is 50 % and 12/12 is 100 % — which is 45°, not "100 % of 90°". Strictly, pitch once meant rise ÷ span (so a 6/12 gable was a "1/4 pitch"); this calculator always uses rise ÷ run.
Limitations
- Common, hip and valley rafters of regular roofs with equal pitches; unequal-pitch hips, jack rafter lengths and compound cuts (hip cheek cuts) are not worked out.
- Rafter lengths are line lengths along the slope from the wall line; where your measuring line, plumb tail or fascia detail differs, adjust the tail.
- It does not size rafters, check spans or loads, or tell you which pitch your roofing needs — follow the span tables of your code and the roofing maker's minimum slope.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
What angle is a 6/12 roof pitch?
atan(6 ÷ 12) = 26.57°. Other common pitches: 3/12 = 14.04°, 4/12 = 18.43°, 8/12 = 33.69°, 9/12 = 36.87°, 12/12 = 45°.
How do I convert a pitch to degrees or percent?
Divide the rise by the run: 4/12 is 0.333. Degrees = atan(0.333) = 18.43°; percent = 0.333 × 100 = 33.3 %. To go back from degrees, take the tangent: tan(30°) = 0.577, which is 6.93 in 12.
What is the pitch multiplier?
The length along the slope for each unit of level run, √(1 + p²): 1.054 for 4/12, 1.118 for 6/12, 1.202 for 8/12 and 1.414 for 12/12. Multiply a run by it for a rafter, or a plan area for the sloped roof area.
How do I measure the pitch of an existing roof?
Hold a level 12 in long against the underside of a rafter or on the roof, level it, and measure straight up (or down) from its far end to the roof: that is the rise in 12. Or measure the rise and the run of a gable end and choose rise and run.
Why is the rafter shortened for the ridge board?
The run and rise are measured to the centre line of the ridge, but each rafter stops at the face of the ridge board, half its thickness short. A 1½ in board takes 3/4 in of level run off each rafter, which on a 6/12 roof is 13/16 in along the rafter.
Is the rafter length the length of wood to buy?
No. It is the line length along the slope. The board must also hold the plumb cuts, so with a rafter depth the calculator gives the shortest board; buy the next stock length up.