Work out the pitch of a roof and the rafter length from the rise and run. Enter the rise and the run and the calculator returns the pitch as an angle, a percentage, and an x:12 ratio, plus the rafter length — or fill in different fields to work backward.
The roof pitch calculator quickly tells you the slope of a roof and the length of rafter you need. Enter the roof's rise and run, and it returns the pitch expressed three ways — as an angle in degrees, as a percentage, and as the familiar x:12 ratio builders use — along with the rafter length. Because the relationships are all connected, you can also work backward: give it a rafter length and an angle, or two of the three lengths, and it fills in the rest. It is the ideal companion for roofers, carpenters, DIY builders, and anyone planning a roof, a shed, or a deck cover.
This page explains what roof pitch is, the formulas the calculator uses, worked examples you can reproduce, how to convert between the different ways of expressing pitch, and answers to the questions people ask most. By the end you will be able to read, calculate, and convert any roof pitch with confidence.
Roof pitch is the steepness or slope of a roof — the slope created by the rafter as it rises from the wall to the ridge. It can be described in two equivalent ways: as the angle the rafter makes with the horizontal, or as the ratio between the roof's vertical rise and its horizontal run. In construction, especially in the United States, pitch is most often written as a ratio in the form x:12 — the number of inches the roof rises for every 12 inches of horizontal run. A "6:12" roof rises 6 inches per foot of run. Elsewhere, and in many calculations, pitch is given as an angle in degrees or as a percentage. All of these describe the same thing: how steep the roof is.
Three measurements define the geometry of a sloping roof, and they form a right triangle:
Because rise, run, and rafter form a right triangle, they are linked by the Pythagorean theorem, and the pitch depends only on the ratio of rise to run.
The calculator uses these standard formulas, where the rise is the vertical height and the run is the horizontal distance:
rafter = √(rise² + run²)
angle = arctan(rise / run)
pitch (%) = (rise / run) × 100
pitch (x:12) = (rise / run) × 12
In words: the rafter length comes from the Pythagorean theorem; the pitch angle is the inverse tangent of rise divided by run; the percentage is simply rise over run as a percent; and the x:12 ratio scales that same ratio to a run of 12. All three pitch expressions — angle, percentage, and x:12 — carry the same information, just in different forms.
Suppose a roof has a rise of 1.5 m and a run of 6 m. First, the rafter length by the Pythagorean theorem:
rafter = √(1.5² + 6²) = √(2.25 + 36) = √38.25 ≈ 6.185 m
Next, the pitch. The ratio rise/run is 1.5/6 = 0.25, so:
pitch (%) = 0.25 × 100 = 25%
angle = arctan(0.25) ≈ 14.04°
pitch (x:12) = 0.25 × 12 = 3, i.e. 3:12
So this roof has a 3:12 pitch, a 25% slope, an angle of about 14 degrees, and needs rafters about 6.185 m long. These are the calculator's default values, so you can press Calculate to confirm them and then enter your own measurements.
One of the most useful things this calculator does is convert between the different ways pitch is written. Roofers in the US quote pitch as x:12; architects and many countries use degrees; and engineers often use a percentage grade. To convert an x:12 ratio to a percentage, divide x by 12 and multiply by 100 (so 6:12 is 50%). To convert x:12 to an angle, take the inverse tangent of x/12 (so 6:12 is arctan(0.5) ≈ 26.57°). To go from an angle to a percentage, take the tangent and multiply by 100. Because every expression is derived from the single ratio of rise to run, the calculator can start from any one of them and produce the others instantly — handy when a plan lists the pitch one way but you need it another.
Roof pitches fall into rough categories that affect how a roof is built and what materials suit it. Flat roofs (technically low-slope, from about 0:12 up to 2:12, or under about 10°) need special membranes because water drains slowly. Low-slope roofs (around 2:12 to 4:12) are common on porches and modern homes. Conventional or medium pitches (4:12 to 9:12, roughly 18° to 37°) are the most common on houses and work with almost any roofing material. Steep roofs (above 9:12, over about 37°) shed water and snow superbly and give a dramatic look, but need extra safety measures and often more material. Knowing your pitch category helps you choose appropriate shingles or tiles, estimate materials, and understand building-code requirements, since many products specify a minimum pitch.
Pitch is one of the most important characteristics of a roof because it influences so much. Steeper roofs shed rain and snow more effectively, reducing the risk of leaks and of snow building up to a dangerous weight — a real concern in northern climates. Pitch also determines how much roofing material you need, because a steeper roof has more surface area than its footprint suggests, and it dictates which materials are suitable, since many shingles and membranes have a minimum recommended slope. It affects attic space, ventilation, and the overall look of a building, and it interacts with wind loads and drainage design. Getting the pitch right — and knowing exactly what it is — is essential for a durable, code-compliant, and attractive roof.
Beyond the pitch itself, the rafter length is one of the most practical outputs of this calculator, because it tells you how long to cut the sloping members that support the roof. The basic rafter length is the hypotenuse of the rise-and-run triangle, found with the Pythagorean theorem. In real construction you will usually add an overhang (the eave that extends beyond the wall) to this figure, and you may need to account for the ridge board thickness and the "bird's mouth" notch where the rafter sits on the wall plate. The number this calculator gives is the theoretical rafter length from the wall plate to the ridge; add your desired overhang to get the length to cut. Knowing it in advance helps you order the right lumber and minimize waste.
If you do not have the plans, you can measure a roof's pitch directly with a level and a tape measure. The classic method uses a 12-inch level: hold it perfectly horizontal against the roof slope (or against a rafter), then measure straight down from the 12-inch mark of the level to the roof surface. That vertical measurement, in inches, is the rise per 12 inches of run — so if it reads 6 inches, the pitch is 6:12. You can do this safely from inside the attic against a rafter, which avoids climbing on the roof. Smartphone apps and digital angle finders can also read the pitch angle directly by resting the phone on the slope. Once you have either the x:12 ratio or the angle, this calculator converts it to every other form and, with one length, gives you the rafter length too.
The pitch of a roof strongly influences which covering materials are appropriate, because water drains at different speeds on different slopes. Asphalt shingles, the most common residential covering, generally require a minimum pitch of about 2:12, and manufacturers often specify extra underlayment between 2:12 and 4:12. Below roughly 2:12 you are in "low-slope" territory, where continuous membranes — such as EPDM rubber, TPO, modified bitumen, or built-up roofing — are used instead of overlapping shingles, because standing water would seep under individual pieces. Clay and concrete tiles, metal panels, and wood shakes each have their own minimum-pitch recommendations. Steeper roofs can use almost any material and shed water and snow readily, but they use more material for the same footprint and demand more labor and safety equipment. Knowing your exact pitch is the first step in choosing a covering that will perform and stay within warranty.
Climate is a major factor in choosing a roof pitch. In regions with heavy snowfall, a steeper roof helps snow slide off before it accumulates to a dangerous weight, reducing the structural load and the risk of ice dams forming at the eaves. In very rainy climates, a good pitch ensures water runs off quickly rather than pooling and finding its way through seams. In hot, dry, or high-wind areas, lower pitches are sometimes preferred because they present less surface area to the wind and can be cheaper to build. The pitch also interacts with gutter and drainage design: steeper roofs deliver water to the gutters faster, which must be sized accordingly. Matching the pitch to the local weather is a balance of shedding water and snow, resisting wind, and controlling cost.
Divide the rise by the run to get the ratio, then express it as needed: multiply by 100 for a percentage, by 12 for the x:12 ratio, or take the inverse tangent for the angle. For a rise of 1.5 and run of 6, the pitch is 25%, 3:12, or about 14°.
A 6:12 pitch means the roof rises 6 units for every 12 units of horizontal run. That equals a 50% slope and an angle of about 26.57°.
Use the Pythagorean theorem: rafter = √(rise² + run²). For a 1.5 m rise and 6 m run, the rafter is √38.25 ≈ 6.185 m, before adding any overhang.
Take the inverse tangent (arctan) of the rise divided by the run, or of x/12 for an x:12 ratio. For example, arctan(4/12) ≈ 18.43°, so a 4:12 pitch is about 18.4 degrees.
In everyday use they are often the same thing — the steepness of the roof. Strictly, "slope" is the ratio of rise to run (as x:12 or a percentage) while "pitch" sometimes refers to rise over the whole span, but most calculators, including this one, treat pitch as the rise-to-run slope.
Roofs steeper than about 9:12 (over roughly 37°) are generally considered steep. They shed water and snow well but require extra safety precautions and often more material to cover.
This Roof Pitch Calculator is provided for general informational and educational purposes. It computes theoretical roof geometry from the values you enter and does not account for overhangs, ridge boards, notches, or local building codes. Always confirm measurements and code requirements before construction.