Roof Pitch, Rise, Run and Rafter Length Explained

Everything here comes from one right triangle, so if you can picture that triangle you can derive any of these numbers. Measure or look up two sides and the geometry gives you the rest, which the Roof Pitch Calculator will confirm along with the pitch, the angle, and the rafter multiplier.

The roof as a triangle

A pitched roof is a right triangle repeated along the length of the building. The horizontal bottom leg is the run, the vertical side is the rise, and the sloping top, the roof surface itself, is the hypotenuse, which is the line a rafter follows. Every roof calculation in this guide is just a question about that triangle: given two of its parts, find a third. Pitch is the relationship between the rise and the run, roof height is the rise, and rafter length is the hypotenuse.

Holding that image in mind is the single most useful thing you can do, because it turns a set of separate formulas into one coherent picture. When you know the pitch, you know the shape of the triangle, and from the shape plus one real dimension (usually the building width) you can scale the triangle up to full size and read off any length you need. The rest of this guide walks around that triangle, corner by corner, showing what each part means and how to calculate it. If you have not measured your pitch yet, start with how to calculate roof pitch, then return to build the triangle out to full size.

What rise means

Rise is the vertical measurement, how far the roof climbs upward. In the pitch ratio it is the first number, the rise per 12 inches of run, so the 6 in a 6/12 pitch is a rise of 6 inches for every foot the roof travels horizontally. That is the unit rise. There is also a total rise, the full vertical height the roof gains from the top of the wall to the ridge, which depends on how wide the building is. The unit rise defines the pitch; the total rise defines how tall the finished roof stands.

Keeping unit rise and total rise separate avoids a lot of confusion. When someone says a roof rises 6 inches, they mean the unit rise that sets the pitch. When they ask how tall the roof is, they mean the total rise measured from wall plate to ridge. The two are linked by the run: total rise equals the unit rise times the number of feet of run. So a 6/12 roof over a 12 foot run gains 6 inches per foot times 12 feet, which is 72 inches, or 6 feet of total rise. Understanding that link is the key to moving from a pitch to a real roof height, covered in the height section below.

What run means

Run is the horizontal measurement, how far the roof travels sideways as it climbs. In the pitch ratio the run is standardised to 12 inches, which is why every pitch is written as a number over 12. But when you scale up to a real building, the run becomes a real distance: the horizontal span from the outside wall to the point directly below the ridge. On a symmetrical gable roof that point is the centre of the building, so the run is half the total width.

This is where more roof calculations go wrong than anywhere else, because people use the full building width as the run instead of half of it. If a house is 24 feet wide, each rafter runs 12 feet horizontally, not 24, because two rafters meet at the ridge in the middle, each covering half the span. Get this right and your rise, height, and rafter length all come out correct; get it wrong and every one of them is doubled or halved. The distinction between run and the full span deserves its own section, which follows shortly, because it is that important.

Finding the pitch from rise and run

If you have measured a rise and a run, the pitch follows directly. This is the reverse of scaling up: instead of starting from a known pitch, you start from measured dimensions and derive the pitch.

The multiplication by 12 converts whatever run you actually measured back onto the standard 12 inch base, so the answer comes out in the familiar x/12 form. If you happen to measure over exactly 12 inches of run, the rise you read is already the pitch, which is the trick behind the quick level-and-tape method. This is the calculation the phrase how to calculate roof pitch from rise and run is asking for, and it is the same formula whether your rise and run are small measurements taken with a level or full building dimensions taken from plans. Feed either into the calculator and it returns the pitch instantly.

Span versus run: the crucial distinction

The span is the full width of the building, wall to wall. The run is half of that on a symmetrical gable, because the roof rises from each wall to a central ridge. This single relationship trips up more first-time roof calculations than any other, so it is worth stating plainly: on a standard gable, run equals span divided by two. A 30 foot wide house has a 15 foot run, and each rafter spans that 15 feet horizontally on its way to the ridge.

The reason the distinction matters so much is that run appears in every downstream calculation. Use the full span as the run and you double the total rise, double the roof height, and roughly double the rafter length, throwing off materials and framing alike. The exceptions are roofs that are not symmetrical gables. A single-slope or lean-to roof rises across the entire span in one plane, so its run is the full width, not half, as the single-pitch roof guide explains. An asymmetrical roof, where the ridge is off-centre, has a different run on each side. Always identify the run correctly for the roof shape before you calculate anything else.

Calculating roof height from pitch

A common question, especially for people planning attic conversions, dormers, or how a house will look, is how tall the roof will stand. That total rise comes straight from the pitch and the run.

So a 6/12 roof on a 24 foot house stands 6 feet tall from the wall plate to the ridge, before you add the ridge board and any raised heel. Steeper pitches stand taller: the same house under a 12/12 roof would rise 12 feet, which is why steep roofs create room for attics and vaulted ceilings while shallow roofs do not. This is the calculation behind questions like how tall is a 4/12 pitch roof, and it depends entirely on getting the run right, since the run is what scales the unit rise up to the full height. For headroom and living-space planning, the total rise is the number that tells you whether the attic is usable.

Calculating rafter length

The rafter is the hypotenuse of the roof triangle, the sloping member that spans from the wall to the ridge. Its length comes from the rise and run by the Pythagorean theorem, or more conveniently from the run and the pitch multiplier.

Both formulas give the same answer, because the pitch multiplier is defined as the slope length divided by the run, the same relationship the Pythagorean theorem expresses. The multiplier version is quicker: look up the multiplier for your pitch, multiply by the run, and you have the rafter length from wall to ridge. This is the theoretical or line length; the actual rafter you cut will be a little longer to include the overhang and a little shorter to account for half the ridge board thickness, both covered below. For the base length, run times multiplier is all you need, and the calculator gives you the multiplier automatically.

Rafter length per foot of run

This chart gives the rafter length for each foot of run at common pitches, which is the multiplier expressed as inches per foot. Multiply the value by your run in feet to get the base rafter length.

To use it, take your run in feet, multiply by the length per foot, and you have the base rafter length in inches. For a 6/12 roof over a 12 foot run, 12 times 13.42 inches is 161 inches, or about 13 feet 5 inches, matching the earlier example. The same multiplier drives the roof area calculation in roof area with pitch, because area and rafter length are two uses of one factor. Keep this chart with the angle chart and you have the full geometry of any common pitch at your fingertips.

Plumb and seat cuts

A rafter is not just cut to length; its ends are cut at angles so it meets the ridge and sits on the wall correctly. The plumb cut is at the top, where the rafter meets the ridge, and it is vertical when the rafter is in place, so its angle equals the roof angle in degrees. The seat cut, or bird’s mouth, is the notch where the rafter rests on the top of the wall, and its angle is the complement of the roof angle, meaning 90 degrees minus it.

For an 8/12 roof at 33.69 degrees, the plumb cut is 33.69 degrees and the seat cut is 56.31 degrees. You mark these with a speed square set to the pitch, as shown in the speed square guide, or with a framing square laid out to the rise and run. Getting the cut angles right is what makes a rafter seat flat on the wall and meet the ridge cleanly, and because the same cuts repeat on every rafter, an error propagates across the whole roof. Convert your pitch to degrees with the degrees guide if you are setting a saw, or read the pitch straight off a speed square if you are marking by hand.

Overhang and the ridge adjustment

The base rafter length reaches from the wall to the centre ridge line, but a real rafter differs at both ends. At the bottom, it usually extends past the wall to form the eave overhang, so you add the horizontal overhang times the pitch multiplier to the base length. A 12 inch overhang on a 6/12 roof adds 12 times 1.118, about 13.4 inches, to the rafter. At the top, half the thickness of the ridge board is subtracted, because the base length was measured to the centre of the ridge and the rafter actually stops at the face of the board.

These two adjustments are small but they matter for a clean job, especially the overhang, which sets how far the eaves project and how the roof sheds water clear of the walls. In practice you calculate the base length from run times multiplier, add the overhang contribution, then subtract half the ridge thickness, and that is the rafter you cut. The bird’s mouth is positioned where the rafter crosses the outside of the wall. The calculator handles the base length and multiplier; the overhang and ridge adjustments are quick additions once you have that.

Worked examples

Here are two full examples that carry a roof from its width all the way to a cut rafter.

Example A shows a wide, medium-pitch roof; Example B a narrower but steeper one. Notice that Example B stands nearly as tall as A despite being 8 feet narrower, because its steeper 9/12 pitch gains height faster. Both base rafter lengths would then get the overhang added and half the ridge thickness subtracted before cutting. Working through examples like these is the best way to internalise how span, run, pitch, height, and rafter length lock together, and you can reproduce any of them in the calculator to check your arithmetic.

Common mistakes

Rafter and height errors almost always come from one of these.

Avoid those five and your rafters will fit. The reliable workflow is to confirm the pitch, halve the span to get the run, calculate height and base rafter length, then add overhang and subtract the ridge, checking each figure against the calculator.

Rafters versus trusses

The rafter length and cut angles in this guide apply when you are stick-framing a roof, cutting and setting each rafter individually. Many modern roofs instead use prefabricated trusses, engineered triangles delivered to site and lifted into place. If you are ordering trusses, you give the supplier the span, the pitch, and the overhang, and they engineer the members for you, so you rarely calculate rafter length by hand. Even then, understanding rise, run, and pitch helps you specify the truss correctly and check that the delivered profile matches your building.

Stick framing still has its place, especially on additions, dormers, complex roofs, and repairs where a truss will not fit or cannot be craned in. There the calculations here are exactly what you need, because you are laying out each rafter yourself from the pitch and the run. Whether you frame with rafters or trusses, the same triangle underlies both, and the pitch you feed into the calculator is the starting point either way. Knowing the geometry means you can talk to a truss supplier or cut your own rafters with equal confidence.

Why steeper roofs cost more to frame

The rafter length chart quietly explains a lot about roofing cost. As the pitch steepens, the multiplier grows, so the rafters get longer for the same building width, which means more lumber per rafter. A 12/12 roof needs rafters about 41 percent longer than the run, against only about 5 percent extra for a 4/12, so the framing material for a steep roof is noticeably greater even before you count the extra roof area to cover.

Steeper roofs also stand taller, which raises the ridge and can mean longer gable-end walls, more scaffolding, and slower, more careful work because the pitch is not walkable. All of that adds labour on top of the extra material. The same steepness that gives a roof its dramatic look and its snow-shedding ability, discussed in why roof pitch matters, is what drives its cost up through both framing and covering. When you weigh a steeper pitch, the rafter length is one of the concrete places that cost shows up, and the pitched roof cost guide puts numbers to it.

Hip, valley and jack rafters

Simple gable roofs use only common rafters, the straight members this guide has focused on. Hip and valley roofs add two more types, and they follow the same triangle logic with a twist. Hip rafters run diagonally from the corners of the building up to the ridge, so their run is the diagonal of the corner rather than a straight side, which makes them longer and sets them at a shallower angle than the common rafters. That is why you should never read a hip rafter to find the roof pitch; it reads low, as noted in the hip roof guide.

Jack rafters are the shorter rafters that run from the wall to a hip or from a valley to the ridge, each one a little shorter than the last as it approaches the corner. They share the common rafter pitch but vary in length, decreasing by a regular amount set by the spacing and the hip angle. Laying out hips, valleys, and jacks by hand is where rafter geometry gets more involved, and most builders lean on framing tables or software for it. For an ordinary gable, though, the common rafter calculations here cover the whole roof, and the calculator gives the multiplier that starts every one of them.

A framing walkthrough from width to rafter

Putting it all together, here is the sequence a framer follows to go from a building width to a finished rafter. Start with the span, the full width of the building, and halve it to get the run for a gable roof. Confirm the pitch, either the design pitch from the plans or a measured one. Multiply the run by the pitch multiplier to get the base rafter length from wall to ridge. Then add the overhang times the multiplier at the bottom, and subtract half the ridge board thickness at the top.

With the length set, mark the plumb cut at the top using the pitch on a speed square, mark the bird’s mouth where the rafter crosses the outside of the wall, and mark the tail cut at the overhang end in whatever style the eave calls for. Cut one rafter, test-fit it, and if it seats flat on the wall and meets the ridge cleanly, use it as the pattern for the rest. This is the whole workflow, and every step traces back to the pitch and the run. Nail those two down, run them through the calculator, and the rest of the roof is repetition. It is the same disciplined chain that makes the area calculation reliable, applied to framing instead of materials.

A note on rafter spacing and count

Calculating one rafter length tells you how long each member is, but a roof needs many rafters, and their spacing sets how many you cut. Rafters are typically spaced 16 or 24 inches on centre, and the number you need runs along the length of the building rather than across its width. To find the count, divide the building length by the spacing in feet and add one for the starting rafter, then double it if the pitch has two sides of common rafters meeting at the ridge.

Spacing is a structural decision tied to the rafter size, the span, and the roof load, including snow, so it is governed by published span tables and your local building code rather than chosen freely on site. A wider spacing needs deeper rafters; a heavy snow load may push you to 16 inch centres for extra strength. The rafter length from this guide is the same regardless of spacing, but the total lumber order depends on both the length and the count, so once you have the length, work out the number from the building length and the spacing to size the full order. The snow guide covers how load influences these choices.

Rafter calculations in metric

The same triangle works in metric units, which matters if you are building from plans drawn in millimetres or metres. Rise and run are measured in the same unit, and the pitch multiplier is a pure ratio, so it does not change with the unit system. A 6/12 pitch has a multiplier of 1.118 whether you work in inches or millimetres, and multiplying a metric run by that multiplier gives a metric rafter length directly. The only adjustment is that many metric drawings express slope in degrees rather than twelfths, so you convert to a pitch or work from the angle.

To calculate a rafter in metric, take the horizontal run in metres, multiply by the pitch multiplier for a rafter length in metres, then add the overhang and subtract half the ridge thickness as before. If the plan gives an angle, use the degrees guide to find the pitch and its multiplier, or take the run divided by the cosine of the angle, which gives the slope length directly. Because the geometry is unit-independent, everything in this guide carries over, and the calculator handles the ratio for you regardless of the units you measure in.

Using the calculator

The geometry here is worth understanding, but the roof pitch calculator removes the arithmetic and the square roots. Enter your rise and run and it returns the pitch, the angle in degrees, and the rafter multiplier together, so you can find the pitch from measured dimensions and get the multiplier for rafter length in one step. Enter a pitch and it works the other way, giving you the multiplier to scale any run into a rafter length. Either direction, it keeps the numbers consistent so your height and rafter figures agree.

From the multiplier you can flow into the connected tools without re-entering anything: use roof area with pitch to size materials from the same factor, or the speed square guide to lay out the cuts by hand. The roof pitch tool sits with the other estimators in the construction calculators category, alongside site tools like the dirt calculator, and the full roofing library is in the roof pitch blog off the homepage. Picture the triangle, get the run right, and every rafter and height follows from it. That one image, a right triangle with the run along the bottom, the rise standing up, and the rafter on the slope, is the whole of roof geometry in a single picture, and once it is fixed in your mind the formulas stop being things to memorise and become things you can rebuild from scratch whenever you need them.

How to calculate roof pitch from rise and run: frequently asked questions