Rafter Calculator: Rafter Length, Count & Board Feet (2026)

Every pitched roof in Waukegan, Gurnee, and the rest of Lake County is a set of rafters cut to the same length, and every one of those rafters is a right triangle. The span of the building gives you the run, the pitch gives you the rise, and the rafter length is the hypotenuse between them. Get that one number right and the whole roof goes up square: the ridge sits level, the eaves line up, and the roof deck takes the sheathing without a fight. Get it wrong by an inch and every rafter is wrong by the same inch, which is why carpenters cut one pattern rafter, test-fit it, and only then cut the rest. This page is the pattern rafter in calculator form. It takes the span, the pitch, the overhang, the spacing, the building length, and the lumber size, and it returns the rafter length in feet and inches, the ridge-to-birdsmouth cut, the tail, the total board length, the rafter count, the board feet, and the lumber material cost range. Every number comes from the same three-step calculation, so the calculator, the worked examples, and the tables on this page all agree with each other.

How the Calculation Works

The calculation has three steps, and each one is simple on its own. First, the run is half the building span. A 28 ft span has a 14 ft run, because each rafter covers half the building from the wall to the ridge. Second, the rise is the run times the pitch divided by 12. At 6/12 pitch, a 14 ft run rises 14 times 6 divided by 12, which is 7 ft. Third, the rafter length is the square root of the run squared plus the rise squared. For that roof it is the square root of 196 plus 49, which is the square root of 245, which is 15.65 ft, or 15 ft 7 13/16 in. That is the rafter length from the center of the ridge to the outside of the wall plate, and it is the number every other cut on the roof is measured from.

Two adjustments turn that theoretical length into a board you can cut. The first is the ridge board. The rafter length is measured to the center of the ridge, but the ridge board itself is 1.5 in thick, so the rafter stops half that thickness short of the center. The calculator subtracts that allowance along the slope, which is 0.75 in times the slope factor, and the result is the ridge-to-birdsmouth length: the length you actually mark on the board. On the 28 ft span at 6/12 pitch, the ridge-to-birdsmouth length is 15 ft 7 in, against 15 ft 7 13/16 in to the ridge center. The second adjustment is the tail. The overhang is measured horizontally from the wall, and the tail is the overhang times the slope factor, so a 12 in overhang at 6/12 pitch gives a 1 ft 1 7/16 in tail. Add the tail to the ridge-to-birdsmouth length and you have the total board length: 16 ft 8 7/16 in for that roof, which is why a 16 ft board is too short and an 18 ft board is the one to order.

The slope factor is the number that ties the pitch to every length on the roof. It is the square root of one plus the pitch over 12 squared, and it tells you how much longer a sloped length is than its horizontal run. At 4/12 pitch the factor is 1.054, at 6/12 it is 1.118, at 8/12 it is 1.202, at 10/12 it is 1.302, and at 12/12 it is 1.414. Multiply any horizontal distance by the factor and you get the sloped length: a 12 in overhang at 12/12 pitch is a 1 ft 5 in tail, while the same overhang at 4/12 pitch is a 1 ft 0 5/8 in tail. The roof pitch calculator works the same triangle from the other direction: give it the rise and the run and it returns the pitch, the angle, and the slope length.

The rafter count is a separate piece of arithmetic. Divide the building length in inches by the spacing and add one: a 40 ft building at 16 in on center is 480 divided by 16, which is 30 spaces, plus one, which is 31 rafters per slope, or 62 rafters for both slopes. The plus one matters: the first rafter sits at the gable end and the last one sits at the far end, so there is always one more rafter than there are spaces. Board feet are the lumber measure: one board foot is a 12 in by 12 in by 1 in block of wood, and a rafter of 2 in by 8 in by 16.70 ft is 22.27 board feet. Multiply by the rafter count and you have the total board feet, which is the number the lumber yard prices from. The calculator prices that total at $1.10 to $1.90 per board foot, a typical range for framing lumber, and the fairness checker below it tells you where any lumber quote sits against that range.

Worked Examples

Four real roofs, worked through the same calculation the calculator runs, so you can check the tool against hand math. All four use a 12 in overhang unless stated otherwise.

Example 1: 28 ft span, 6/12 pitch, 40 ft long, 2×8 at 16 in on center

The standard Waukegan two-story roof. The run is 14 ft and the rise is 7 ft, so the rafter length is the square root of 196 plus 49, which is 15 ft 7 13/16 in from ridge center to plate. After the 1.5 in ridge board allowance, the ridge-to-birdsmouth cut is 15 ft 7 in. The 12 in overhang gives a 1 ft 1 7/16 in tail, so each board is 16 ft 8 7/16 in long. The roof angle is 26.6 degrees. The rafter count is 31 per slope and 62 total, the board feet are 1,380.6 in total at 22.27 per rafter, and the lumber material runs $1,518 to $2,624, with a likely cost near $2,071. This is the default the calculator opens with, so you can change any input and watch the numbers move.

Example 2: 24 ft span, 4/12 pitch, 32 ft long, 2×6 at 24 in on center

A low-slope ranch. The run is 12 ft and the rise is 4 ft, so the rafter length is the square root of 144 plus 16, which is 12 ft 7 13/16 in, and the ridge-to-birdsmouth cut is 12 ft 7 in. The 12 in overhang gives a 1 ft 0 5/8 in tail, so each board is 13 ft 7 5/8 in long. The roof angle is 18.4 degrees. The rafter count is 17 per slope and 34 total, the board feet are 463.7 in total at 13.64 per rafter, and the lumber material runs $510 to $881. Notice how much less lumber a low, short roof needs: a third of the board feet of Example 1, even though the building is only a little smaller.

Example 3: 20 ft span, 12/12 pitch, 28 ft long, 2×10 at 16 in on center

A steep gable, the kind of roof that sheds snow fast and is hard to stand on. The run is 10 ft and the rise is 10 ft, so the rafter length is the square root of 100 plus 100, which is 14 ft 1 11/16 in, and the ridge-to-birdsmouth cut is 14 ft 0 5/8 in. The 18 in overhang gives a 2 ft 1 7/16 in tail, so each board is 16 ft 2 1/8 in long. The roof angle is 45.0 degrees. The rafter count is 22 per slope and 44 total, the board feet are 1,186.2 in total at 26.96 per rafter, and the lumber material runs $1,304 to $2,254. The steep pitch makes the tail long: an 18 in overhang on a 12/12 roof is over 2 ft of tail board.

Example 4: 36 ft span, 8/12 pitch, 50 ft long, 2×12 at 16 in on center

A wide, long roof that needs big lumber. The run is 18 ft and the rise is 12 ft, so the rafter length is the square root of 324 plus 144, which is 21 ft 7 5/8 in, and the ridge-to-birdsmouth cut is 21 ft 6 11/16 in. The 24 in overhang gives a 2 ft 4 7/8 in tail, so each board is 23 ft 11 9/16 in long. The roof angle is 33.7 degrees. The rafter count is 38 per slope and 76 total, the board feet are 3,642.2 in total at 47.92 per rafter, and the lumber material runs $4,006 to $6,921. Boards over 20 ft long are a special order at most yards, so check availability and price before you promise a delivery date.

Rafter Length by Pitch and Span

Most roofs in Lake County fall into a small set of spans and pitches, so the common lengths are worth knowing by heart. The table below gives the rafter length from ridge center to wall plate for the usual runs at the usual pitches. Read it by finding your pitch in the left column and your run across the top. A 28 ft span at 6/12 pitch has a 14 ft run, so the length is 15 ft 7 13/16 in. A 24 ft span at 8/12 pitch has a 12 ft run, so the length is 14 ft 5 1/16 in. These are the ridge-to-plate lengths: subtract the ridge board allowance for the cut length, and add the tail for the board length. The full chart, with more pitches and runs and the board lengths with tails, is in the rafter length chart post.

Hip Rafters, Valley Rafters, and Jack Rafters

A gable roof has only common rafters, and the calculator above covers it completely. A hip roof adds three more members. The hip rafter runs diagonally from the corner of the building to the end of the ridge, and it is longer than a common rafter on the same roof: its length is the square root of two times the run squared plus the rise squared. On the 28 ft span at 6/12 pitch from Example 1, the hip rafter is exactly 21 ft from ridge to plate, against 15 ft 7 13/16 in for the common rafter. The jack rafters are the short rafters that frame into the hip: each one is a common rafter shortened in proportion to its distance from the corner. A jack rafter 7 ft from the corner on that same roof has a 7 ft run and a 3.5 ft rise, so it is 7 ft 9 15/16 in long. The valley rafter is the mirror image of the hip: it runs diagonally where two roof slopes meet in a valley, and it uses the same diagonal length as the hip. The hip rafter calculator post works the whole hip roof step by step, and the common rafter vs jack rafter post explains which member goes where and how each one is cut.

Shed Roofs Are a Single Slope

A shed roof has no ridge in the middle: one wall is high and the other is low, and each rafter runs the full span from the high wall to the low wall. The math is the same right triangle, but the run is the full span instead of half of it. A 12 ft shed span at 3/12 pitch rises 3 ft, so the rafter is 12 ft 4 7/16 in long. A 10 ft shed at 4/12 pitch rises 3.33 ft, so the rafter is 10 ft 6 1/2 in. A 14 ft shed at 2/12 pitch rises 2.33 ft, so the rafter is 14 ft 2 5/16 in. The low pitch is the thing to watch on a shed: at 2/12 or 3/12 the roof sheds water slowly, so the overhang matters more and the roofing material must be rated for low slope. The shed rafter length calculator post covers shed roofs, lean-to roofs, and the rafter spacing a metal shed roof needs.

What Size Rafters Do You Need?

The rafter length tells you how long the board is. The lumber size tells you how deep it must be, and depth is what carries the load. A longer rafter needs a deeper board, a wider spacing needs a deeper board, and a heavier snow load needs a deeper board. Lake County roofs carry the Chicago area snow load, which is 25 psf ground snow load per ASCE 7, so the spans below are shorter than the spans in a warm-climate table. The table gives rule-of-thumb maximum runs that many framers use as a starting point: the run is half the span on a gable roof, so a 28 ft span is a 14 ft run and a 2×8 at 16 in on center fits it.

These are starting points, not code figures. The real maximum depends on the lumber species and grade, the snow load, whether the rafter has a ceiling joist tying it or a ridge beam carrying it, and the local code. A 2×8 that works at 16 in on center may not work at 24 in on center on the same span, and a low-slope roof needs deeper rafters than a steep roof on the same span because the load sits flatter. If your span is near the top of a row in the table, go one size up: the cost of the deeper board is small against the cost of a sagging roof. And always confirm the final size with the Lake County building department or a structural engineer before you cut. The rafter spacing and size post compares 2×6, 2×8, 2×10, and 2×12 in detail, including the 16 in and 24 in spacing choice and the spacing a metal roof shed needs.

How Many Rafters and How Much Lumber

Once the length and the size are set, the count and the board feet follow. A 40 ft building at 16 in on center needs 31 rafters per slope and 62 in total, as Example 1 shows. The same building at 24 in on center needs 21 per slope and 42 in total, which saves 20 boards but asks each board to carry more. The board feet are what the yard prices: 62 rafters of 2×8 at 16 ft 8 7/16 in each are 1,380.6 board feet, and at $1.10 to $1.90 per board foot the material runs $1,518 to $2,624. Order a few extra boards: one or two spares for a miscut, and one straight board to use as the pattern rafter. A crooked board makes a crooked pattern, and a crooked pattern makes a crooked roof, so pick the straightest board in the pile for the pattern and sight down every board before you cut it.

The sheathing goes on the rafters, so the rafter layout decides the sheathing layout too. Rafters at 16 in on center take standard 4 ft by 8 ft sheathing with the joints landing on rafters. If the rafters are at 24 in on center, the sheathing must be rated for the wider spacing. The roof sheathing calculator sizes the sheathing and the fasteners for the rafter layout you choose here, and it is the natural next step after the rafter count is set.

Five Mistakes That Waste Rafters

First, cutting the birdsmouth too deep. The seat cut must never take more than a third of the rafter depth: on a 2×8, which is 7.25 in deep, the seat cut must leave at least 4.8 in of wood above it. A birdsmouth cut too deep is the most common way a rafter fails, and it cannot be fixed by adding nails. Second, forgetting the ridge board allowance. A rafter cut to the ridge center length is 13/16 in too long on a 6/12 roof with a 1.5 in ridge board, and the ridge will not sit level. Third, measuring the run to the outside of the wall instead of to the wall plate. The run ends at the inside face of the wall plate, not at the siding, and the difference is the wall thickness. Fourth, forgetting the tail. A rafter cut without the tail ends flush with the wall, and the roof has no overhang at all. Fifth, cutting all the rafters before test-fitting the pattern. Cut one, set it in place, check the ridge height and the birdsmouth seat, and only then cut the rest. The rafter length mistakes post works through each of these with the fix for each one, including the birdsmouth depth rule and the right fasteners for rafter connections.

How to Read a Lumber Quote

Use the fairness checker in the calculator. Enter the lumber quote total, and it tells you whether the number sits below, inside, or above the typical material range for your board feet and lumber size. A quote below the range is not automatically a bargain: check that it covers the full board count, the right lumber size, and the grade you asked for, because a low total often means fewer boards or a lower grade. A quote inside the range is fair if it names the lumber size, the board count, and the grade in writing. A quote above the range is not automatically too high: a higher grade, longer boards, delivery, or the ridge board and hardware can explain it, but the quote should say so. What should worry you is a quote that names no size, no count, and no grade, because there is nothing to check it against. Remember that the checker covers material only. Labor to cut and install the rafters is a separate number, and the final quote for the whole job comes after an inspection of the roof, the span, and the existing framing.

Three questions to ask any contractor before you sign: first, what is the rafter length, the lumber size, and the spacing, and does the length match the span and pitch of your roof? Second, is the ridge board, the birdsmouth cut, and the tail included in the board length, or is the quote for the ridge-to-plate length only? Third, how will the crew handle the snow load and the ventilation, and will they check the finished ridge height before they cut the rest of the rafters? A contractor who answers all three clearly is the one to hire. A contractor who cannot answer them is guessing, and the roof frame is not the place to guess.

Related Guides

• How to Calculate Rafter Length
• Rafter Length Chart
• Hip Rafter Calculator
• Shed Rafter Length Calculator
• Rafter Spacing and Size
• Common Rafter vs Jack Rafter
• Rafter Length Mistakes
• Roof Pitch Calculator
• Roof Sheathing Calculator
• How to Calculate Rafter Length Using Roof Pitch: A Carpenter’s Guide
• All Roofing Calculators

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