A gambrel roof is the classic barn profile: a steep lower slope, a break, and a shallow upper slope to the ridge. It exists because that shape buys a great deal of usable floor area under the roof without pushing the ridge any higher than a conventional gable would. This calculator gives you the geometry of one: both rafter lengths, the position of the break, the angles at every cut, and the surface area of the finished roof.
Arb Digital publishes this as a layout and planning tool. Our rafter length calculator handles a single-slope common rafter, along with hips and jacks; a gambrel is two slopes meeting at a break, and that break is what this page is about. The roof pitch calculator converts a slope between rise per 12, degrees and percentage grade, which is useful in both.
What This Gambrel Roof Calculator Does
It solves the half-section of the roof as two right triangles sitting on top of each other. From the wall plate, the lower slope runs out to the break; from the break, the upper slope runs to the ridge at the centre of the span. Each triangle has a horizontal run, a vertical rise and a hypotenuse, and the hypotenuse is the rafter.
You can drive it from either end. In pitch mode you give the two slopes and the tool tells you how high the ridge ends up. In height mode you give the ridge height and the break height and it tells you what slopes that implies. The second is usually the more practical one, because heights are what get constrained — by a planning restriction, by matching an existing building, or by the headroom you need at the centre of the upstairs floor.
It also reports the roof surface area over the building length, the interior angle at the break where the two rafters meet, the tail length that the overhang adds, and the shortening at the ridge for half the ridge board.
How to Use It
- Enter the span and the building length. Span is across the building; length is used only for the area figure.
- Set the horizontal run of the lower slope. This is where the break sits, and it has to be less than half the span.
- Choose pitch mode or height mode. Pitch mode reads the two slope boxes; height mode reads the total and break height boxes.
- Add the overhang and ridge thickness. These do not change the theoretical geometry, but they change the timber you cut.
- Read the angles. The slope angles are what you set a saw to; the break angle is what a gusset plate has to hold.
The Formula and How It Is Calculated
Take half the span. The lower run is what you entered; the upper run is half the span minus the lower run. Each slope's rise is its run multiplied by its slope ratio, and its rafter length is the square root of run squared plus rise squared. The total height is the sum of the two rises. The slope angle is the arctangent of rise over run, and the interior angle at the break is 180 degrees minus the difference between the two slope angles.
In height mode the arithmetic runs backwards: the lower rise is the break height, the upper rise is the total height minus the break height, and each slope ratio comes out as rise divided by run.
Roof surface area is 2 × (lower rafter + upper rafter) × building length, the two coming from the two sides of the roof. The tail length added by an overhang is the horizontal overhang divided by the cosine of the lower slope angle. The ridge shortening on the upper rafter is half the ridge thickness divided by the cosine of the upper slope angle.
Worked example against the loaded values. A 24 foot span gives a 12 foot half-span. With a 6 foot lower run at 18 in 12, the lower rise is 9 feet and the lower rafter is √(36 + 81) = 10.817 feet, at 56.31 degrees. The upper run is 12 − 6 = 6 feet at 6 in 12, so the upper rise is 3 feet and the upper rafter is √(36 + 9) = 6.708 feet, at 26.57 degrees. Total height is 12 feet, the break sits 6 feet in and 9 feet up, and the interior angle there is 180 − (56.31 − 26.57) = 150.26 degrees. Over a 40 foot building the roof surface is 2 × 17.525 × 40 = 1,402 square feet before overhangs. A 1 foot overhang adds 1.803 feet of tail to each lower rafter.
Why the Gambrel Shape Exists
Compare the worked example with a plain gable of the same span and ridge height. A 24 foot span at 12 feet of rise is a 12 in 12 gable: a single straight slope from plate to ridge at 45 degrees. Now look at the floor area you could stand up in under each.
Under the gable, the roof plane cuts in at 45 degrees from the eave, so the width where you have, say, six feet of headroom is narrow and the walls slope away immediately. Under the gambrel, the lower slope at 56 degrees is nearly vertical for the first six feet of run, so the space at knee-wall height is twelve feet wide and the ceiling only starts closing in above the break line, three feet below the ridge.
That is the whole point of the shape. It converts an attic into a floor. Historically it was a hay loft; on a modern house or garage it is a room, and the break line is where the collar or the ceiling usually goes. The trade-off is complexity: two sets of rafters, two sets of cuts, a joint at the break that has to be engineered, and a valley-free but awkward junction wherever a dormer meets it.
The Break Is a Structural Joint, Not Just a Cut
This is the part a geometry calculator cannot answer, and it is the part that matters most.
At the break, the two rafters meet at an angle and the roof wants to spread. On the lower, steep slope the load pushes mostly straight down. On the upper, shallow slope a much larger share becomes horizontal thrust. Where those two meet is a kink in the load path, and the joint has to resist it. Traditionally that is done with a gusset plate on each side, a purlin plate running along the break line carried on posts, or a collar tie at the break level. Modern gambrel buildings are very often built with engineered trusses precisely because that joint and the ties around it are worth designing rather than improvising. Timber design in the United States follows the American Wood Council National Design Specification for Wood Construction, applied through whichever building code your jurisdiction has adopted from the ICC Digital Codes library, with local amendments on top.
None of that is decided by this page. This page gives lengths and angles. Member sizes, the joint at the break, the ties that stop the walls spreading and the connections at the plate are structural design. Our wood beam span calculator runs bending, shear and deflection checks on a timber member, and the beam load calculator gives reactions and moments, but a gambrel frame with a break joint and a knee wall is a frame, not an isolated beam, and it belongs with a licensed engineer or an engineered truss supplier. Load cases matter too: the shallow upper slope collects far more snow than the steep lower one, which our snow load calculator covers.
Theoretical Length Against the Board You Cut
Every length on this page is a theoretical dimension between the intersection points of the roof's centrelines. Three things happen between that and the timber.
First, the ridge deduction. Two upper rafters meet at the centre of the span, but a ridge board sits between them, so each rafter is shortened by half the ridge thickness measured along its own slope. The tool reports that shortening.
Second, the birdsmouth. The lower rafter does not meet the wall at a point; it is notched to sit on the plate, and where you measure from on the plate depends on how the birdsmouth is laid out. Getting this convention right is the single most common source of a whole roof being consistently wrong by an inch.
Third, the tail. The overhang length reported here is a horizontal projection converted to a length along the slope. The actual tail also depends on how you cut the end — plumb, square, or plumb and level for a soffit — and on whether a fascia is applied over it.
Cut one rafter, offer it up, and check it before you cut forty. That advice is older than any calculator and it has not stopped being right.
Estimating the Covering From the Area
The surface area figure is the starting point for materials, not the finished quantity. It excludes the overhang unless you widen the span you enter, it assumes a plain rectangle with no dormers, hips or projections, and it makes no allowance for waste, which on a gambrel is higher than on a simple gable because of the extra course of cuts at the break line.
The break also introduces a detail the plain area hides: the transition itself needs flashing or a proper closure, and the shallow upper slope may be at or below the minimum slope for the covering you have chosen. A shingle that is fine at 18 in 12 on the lower slope may need a different underlayment specification, or a different product altogether, at 6 in 12 above the break. Take the area from here and put it through our roofing calculator for squares, bundles, underlayment and waste.
Arb Digital builds free calculators and interactive tools that earn search traffic for roofing, timber frame and construction businesses. Browse the full library, or tell us what your customers keep asking you to work out.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Setting the lower run at or beyond half the span — there is then no upper slope left, and the roof is a steep gable rather than a gambrel.
- Treating the break as a carpentry detail — it is a change in the load path, and the joint, the ties and the knee wall need designing.
- Cutting to the theoretical length — the ridge deduction and the birdsmouth both move the real dimension, and the error repeats on every rafter.
- Forgetting the shallow slope collects more snow — the upper plane sheds far less than the steep lower one, and the load case differs across the break.
- Assuming one covering suits both slopes — the upper slope may fall below the minimum pitch a product is rated for, which is a specification issue, not a quantity one.
Related Free Tools From Arb Digital
Pair this with the rafter length calculator for single-slope, hip and jack rafters, the roof pitch calculator for slope conversions, the roofing calculator for coverings and waste, the snow load calculator for the load on each plane and the birdsmouth cut calculator for the seat cut at the plate. The full free online tools hub lists every calculator we publish.
Frequently Asked Questions
The rafter length calculator solves a single straight slope from plate to ridge, along with hip and jack rafters. A gambrel has two slopes meeting at a break, so it needs two rafter solutions, the position and height of that break, and the interior angle where the two meet.
The tool does not prescribe a position, because it is a design decision about the room underneath. Moving the break outward widens the upstairs floor and steepens nothing; moving it inward lowers the shoulders. What it must be is less than half the span, or there is no upper slope.
Many traditional barns were laid out from a semicircle, with the four rafters forming equal chords, which produces slopes near 60 and 30 degrees. That is a drafting method rather than a rule, and this tool lets you set any two slopes rather than assuming one convention.
No. It gives lengths, angles and areas only. Member sizes, the joint at the break, the ties that resist spreading and the connection at the plate are structural design work for a licensed engineer or an engineered truss supplier.
Because a shallow plane sheds far less than a steep one, so the two slopes of a gambrel carry different snow loads, and drift can build at the break where the slope changes. Load cases across the break are a design matter, not a geometry one.
Not directly. They are theoretical centreline dimensions. Subtract half the ridge thickness along the slope at the top, lay out the birdsmouth consistently at the plate, then cut one rafter and test-fit it before cutting the rest.
Yes. Switch the unit selector and all lengths are read and reported in metres. Pitch can still be entered as rise per 12 because that is a ratio, or you can switch the pitch selector to degrees.
No. The surface area covers the roof between the wall lines over the building length you entered. The overhang is reported separately as a tail length, and dormers, projections and waste are not included at all.
This tool computes roof geometry from dimensions you supply, for layout and planning only. It is not a structural design, it does not size rafters or the joint at the break, and it does not check any load case. Framing, connections and bracing for a gambrel roof must be designed by a licensed engineer or supplied as engineered trusses, and approved by the building department having jurisdiction.
