Gambrel Roof Calculator

About the Gambrel Roof Calculator

A free tool for working out rafter lengths, pitch angles, total height, roof area and attic volume for gambrel and barn roofs — with the formulas behind every figure shown on the page, not buried in a black box.

What this calculator does

Type in a building width, a lower pitch, an upper pitch and where the knuckle (the bend partway up the roof) sits along the half-span, and the gambrel roof calculator returns the lower and upper rafter lengths, the total ridge height, the roof area including overhang, and the attic volume enclosed underneath. Every one of those outputs is the direct result of trigonometry on the inputs you gave it — there is no lookup table, no rounding to the nearest stock size, and no hidden safety margin baked in silently. Change the lower pitch by one degree and every downstream number recomputes from scratch, live, using the identical functions at build time and in the browser.

Beyond the calculator itself, the site works through the framing sequence in more detail on dedicated pages — truss design for how the lower and upper rafters, purlin and collar tie fit together at the knuckle, and the framing guide for seat cuts, heel cuts and how the truss lands on the wall plate. Those pages, and the roughly two dozen others linked from the HTML sitemap, all share the same underlying geometry engine as the homepage calculator.

Two calculation methods, not one

A gambrel roof has two different, equally legitimate ways to arrive at a cross-section, and the calculator supports both as tabs rather than picking one for you.

Two-Pitch
You choose the lower pitch angle, the upper pitch angle, and the knuckle position along the half-span independently — three free inputs. Total height is whatever falls out of those three choices: H = y1 + y2, the sum of the rise of the lower rafter and the rise of the upper rafter. This is the method to reach for when you have a target ridge height, a headroom figure to hit inside the attic, or a timber length you need to match.
Half-Circle
You choose one pitch angle; the upper pitch is locked exactly 45° shallower than the lower one, because the knuckle and the ridge are both constrained to sit on a semicircle of radius equal to half the building width. The consequence is that total height always comes out to exactly H = W / 2, regardless of which lower pitch you pick — only the knuckle position moves along that fixed semicircle. This is the traditional barn-roof construction, and the one to use when the classic rounded gambrel silhouette matters more than hitting a specific height.

Both methods are exact solutions of the same right-triangle geometry, worked from the same span and rafter-length relationships — neither one is an approximation of the other. The Methods section on the homepage walks through both derivations with a worked numeric example.

Accuracy and engineering disclaimer

Rafter lengths, pitch angles, roof area and attic volume for gambrel and barn roofs are all worked from the same formulas the calculator uses, with the geometry shown rather than hidden. Given accurate inputs, the trigonometry is exact. What it cannot account for is your local building code, wind and snow load requirements specific to your site, lumber grade and species, or the judgment of a licensed engineer.

Results are design aids, not stamped engineering. Check span tables, load requirements and structural sizing against your local code before you build.

Why this site exists

Most roof calculators online return a single number and stop — no working shown, no way to check it, no way to adapt it to a case the tool didn't anticipate. That is backwards for a problem that is, underneath, plain geometry: a span, two pitch angles and a knuckle position determine everything else through triangles anyone can verify with a framing square. This site shows that math instead of hiding it, on every page, so the same formulas that drive the sliders on the homepage are printed right below them.

That's also why there are dedicated pages for rafter length, pitch, angles, area, sheathing, snow load, dormers, and the rest rather than one page trying to cover everything — each one is worked from the same small set of functions, so the numbers never drift out of agreement with each other as the site grows.

Frequently asked questions

How accurate is this calculator?
The rafter lengths, pitch angles, height, roof area and attic volume are all solved from the same trigonometric formulas shown on the homepage — not looked up from a table or approximated. Given the same span, pitch and knuckle position, the numbers will match a framing square or CAD model to within rounding. What the calculator cannot know is your local code, your actual lumber grade, or site conditions, which is why the results are design aids, not stamped engineering.
What's the difference between the two methods?
The two-pitch method lets you choose the lower pitch, the upper pitch and where the knuckle sits along the half-span independently — three free inputs, with total height falling out of those choices. The half-circle method locks the upper pitch 45° below the lower pitch and forces the ridge height to equal exactly half the building width, because the knuckle and ridge are constrained to sit on a semicircle struck from the center of the wall-plate line. Two-pitch gives you control over height; half-circle gives you the traditional barn proportion.
Can I use this for a real building project?
Yes, as a starting point for laying out rafters, ordering lumber and roofing material, and checking that a design will clear the headroom you need. It is not a substitute for a stamped engineering drawing, and snow load, wind load and span-table lumber sizing should still be checked against your local building code before you cut anything.
Why show the formulas instead of just giving an answer?
Because a number with no derivation is not verifiable. Every figure on this site is worked from the same formulas the calculator uses, with the geometry shown rather than hidden, so you can check the math yourself, adapt it to a case the calculator does not cover, or just understand why moving the knuckle changes the ridge height the way it does.