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.