Gambrel Roof Calculator

Gambrel Roof Angle Calculator

Enter one pitch and this calculator returns the other. Under the half-circle (barn) method, a gambrel roof's two pitches are locked together — the upper pitch is always exactly 45° shallower than the lower one — so a single input is all this page needs.

Half-circle method — one angle in, one angle out
°
Valid half-circle range: 46°–84°.
ft
Wall-plate to wall-plate width.

Result

Upper pitch φ
15.0°
3.2:12
Lower pitch, rise-in-12
20.8:12
θ = 60.0°
Upper pitch, rise-in-12
3.2:12
φ = θ − 45°
Lower rafter R1
12.00 ft
at W = 24.0 ft
Upper rafter R2
6.21 ft
Total height H
12.00 ft
H = W ÷ 2, always, under this method

θ − φ = 60.0° − 15.0° = 45.0°, for any lower pitch in range.

Why θ − φ Is Always 45°

This applies only to the half-circle method — where the knuckle and ridge are laid out on a semicircle struck from the centre of the span, the traditional way barns were framed with nothing more than a peg and a length of string. Under the alternative two-pitch method described on the home page, both pitches are chosen independently and this 45° relationship does not hold at all; a 60° lower pitch there can pair with anything from roughly 3° to just under 60°.

The short version of why it holds: every point on the semicircle, including the knuckle and the ridge, sees the span's two endpoints at a right angle (a circle theorem). That right angle splits into two smaller angles that share a term related to how far round the arc the knuckle sits — and that shared term cancels out when you subtract the upper pitch from the lower one, leaving a plain 45° no matter where the knuckle falls. The full derivation, with the diagram it needs to make sense, lives on the home page; this page exists to give the answer fast, not to re-prove it.

Reference

Lower Pitch to Upper Pitch, 46° to 84°

Every row below is the half-circle method's valid range, in 2° steps, each showing the resulting upper pitch and both angles converted to rise-in-12. Rafter lengths assume a 24 ft span; use the calculator above for any other width.

Gambrel lower and upper pitch pairs under the half-circle method
Lower θ Upper φ θ rise-in-12 φ rise-in-12 R1 (24 ft span) R2 (24 ft span)
46° 1° 12.4:12 0.2:12 16.67 ft 0.42 ft
48° 3° 13.3:12 0.6:12 16.06 ft 1.26 ft
50° 5° 14.3:12 1.0:12 15.43 ft 2.09 ft
52° 7° 15.4:12 1.5:12 14.78 ft 2.92 ft
54° 9° 16.5:12 1.9:12 14.11 ft 3.75 ft
56° 11° 17.8:12 2.3:12 13.42 ft 4.58 ft
58° 13° 19.2:12 2.8:12 12.72 ft 5.40 ft
60° 15° 20.8:12 3.2:12 12.00 ft 6.21 ft
62° 17° 22.6:12 3.7:12 11.27 ft 7.02 ft
64° 19° 24.6:12 4.1:12 10.52 ft 7.81 ft
66° 21° 27.0:12 4.6:12 9.76 ft 8.60 ft
68° 23° 29.7:12 5.1:12 8.99 ft 9.38 ft
70° 25° 33.0:12 5.6:12 8.21 ft 10.14 ft
72° 27° 36.9:12 6.1:12 7.42 ft 10.90 ft
74° 29° 41.8:12 6.7:12 6.62 ft 11.64 ft
76° 31° 48.1:12 7.2:12 5.81 ft 12.36 ft
78° 33° 56.5:12 7.8:12 4.99 ft 13.07 ft
80° 35° 68.1:12 8.4:12 4.17 ft 13.77 ft
82° 37° 85.4:12 9.0:12 3.34 ft 14.44 ft
84° 39° 114.2:12 9.7:12 2.51 ft 15.10 ft

Notice how fast the lower pitch's rise-in-12 climbs near the top of the range — 68.1:12 at 80° against 20.8:12 at 60° — while the upper pitch's rise-in-12 climbs much more gently, because the upper pitch never leaves the shallow end of the scale (1° to 39° across the whole table).

Two Ways to Set the Upper Pitch

A gambrel roof's upper pitch comes from one of two different processes, and it matters which one you are using before this calculator's answer applies.

Half-circle
φ = θ − 45°, fixed by the semicircle construction. This page's calculator and table use this method.
Two-pitch
φ is chosen independently, typically 15°–30°, along with a separate knuckle position. Use the home page calculator for this method.

Half-circle relationship

φ = θ − 45°

H = W ÷ 2

Holds for every knuckle position on the arc — H is fixed by the span alone, not by θ or φ individually.

If your design brief specifies both pitches directly rather than one pitch and a rule for the other, you are working under the two-pitch method — go to the pitch calculator to convert each figure separately, then the home page calculator to solve rafter lengths.

How to Find Your Gambrel Roof Angles

  1. Pick the method

    This calculator only applies to the half-circle (barn) method, where the knuckle and ridge sit on a semicircle struck from the centre of the span. If you are choosing both pitches independently instead, use the two-pitch method on the home page — the 45° rule below does not apply there.

  2. Enter the lower pitch θ

    Type the lower pitch in degrees, from 46° to 84°. Most gambrel trusses land between 55° and 70°; the traditional barn figure is 67.5°.

  3. Read the upper pitch φ

    The calculator returns φ = θ − 45° instantly, along with the rise-in-12 notation for both angles. A 60° lower pitch always returns a 15° upper pitch under this method.

  4. Add a span for rafter lengths

    Enter the building width W to see both rafter lengths, R1 and R2, and the total ridge height H, which under this method always equals exactly half the span.

Gambrel Roof Angle Questions

How do you find the upper pitch of a gambrel roof?

Under the half-circle method, subtract 45° from the lower pitch. A 60° lower pitch gives a 15° upper pitch; a 70° lower pitch gives a 25° upper pitch. The relationship holds for every lower pitch from 46° to 84°, because it comes from the geometry of a semicircle, not from a rule of thumb. Under the two-pitch method the upper pitch is not derived at all — it is chosen independently, typically between 15° and 30°, on the home page calculator.

Why is the difference between the two gambrel pitches always 45 degrees?

Because the half-circle construction puts the eave, the knuckle and the ridge all on the same semicircle. Every point on a circle forms a right angle with the diameter's endpoints (Thales' theorem), and working through the two resulting isosceles triangles shows the lower pitch and upper pitch always differ by exactly half of 90°. See the full geometric proof on the home page — it is a short argument, but it takes a diagram to follow, so it is not repeated here.

Does the 45 degree rule apply to every gambrel roof?

No — only to roofs built with the half-circle method. That is the traditional barn construction, where a compass or a string-and-peg can lay out the whole roof from the span alone. Roofs built with the two-pitch method choose both angles independently and are not bound by any fixed difference between them; a 60° lower pitch can pair with anything from about 3° up to just under 60°, not only 15°.

What is the upper pitch for a 67.5° lower pitch?

A 67.5° lower pitch pairs with a 22.5° upper pitch — 67.5 − 45 = 22.5. That is the traditional barn split, the result of dividing a semicircle into four equal 45° arcs. Converted to rise-in-12, that is roughly 29.0:12 over 5.0:12. See the full dimensions table for what those angles produce across a range of spans.

What rafter lengths does a 60° lower pitch give on a 24 ft span?

On a 24 ft span, a 60° lower pitch gives a 12.00 ft lower rafter and a 6.21 ft upper rafter, with a total ridge height of 12.00 ft — exactly half the span, as it always is under the half-circle method. Enter your own span in the calculator above to get the matching figures, or see the rafter length calculator for cut lengths that include overhang.