What is a gambrel roof?
A gambrel roof is a two-slope roof on each side of the ridge: a steep lower slope that gives headroom in the attic and a shallow upper slope above it. It is the classic barn roof, also used on sheds, garages and Dutch Colonial houses. This barn roof calculator works out both slopes from the building width.
The half-circle gambrel
The classic barn gambrel puts all four rafter joints on a half circle whose diameter is the building width: the eaves, the two knees and the ridge sit on the arc at 45° steps. That gives a 67.5° lower slope, a 22.5° upper slope and four rafters of equal length, 0.765 times half the span. It is the default in the calculator because it is easy to lay out with a string and a nail on the shop floor.
| Width | Ridge height | Knee height | Each rafter |
|---|---|---|---|
| 8′ 0″ | 4′ 0″ | 2′ 9-15/16″ | 3′ 3/4″ |
| 10′ 0″ | 5′ 0″ | 3′ 6-7/16″ | 3′ 9-15/16″ |
| 12′ 0″ | 6′ 0″ | 4′ 2-15/16″ | 4′ 7-1/8″ |
| 16′ 0″ | 8′ 0″ | 5′ 7-7/8″ | 6′ 1-1/2″ |
| 20′ 0″ | 10′ 0″ | 7′ 7/8″ | 7′ 7-7/8″ |
| 24′ 0″ | 12′ 0″ | 8′ 5-13/16″ | 9′ 2-3/16″ |
Other gambrel angles
Another common pair is 60° and 30°, and some builders set the knee height first to get headroom in a loft. Change the angles and, under More options, the width of the lower section. The upper slope must still suit the roofing: shingles need at least 2/12 (9.5°)[2], so a 22.5° upper slope (4.97/12) is fine without double underlayment.
Cutting the trusses
- Knee joint. Each rafter is mitred at half the angle between the slopes, (lower − upper) ÷ 2 from square: 22.5° on the half-circle layout. Join with plywood gussets on both faces.
- Ridge. The upper rafters meet at a plumb cut, (90° − upper angle) from the rafter edge, against a ridge board or each other with a gusset.
- Seat. The lower rafter sits on the wall plate with a birdsmouth or a gusset.
Build one truss on a flat floor, check it against the diagram, and use it as the pattern. For a single-slope outbuilding the shed roof pitch calculator is simpler, and the rafter calculator handles a regular gable.
Sizing gambrel rafters
Each slope is a rafter with its own pitch and run, so size it from the rafter span tables for that slope's horizontal span[3]. The IRC measures rafter spans on the horizontal projection[1]. The steep lower rafters carry less snow but more wind. Count the panels or squares with the roof calculator one slope at a time.
Frequently asked questions
Can I use this as a barn roof calculator?
Yes. A barn roof is usually a gambrel: enter the barn width and the two slope angles to get both rafter lengths, the knee and ridge heights and the gusset angles.
What angles are used for a gambrel roof?
The half-circle layout uses 67.5° for the lower slope and 22.5° for the upper slope. 60°/30° is another common pair.
How do I calculate a gambrel roof?
Split each side into a lower and an upper section. Rise = level width × tan(angle) and rafter length = level width ÷ cos(angle) for each.
How tall is a gambrel roof on a 16 ft shed?
With the half-circle layout the ridge is half the width above the walls: 8 ft.
What is the pitch of a 22.5° roof?
4.97/12.