Gambrel Roof Calculator for 14 Feet

This calculator works out the rafter lengths, roof height, and material board feet for a gambrel roof with a 14-foot span. You enter the total width (14 ft by default), the pitch angles for the upper and lower slopes, and the overhang; you get back the lower and upper rafter lengths, the peak height, and the total board feet needed for one side. The result is the exact geometric answer for the dimensions you give, so you can order lumber with confidence.

Formula

The gambrel roof is a five-sided polygon: two lower slopes that are steeper, and two upper slopes that are shallower, meeting at a central ridge. For a symmetrical gambrel (the usual case), each half is a pair of right triangles.

Let S be the total span (ft), O the overhang (ft), θ_L the lower slope angle (degrees), and θ_U the upper slope angle (degrees). The horizontal run of the lower slope is S/2 + O (half the span plus the overhang), and the run of the upper slope is S/2.

• Lower rafter length = (S/2 + O) / cos(θ_L)
• Upper rafter length = (S/2) / cos(θ_U)
• Lower rise = (S/2) × tan(θ_L)
• Upper rise = (S/2) × tan(θ_U)
• Peak height = lower rise + upper rise

All angles are measured from horizontal. The cosine and tangent functions are standard trigonometric ratios; your calculator must be in degree mode for these to work.

Worked Example

Using the default values: span = 14 ft, lower pitch = 30°, upper pitch = 20°, overhang = 1 ft.

1. Half span = 14/2 = 7 ft. Lower run = 7 + 1 = 8 ft.
2. Lower rafter length = 8 / cos(30°) = 8 / 0.8660 = 9.24 ft.
3. Upper run = 7 ft. Upper rafter length = 7 / cos(20°) = 7 / 0.9397 = 7.45 ft.
4. Lower rise = 7 × tan(30°) = 7 × 0.5774 = 4.04 ft.
5. Upper rise = 7 × tan(20°) = 7 × 0.3640 = 2.55 ft.
6. Peak height = 4.04 + 2.55 = 6.59 ft.
7. Board feet per side (using 2×4 lumber): (9.24 + 7.45) × 2 × 4 / 12 = 16.69 × 8 / 12 = 11.13, rounded up to 12 board-feet.

The calculator returns 9.24 ft, 7.45 ft, 6.59 ft, and 12 board-feet, matching these steps.

Why Use a Gambrel Roof?

The gambrel shape is popular for barns, sheds, and workshops because it creates a nearly full-height interior attic or loft. Compared to a simple gable, the steeper lower slope sheds rain and snow well, while the shallower upper slope reduces the total roof height for a given span. That means you get more usable headroom without building a towering peak.

For a 14-foot span, the gambrel is a good fit for a small barn or a large shed. The exact angles you choose affect both the look and the usable space. A common choice is 30° lower and 20° upper, as in the default, which gives a balanced profile. Some builders use 35° lower and 15° upper for a more dramatic shape, but that increases the lower rafter length and the overall height.

This calculator gives you the pure geometry. It does not account for lumber thickness, ridge board size, or birdsmouth cuts—those add a few inches to each rafter. For a professional build, add 1–2% for cutting waste and always check with a local framing square or a qualified builder.

How to Choose Your Angles

Your choice of lower and upper pitch depends on the climate, the desired headroom, and the roof material.

• Snow load: Steeper lower slopes (30–40°) let snow slide off more easily. Shallower upper slopes (15–25°) still accumulate snow, but the total area is smaller.
• Headroom: The lower rise determines the height of the loft walls. For a 14-ft span, a 30° lower pitch gives about 4 ft of wall height at the kneewall, which is enough for a small storage loft.
• Material: Asphalt shingles work on any slope above 2:12 (about 9.5°). Metal roofing can go lower, but the gambrel’s lower slope is usually steep enough.
• Aesthetics: The ratio of lower to upper pitch changes the silhouette. A 2:1 ratio (e.g., 30° and 15°) looks classic; a 1.5:1 ratio looks more modern.

Keep both angles between 10° and 60° for structural sense. The calculator will accept up to 89°, but a lower slope above 60° is essentially a wall, and an upper slope below 10° may not shed water well.

Common Mistakes and Misconceptions

A frequent error is using the total span instead of half the span for the run. Remember, each rafter only covers half the roof. Another is mixing degrees and radians—always work in degrees. Also, the overhang adds to the lower rafter length, but not to the upper rafter. If you forget the overhang, your lower rafter will be short by exactly that amount.

A common misconception is that the peak height equals the upper rise plus the lower rise, which is correct, but some people mistakenly use the full span for the rise calculation. That would double the height. Always use half the span for both rises.

Finally, board feet is a volume measure (1 board foot = 1 ft × 1 ft × 1 in). The calculator uses nominal 2×4 lumber (2 in × 4 in) and multiplies the total rafter length by the cross-section area, then divides by 12. If you use different lumber, adjust the formula accordingly—for example, 2×6 would be 2×6/12 = 1.0 board-ft per linear foot.

Cost and Material Considerations

For a 14-ft gambrel, you will need two lower rafters and two upper rafters per truss, plus a ridge board, collar ties, and sheathing. The calculator gives the length per side, so multiply by 2 for the total rafter length per truss. If you space trusses 24 inches on center, a 14-ft wide shed that is 12 ft long would need about 7 trusses (12 ft / 2 ft + 1).

Lumber is sold in 8, 10, 12, 16, and 20-foot lengths. A 9.24-ft lower rafter means you need a 10-ft board; a 7.45-ft upper rafter needs an 8-ft board. The board-feet output helps you estimate volume, but you will buy by the piece. Always add 10% for waste and mistakes.

Prices vary by region and lumber grade, so this calculator does not include cost. You can multiply the total board feet by your local price per board-foot to get a rough material cost. For a 14-ft span, expect to use roughly 100–150 board-feet for the entire roof framing, depending on truss spacing and lumber size.

Safety and Structural Notes

This calculator is for geometric layout only. It does not calculate load-bearing capacity, rafter sizing, or connection details. A gambrel roof must withstand dead load (roofing, sheathing) and live load (snow, wind). The angles affect how loads are transferred: steeper lower slopes push outward more, so you need stronger wall connections or collar ties.

For a 14-ft span, typical rafter spacing is 16 or 24 inches on center, but the correct size (2×4, 2×6, etc.) depends on the snow load in your area. A 2×4 rafter may be fine for a small shed with light roofing, but a 2×6 or larger is often required for a barn. Always consult a structural engineer or local building code for rafter sizing and connections.

When cutting rafters, use a framing square or a speed square to mark the plumb cut and seat cut. The birdsmouth should not exceed one-third of the rafter depth, or it weakens the rafter. Wear safety glasses and use proper supports when working at height. If you are not experienced with roof framing, hire a professional.

Frequently Asked Questions

What is the best pitch for a 14-foot gambrel roof? The best pitch depends on your climate and use. A 30° lower and 20° upper is a balanced default that works for most sheds. For heavy snow, go steeper (35–40° lower) to shed snow. For more headroom, increase the lower pitch, but that raises the peak.

How do I measure the span for a gambrel roof? The span is the distance between the outside edges of the wall plates (the top of the walls). Measure from the outside of one wall to the outside of the opposite wall. Do not include the overhang in the span—the overhang is added separately.

Can I use this calculator for a metal roof? Yes, the geometry is the same. Metal roofing can be installed on lower slopes, but the minimum slope depends on the specific panel and manufacturer. Check the panel’s instructions for the minimum pitch, usually 3:12 (about 14°) for standing seam.

Does the ridge board affect rafter length? Yes, a ridge board takes a small amount of space. If you use a 1.5-inch-thick ridge board, subtract half of that (0.75 in) from the upper run before calculating the upper rafter length. This calculator ignores the ridge board, so add a few inches to your cuts for safety.

How much headroom will I get in the loft? The headroom at the kneewall is the lower rise. For a 14-ft span with a 30° lower pitch, the lower rise is about 4 ft. The peak height is about 6.6 ft, so you get a walkable loft in the center. To get more headroom, increase the lower pitch or the span.

What is the difference between a gambrel and a mansard roof? A gambrel has two slopes on each side, while a mansard has four slopes (curved or straight) on all sides. A gambrel is essentially a two-sided mansard. The gambrel is simpler and more common for barns and sheds; the mansard is used on full buildings to add a usable top floor.

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in span | Total span | ft | 14 | 0 | 100
in lower_pitch | Lower slope angle | deg | 30 | 0 | 89
in upper_pitch | Upper slope angle | deg | 20 | 0 | 89
in overhang | Overhang | ft | 1 | 0 | 10
out lower_len | Lower rafter length (one side) | ft | (span/2 + overhang) / cosd(lower_pitch) | 2
out upper_len | Upper rafter length (one side) | ft | (span/2) / cosd(upper_pitch) | 2
out height | Peak height above wall | ft | (span/2) * tand(lower_pitch) + (span/2) * tand(upper_pitch) | 2
out boardft | Board feet per side (2x4) | board-ft | ceil(round((lower_len + upper_len) * 2 * 4 / 12, 6)) | 0