Gambrel Roof Calculator: Calculate Angles, Rafters and Roof Area

Quick Answer

Use the gambrel roof calculator above to estimate:

• Upper and lower roof angles
• Upper and lower roof pitches
• Rafter section lengths
• Roof rise and ridge height
• Gambrel break-point location
• Total roof surface area
• Required number of trusses
• Approximate attic area and volume

A gambrel roof has two slopes on each side. The lower section is steeper, while the upper section has a shallower pitch.

For one side of the roof:

Lower run + Upper run = Building width ÷ 2

The rise of each section is:

Rise = Run × tan(Angle)

The rafter length of each section is:

Rafter length = Run ÷ cos(Angle)

The calculator determines the roof’s geometry only. Truss member sizes, connector plates, bracing, bearings and load capacity must come from approved plans or an engineered truss design.

How to Use the Gambrel Roof Calculator

Enter the dimensions requested by the calculator.

1. Enter the Building Width

Measure the horizontal distance between the outside bearing walls.

For a symmetrical gambrel roof:

Half-span = Building width ÷ 2

A 12-foot-wide shed has:

12 ÷ 2 = 6 feet of horizontal run on each side

Do not include the horizontal eave overhang in the structural building width unless the calculator specifically requests the complete roof width.

2. Enter the Building Length

Measure the building from one gable end to the other.

The length is mainly used to calculate:

• Total roof square footage
• Number of trusses
• Sheathing requirements
• Roofing-material quantities

If the roof extends beyond both gable walls, add the end overhangs separately.

3. Enter the Upper Roof Angle or Pitch

The upper section runs from the ridge to the gambrel joint.

It is normally shallower than the lower section.

Depending on the calculator, enter it as:

• Degrees
• Rise per 12 inches
• Percentage slope

4. Enter the Lower Roof Angle or Pitch

The lower section runs from the gambrel joint to the outside wall.

Its angle must be steeper than the upper angle for the shape to remain a gambrel roof.

5. Enter One Run or Break-Point Position

To solve a custom design, the calculator needs to know where the upper and lower sections meet.

You may enter:

• Lower horizontal run
• Upper horizontal run
• Distance of the joint from the outside wall
• Percentage of the half-span assigned to either section

Once one run is known:

Other run = Half-span − Known run

6. Enter the Overhangs

There may be two types of overhang:

• Eave overhang: Extension beyond the side walls
• Gable overhang: Extension beyond each end wall

Check whether the eave overhang is measured horizontally or along the sloped rafter. Those are not the same length.

7. Select Imperial or Metric Units

Use one consistent unit system throughout the calculation.

Imperial inputs may include:

• Feet
• Inches
• Feet and fractional inches

Metric inputs may include:

• Millimetres
• Centimetres
• Metres

Do not enter the building width in feet and the rafter run in inches unless the calculator converts them automatically. Buildings already contain enough opportunities for surprise.

Gambrel Roof Dimensions Explained

A symmetrical gambrel roof can be divided into four right triangles:

• Two lower roof sections
• Two upper roof sections

The main dimensions are:

For one side:

Lower run + Upper run = Half-span

For the complete roof height:

Lower rise + Upper rise = Total roof rise

Gambrel Roof Calculation Formulas

Let:

• W = Building width
• L = Building length
• x₁ = Lower run
• x₂ = Upper run
• θ = Lower angle
• φ = Upper angle
• y₁ = Lower rise
• y₂ = Upper rise
• R₁ = Lower rafter length
• R₂ = Upper rafter length

Half-Span

Half-span = W ÷ 2

Upper Run

When the lower run is known:

x₂ = W ÷ 2 − x₁

Lower Run

When the upper run is known:

x₁ = W ÷ 2 − x₂

Lower Rise

y₁ = x₁ × tan(θ)

Upper Rise

y₂ = x₂ × tan(φ)

Total Roof Rise

Total rise = y₁ + y₂

Lower Rafter Length

R₁ = x₁ ÷ cos(θ)

The Pythagorean form is:

R₁ = √(x₁² + y₁²)

Upper Rafter Length

R₂ = x₂ ÷ cos(φ)

Or:

R₂ = √(x₂² + y₂²)

Total Sloped Length per Side

Sloped length per side = R₁ + R₂

The complete roof has two identical sides:

Total sloped cross-section = 2 × (R₁ + R₂)

Gambrel Roof Calculation Example

Assume:

• Building width: 12 ft
• Building length: 20 ft
• Lower run: 2 ft
• Upper run: 4 ft
• Lower angle: 60°
• Upper angle: 30°
• No overhangs

Lower Rise

2 × tan(60°) = 3.46 ft

Upper Rise

4 × tan(30°) = 2.31 ft

Total Roof Rise

3.46 + 2.31 = 5.77 ft

Lower Rafter

2 ÷ cos(60°) = 4.00 ft

Upper Rafter

4 ÷ cos(30°) = 4.62 ft

Total Rafter Length per Side

4.00 + 4.62 = 8.62 ft

Roof Area

2 × 20 × 8.62 = 344.8 sq ft

The roof has approximately:

• 5.77 ft of total rise
• 4.00 ft lower rafter sections
• 4.62 ft upper rafter sections
• 344.8 sq ft of roof surface before overhangs and waste

Gambrel Roof Pitch Calculator

Roof pitch can be expressed as an angle or as vertical rise per 12 inches of horizontal run.

Convert Angle to Pitch

Pitch per 12 = tan(Angle) × 12

Example for 30°:

tan(30°) × 12 = 6.93

A 30-degree roof angle is approximately:

6.93:12

Convert Pitch to Angle

Angle = arctan(Rise ÷ 12)

Example for a 6:12 pitch:

arctan(6 ÷ 12) = 26.57°

Gambrel Roof Angles Chart

Steep lower slopes can have pitch ratios greater than 12:12. That does not mean the calculation is wrong. It means the roof rises more than 12 inches for every 12 inches of horizontal run.

Are There Standard Gambrel Roof Angles?

There is no mandatory angle combination for every gambrel roof.

The correct angles depend on:

• Building width
• Desired ridge height
• Attic headroom
• Roofing material
• Snow and wind loads
• Truss design
• Architectural appearance
• Local building requirements

A useful geometric layout uses:

• 60° lower sections
• 30° upper sections
• Equal-length upper and lower rafter sections

This creates a roof rise equal to half the building width.

It is an example, not a structural specification.

Another layout may use a much shallower upper section or move the gambrel joint farther toward the outside wall to create more interior headroom.

Equal-Rafter 60° and 30° Gambrel Formula

When all four roof sections have equal sloped lengths:

Rafter section length = Half-span ÷ [cos(60°) + cos(30°)]

10-Foot-Wide Roof

• Half-span: 5.00 ft
• Each rafter section: 3.66 ft
• Lower run: 1.83 ft
• Upper run: 3.17 ft
• Lower rise: 3.17 ft
• Upper rise: 1.83 ft
• Total roof rise: 5.00 ft

12-Foot-Wide Roof

• Half-span: 6.00 ft
• Each rafter section: 4.39 ft
• Lower run: 2.20 ft
• Upper run: 3.80 ft
• Total roof rise: 6.00 ft

16-Foot-Wide Roof

• Half-span: 8.00 ft
• Each rafter section: 5.86 ft
• Lower run: 2.93 ft
• Upper run: 5.07 ft
• Total roof rise: 8.00 ft

20-Foot-Wide Roof

• Half-span: 10.00 ft
• Each rafter section: 7.32 ft
• Lower run: 3.66 ft
• Upper run: 6.34 ft
• Total roof rise: 10.00 ft

This table provides layout geometry only. It does not determine suitable lumber, gusset plates, fasteners or structural capacity.

Gambrel Roof Angles for a 10-Foot-Wide Building

A 10-foot building does not require one fixed pair of angles.

The width determines the available horizontal span. The chosen roof height and joint position determine the angles.

For the equal-rafter example above:

• Lower angle: 60°
• Upper angle: 30°
• Roof rise: 5 ft
• Each section: approximately 3.66 ft long

A lower roof rise could use shallower slopes. A taller roof could use steeper lower sections or move the break point.

Two 10-foot-wide buildings can therefore have completely different gambrel profiles while sharing the same wall span.

12-Foot Gambrel Roof Truss Calculator

For a 12-foot span:

Half-span = 6 ft

The two horizontal runs must total 6 feet on each side.

Example custom layout:

• Lower run: 2 ft
• Upper run: 4 ft
• Lower angle: 60°
• Upper angle: 30°

Results:

• Lower rise: 3.46 ft
• Upper rise: 2.31 ft
• Total rise: 5.77 ft
• Lower rafter: 4.00 ft
• Upper rafter: 4.62 ft

Changing the joint to a 3-foot lower run and 3-foot upper run would create different rafter lengths and a different roof height, despite the same 12-foot span.

16-Foot Gambrel Roof Truss Calculator

For a 16-foot span:

Half-span = 8 ft

Example with equal 60° and 30° sections:

• Each rafter section: 5.86 ft
• Lower run: 2.93 ft
• Upper run: 5.07 ft
• Total rise: 8 ft

These measurements can help create a full-size layout diagram or preliminary material estimate.

They cannot establish:

• Lumber species
• Lumber grade
• Chord size
• Web arrangement
• Gusset dimensions
• Connector capacity
• Allowable snow load
• Wind resistance
• Required bracing

Those values belong in the engineered truss documentation.

How to Calculate Gambrel Roof Square Footage

Roof square footage uses the sloped rafter lengths rather than the building’s flat footprint.

Without overhangs:

Roof area = 2 × Building length × (Lower rafter + Upper rafter)

Example

• Length: 24 ft
• Lower rafter: 5 ft
• Upper rafter: 6 ft

Area = 2 × 24 × (5 + 6)

Area = 528 sq ft

The roof surface covers 528 square feet before overhangs.

Roof Area With Gable and Eave Overhangs

Let:

• L = Building length
• g = Gable overhang at each end
• e = Horizontal eave overhang
• θ = Lower roof angle

Effective Roof Length

Effective length = L + 2g

Sloped Eave Extension

When the eave overhang is measured horizontally:

Sloped eave extension = e ÷ cos(θ)

Complete Roof Area

Roof area = 2 × Effective length × (R₁ + R₂ + Sloped eave extension)

If the calculator asks for the overhang measured directly along the rafter, add that sloped dimension without converting it.

Example

• Building length: 24 ft
• Gable overhang: 1 ft at each end
• Lower rafter: 5 ft
• Upper rafter: 6 ft
• Horizontal eave overhang: 1 ft
• Lower angle: 60°

Effective length:

24 + 2 = 26 ft

Sloped eave extension:

1 ÷ cos(60°) = 2 ft

Roof area:

2 × 26 × (5 + 6 + 2) = 676 sq ft

Use the roofing manufacturer’s recommended waste allowance when estimating shingles, panels or underlayment.

How Many Roofing Squares Are Needed?

Roofing materials are often sold by the roofing square.

1 roofing square = 100 sq ft

Use:

Roofing squares = Roof area ÷ 100

Example:

676 ÷ 100 = 6.76 roofing squares

This is the net area before any project-specific waste allowance.

Gambrel Roof Truss Count

To estimate the number of trusses:

Truss count = Ceiling(Building length ÷ Truss spacing) + 1

The spacing and building length must use the same units.

Example at 24-Inch Spacing

• Building length: 24 ft
• Spacing: 24 inches or 2 ft

24 ÷ 2 = 12 spaces

12 + 1 = 13 trusses

Example at 16-Inch Spacing

• Building length: 24 ft
• Spacing: 16 inches or 1.333 ft

24 ÷ 1.333 = 18 spaces

18 + 1 = 19 trusses

Do not choose the spacing based only on material savings. The required truss spacing must match the approved design, sheathing span rating and project loads.

Gambrel Attic Area and Volume

A gambrel roof can create more usable upper-level space than a simple triangular roof of similar overall height.

The approximate cross-sectional area is:

Cross-sectional area = x₁y₁ + x₂y₂ + 2x₂y₁

Approximate attic volume:

Attic volume = Cross-sectional area × Building length

Example

Using:

• Lower run: 2 ft
• Lower rise: 3.46 ft
• Upper run: 4 ft
• Upper rise: 2.31 ft
• Building length: 20 ft

Cross-sectional area:

(2 × 3.46) + (4 × 2.31) + (2 × 4 × 3.46)

6.92 + 9.24 + 27.68 = 43.84 sq ft

Attic volume:

43.84 × 20 = 876.8 cu ft

This is gross geometric volume. It does not subtract:

• Truss webs
• Ceiling framing
• Insulation
• Ventilation channels
• Knee walls
• Mechanical equipment
• Required headroom

Imperial Gambrel Roof Calculator

For imperial calculations, convert all measurements to feet before applying the formulas.

Inches to Feet

Feet = Inches ÷ 12

Example:

18 inches ÷ 12 = 1.5 ft

Feet and Inches

A measurement of 5 ft 8 in becomes:

5 + 8 ÷ 12 = 5.667 ft

Perform the calculation in decimal feet and convert the final rafter lengths back into feet and inches.

Metric Gambrel Roof Calculator

For metric calculations, keep all inputs in metres or millimetres.

Example:

• Building width: 4.8 m
• Lower run: 0.9 m
• Upper run: 1.5 m
• Lower angle: 60°
• Upper angle: 30°

Lower rise:

0.9 × tan(60°) = 1.559 m

Upper rise:

1.5 × tan(30°) = 0.866 m

Total rise:

1.559 + 0.866 = 2.425 m

Lower rafter:

0.9 ÷ cos(60°) = 1.800 m

Upper rafter:

1.5 ÷ cos(30°) = 1.732 m

The formulas are identical in metric and imperial units. Only the measurement unit changes.

Geometry Calculator Versus Structural Truss Design

A gambrel calculator can determine shape and dimensions.

It cannot confirm that the roof will safely carry:

• Roofing dead load
• Ceiling load
• Attic storage
• Habitable-room load
• Snow
• Wind uplift
• Seismic forces
• Solar panels
• Mechanical equipment
• Concentrated loads

The 2024 IRC requires truss design drawings to identify items including span, spacing, joint locations, bearing widths, design loads, reactions and required permanent bracing.

Metal-plate-connected wood trusses are designed under standards such as ANSI/TPI 1-2022, which establishes requirements for truss members, joints, connector plates, manufacturing and design responsibilities. That edition is referenced by the 2024 International Codes.

Use the calculator for preliminary geometry and material planning. Use an approved truss drawing for construction.

Are Gambrel Rafter Span Tables Available?

Span tables are commonly available for individual sawn rafters, but they depend on:

• Lumber species
• Lumber grade
• Rafter size
• Rafter spacing
• Horizontal projected span
• Roof live load
• Snow load
• Dead load
• Ceiling attachment
• Deflection limit

The American Wood Council provides rafter span resources covering different species, grades, loads and deflection limits.

A manufactured gambrel truss is not sized from a simple rafter table. The complete truss must be designed as a connected structural system.

Common Gambrel Roof Design Mistakes

Treating Both Pitches as One Pitch

A gambrel roof contains two separate angles on each side.

Calculate each section independently.

Forgetting That the Runs Must Match the Half-Span

For a symmetrical roof:

Lower run + Upper run = Half the building width

If they do not match, the roof will not meet at the ridge over the centreline.

Using Degrees as Pitch Numbers

A 30° roof is not a 30:12 pitch.

A 30° angle is approximately 6.93:12.

Measuring Overhang Along the Wrong Direction

A one-foot horizontal overhang on a 60° slope requires two feet of sloped rafter extension.

Calculating Roof Area From the Footprint

A 20 × 30-foot building has a 600-square-foot footprint, but its roof area is greater because the roof surfaces are sloped.

Ignoring Actual Lumber Dimensions

A nominal 2 × 6 is not actually 2 inches by 6 inches.

Use finished lumber dimensions when laying out joints, birdsmouths and gussets.

Choosing Truss Members From Geometry Alone

Rafter length does not determine member size.

Loads, spacing, grade, connections, deflection and bracing are also required.

Adding Unplanned Interior Supports

A truss should bear only where its design drawing specifies. Additional support can change the truss force distribution rather than automatically making it safer.

Disadvantages of a Gambrel Roof

More Complex Framing

A gambrel roof has more joints, cuts and connections than a simple gable roof.

Greater Dependence on Accurate Layout

Small errors at the gambrel joints can prevent the ridge and eaves from aligning correctly.

More Structural Design Variables

The two roof pitches change how snow, wind and dead loads act on the roof. The design drawing must address the project’s actual loads and bearing conditions. The IRC requires those loads and reactions to appear in the truss documentation.

More Roof Surface Area

A tall gambrel profile can require more sheathing, roofing and underlayment than a simpler low-pitch roof over the same footprint.

Additional Weatherproofing Details

Each slope transition requires careful sheathing, underlayment and roofing installation.

Usable Attic Space Can Increase Loads

A gambrel roof may create enough space for storage or a room, but that does not mean the bottom chord was designed as a floor.

Storage and habitable-space loads must be included in the truss design.

Frequently Asked Questions

How do I calculate the dimensions of gambrel roof trusses?

Start with the building width, roof angles and position of the gambrel joint.

For one side:

Lower run + Upper run = Building width ÷ 2

Then calculate:

Lower rise = Lower run × tan(Lower angle)

Upper rise = Upper run × tan(Upper angle)

Lower rafter = Lower run ÷ cos(Lower angle)

Upper rafter = Upper run ÷ cos(Upper angle)

These formulas calculate geometry. The final truss members and connections must follow an engineered or approved truss drawing.

How do you estimate the square footage of a gambrel roof?

Add the upper and lower rafter lengths, multiply by the roof length and then multiply by two:

Roof area = 2 × Roof length × (Upper rafter + Lower rafter)

Add eave and gable overhangs before calculating the final material quantity.

What are the angles of a 10-foot-wide gambrel roof?

Building width alone does not determine the angles.

One equal-rafter example uses:

• 60° lower angles
• 30° upper angles
• 3.66-foot rafter sections
• 5-foot total roof rise

A 10-foot roof can use other angle combinations when a different height or attic shape is required.

What are the span tables for gambrel roof trusses?

There is no single universal gambrel-truss span table.

Truss capacity depends on span, pitch, spacing, lumber, connector plates, bearing points, snow, wind, dead load and any attic or ceiling load.

Current codes require individual truss drawings to state the span, spacing, bearings, design loads, reactions and bracing requirements.

What are the disadvantages of a gambrel roof?

The main disadvantages are:

• More complicated framing
• More structural joints
• Greater chance of layout errors
• Additional slope-transition detailing
• Potentially greater roofing area
• More demanding wind and snow-load design
• Risk of treating attic space as usable when the trusses were not designed for it

How far can a roof truss span without support?

There is no universal maximum span.

A truss can span between two exterior bearing walls without an interior support when it has been specifically designed as a clear-span truss.

Its allowable span depends on:

• Truss shape
• Overall depth
• Lumber grade
• Truss spacing
• Snow and wind loads
• Ceiling and attic loads
• Deflection limits
• Bearing capacity
• Connector plates
• Bracing

Do not infer a safe span from a geometric calculator.

What size truss is needed for a 20-foot span?

The truss’s overall span would be 20 feet between its designated bearing points.

That does not determine the required lumber or connector size.

A 20-foot gambrel truss must be designed using the project’s:

• Roof pitch
• Truss spacing
• Snow and wind loads
• Roofing weight
• Ceiling load
• Attic use
• Bearing width
• Overhang
• Local code

The truss manufacturer or structural designer should provide the member sizes and connector-plate layout.

Do roof trusses need load-bearing walls?

Roof trusses require support at their designated bearing locations.

Many residential trusses are designed to span from one exterior bearing wall to the other without an interior bearing wall. Other trusses are designed with one or more interior bearing points.

The approved truss drawing must identify the required bearing locations and reaction forces.

An interior partition should not be assumed to support a truss unless the plans identify it as a bearing wall.

What truss design is best for a 50-foot span?

There is no single best design for every 50-foot building.

Possible options include:

• Engineered wood roof trusses
• Attic trusses
• Parallel-chord trusses
• Steel trusses
• Open-web steel joists
• Hybrid wood-and-steel systems

The best option depends on:

• Required roof shape
• Clear-span requirement
• Building use
• Snow and wind loads
• Ceiling or storage load
• Mechanical systems
• Transportation limits
• Available bearing width
• Fire-resistance requirements
• Local material and installation costs

A 50-foot gambrel truss is an engineered structural component, not a suitable DIY sizing exercise. ANSI/TPI 1 establishes the design framework for metal-plate-connected wood trusses, while the project-specific truss drawing supplies the actual members, joints, loads and bearings.

Is a gambrel roof the same as a hip roof?

No.

A gambrel roof has two sloped faces and a gable at each end, with two pitches on each face.

A hip roof slopes downward on all sides and normally has no vertical gable ends.

A hip roof calculator cannot accurately calculate gambrel geometry.

Can a gambrel roof contain a room?

It can, but the roof must be designed for that purpose.

A habitable room may require:

• Floor live-load capacity
• Suitable headroom
• Stair access
• Emergency escape
• Insulation
• Ventilation
• Fire separation
• Structural floor framing

The presence of empty space does not automatically make a truss suitable as an attic-room floor.

Final Gambrel Roof Checklist

Before using the calculator result for material planning, confirm:

• Building width
• Building length
• Upper angle or pitch
• Lower angle or pitch
• Lower run
• Upper run
• Total roof rise
• Upper rafter length
• Lower rafter length
• Eave overhang
• Gable overhang
• Truss spacing
• Roof surface area
• Roofing waste allowance
• Local snow load
• Local wind load
• Roofing dead load
• Ceiling or attic load
• Bearing locations
• Permanent bracing
• Approved truss drawings

The calculator provides accurate geometric estimates from the values entered. It does not certify structural capacity or replace engineering, truss-manufacturer documentation or local building approval.