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Roofing & Siding

Roof Truss Calculator

Truss count, rise, top chord length and pitch angle for a simple gable roof, from the span and the pitch.

Your measurements

Span is the outside-to-outside width the trusses bear on, not the ridge length.

Roof geometry
Measured horizontally from the wall, not along the slope.
Building
Set by the engineered design and the loads, not by preference.

Your result

Sample values

21

Trusses

6.00

Rise, ft

14.53

Top chord length, ft

26.57

Pitch angle, degrees

24 ft span at 6:12, 12 in overhang, 24 in centres over 40 ft.

Geometry summary

Measure Value
Half span 12.00 ft
Rise at ridge 6.00 ft
Top chord, including overhang 14.53 ft
Overall width with overhangs 26.00 ft
Pitch angle 26.57°

How to use this calculator

Enter the span the trusses bear on, measured outside to outside of the supporting walls, and the pitch as rise per 12 of run. The rise and chord lengths follow from those two numbers alone.

The truss count assumes one truss at each end plus even spacing between, which is why it is one more than the length divided by the spacing. Girder trusses, hip sets and anything carrying a point load are extra and come from the engineered design.

Formula

Rise = (Span ÷ 2) × (Pitch ÷ 12)

Slope factor = √(1 + (Pitch ÷ 12)²)

Top chord = (Span ÷ 2 + Overhang) × Slope factor

Trusses = floor(Building length ÷ Spacing) + 1

Angle = arctan(Pitch ÷ 12)

Pitch
rise per 12 of run — not the same as the angle
Angle
the pitch expressed in degrees: 6:12 is 26.57°, not 6°

Overhang is horizontal, so it is multiplied by the slope factor along with the run.

Worked example

A 24 ft span at 6:12 with a 12 in overhang, 24 in centres over a 40 ft building.

  1. Half span: 24 ÷ 2 = 12 ft
  2. Rise: 12 × (6 ÷ 12) = 6 ft
  3. Slope factor: √(1 + 0.25) = 1.1180
  4. Top chord: (12 + 1) × 1.1180 = 14.53 ft
  5. Trusses: floor(40 ft ÷ 2 ft) + 1 = 21
  6. Angle: arctan(0.5) = 26.57°

21 trusses, 6.00 ft rise, 14.53 ft top chord

Understanding your results

Pitch and angle are not the same thing and mixing them up is the most common error on a roof. A 6:12 roof is a 26.57 degree roof. Entering 6 into a calculator expecting degrees gives a roof less than half as steep, and every length that follows is wrong.

Top chord length includes the overhang because that is how a truss is manufactured and delivered. If you are pricing timber rather than trusses, that length is what you need; if you are checking a supplier quote, confirm whether their figure includes the tail.

Questions

About this calculator

Ask something else

No. Pitch is a ratio of rise to a 12 inch run; the angle is that ratio expressed in degrees. A 6:12 pitch is 26.57 degrees and a 12:12 pitch is 45 degrees. This calculator shows both so the two cannot be confused.

Because there is a truss at both ends. Ten spaces need eleven trusses, the same way a fence with ten bays needs eleven posts. Forgetting the last one is the classic off-by-one on any framing takeoff.

No. It gives geometry, not engineering. Web layout, chord sizes, plate sizes and bearing details all come from a truss designer working to your loads and span, and in most places the design has to be signed off before it can be built.

No. Rise is set by the span and pitch alone. The overhang extends the top chord past the wall at the same slope, so it lengthens the chord and the overall width without raising the ridge.

Keep going

All Roofing & Siding tools
Estimates, not specifications. Results are based on the values you enter and on typical material properties. Densities, coverage rates and product sizes vary between suppliers, so confirm quantities against your supplier's data before ordering. Structural work must be signed off by a qualified professional and meet your local building code.