# How many roof trusses do I need?

Computes how many gable roof trusses a building needs at a spacing, and each truss’s rise, top chord length with the overhang, bottom chord, and roof angle, from the span and pitch.

- Page: https://www.acalculator.org/construction/roof-truss-calculator
- JSON spec: https://www.acalculator.org/construction/roof-truss-calculator.json
- Version: 2a22d281e590

## Default answer

Example with the default inputs (Building length 30 ft, Span 24 ft, Roof pitch (rise per 12) 6, Overhang 1 ft, Truss spacing 24 in): You need 16 trusses, each 6 ft high with a 14.53 ft top chord.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| l | Building length | The length of the roof along the ridge, end wall to end wall. |
| span | Span | The width of the building the trusses cross, outside wall to outside wall. |
| pitch | Roof pitch (rise per 12) | How many inches the roof rises for every 12 inches across: 6 means a 6/12 pitch. |
| oh | Overhang | How far the roof sticks out past each wall, measured level. 0 for none. |
| oc | Truss spacing | The distance from the centre of one truss to the next, usually 24 in or 16 in. |
| price | Price per truss | What one truss costs. Leave empty to skip the cost. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| count | Trusses | Building length ÷ spacing, rounded up, plus 1 for the truss at the far end. |
| rise | Truss height (ft) | Half the span × pitch ÷ 12: the height of the peak above the walls, in feet. |
| top | Top chord with overhang (ft) | One sloped side, from the peak to the end of the overhang, in feet. |
| bottom | Bottom chord (ft) | The span, in feet. |
| riseM | Truss height (m) | The truss height in metres. |
| topM | Top chord with overhang (m) | One sloped side in metres. |
| bottomM | Bottom chord (m) | The span in metres. |
| angle | Roof angle | The slope of the roof in degrees: arctan(pitch ÷ 12). |
| chords | Chord length in all trusses (ft) | Trusses × (2 top chords + 1 bottom chord), in feet. |
| cost | Cost of the trusses | Trusses × the price per truss. |

## Method

Trusses = building length ÷ spacing, rounded up, + 1; height = span ÷ 2 × pitch ÷ 12; top chord = (span ÷ 2 + overhang) × √(1 + (pitch ÷ 12)²); bottom chord = span; angle = arctan(pitch ÷ 12).

## Assumptions

- Common (gable) trusses with the peak in the middle and the same pitch both sides.
- Trusses 24 in on center by default; 16 in is the other common spacing (Fonthill Lumber, a truss maker).
- The overhang is measured level from the wall; chord lengths are along the outside line of the roof, before any cut at the peak or the tail.

## Worked examples

1. l = 9.144, span = 7.3152, pitch = 6, oh = 0.3048, oc = 0.6096, price = $150.00 gives count = 16, rise = 6, top = 14.534442, bottom = 24, angle = 26.565051, cost = $2,400.00. Source: Fonthill Lumber, Roof Truss Spacing Guide (trusses 16 or 24 in on center), https://fonthilllumber.ca/roof-truss-spacing-explained-for-ontario-builders.html; Pythagorean theorem (OpenStax, Prealgebra 2e, §9.3, https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem).
2. l = 12.192, span = 9.7536, pitch = 9, oh = 0, oc = 0.4064 gives count = 31, rise = 12, top = 20, chords = 2,232. Source: Pythagorean theorem (OpenStax, Prealgebra 2e, §9.3, https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem): 12-16-20 right triangle.
3. l = 10, span = 8, pitch = 6, oh = 0.5, oc = 0.6 gives count = 18, riseM = 2, topM = 5.031153, bottomM = 8. Source: Pythagorean theorem (OpenStax, Prealgebra 2e, §9.3, https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem).

## FAQ

### How many trusses do I need?

Divide the building length by the spacing, round up, and add 1 for the truss at the far end. A 30 ft building with trusses 24 in (2 ft) apart needs 30 ÷ 2 + 1 = 16 trusses.

### How far apart are roof trusses?

Usually 24 in on center, and 16 in where the roof is heavier or the snow load is high. Fonthill Lumber, a truss maker, lists 16 and 24 in as the common spacings. The truss maker’s design sets the spacing for your roof.

### How do I find the length of the top chord?

The top chord is the hypotenuse of a right triangle. Its level run is half the span plus the overhang, and its slope factor is √(1 + (pitch ÷ 12)²). For a 24 ft span, 6/12 pitch and 1 ft overhang: (12 + 1) × √1.25 = 14.53 ft.

### How tall is a truss?

Half the span × pitch ÷ 12. A 24 ft span at 6/12 pitch rises 12 × 6 ÷ 12 = 6 ft from the top of the walls to the peak.

### What does a 6/12 pitch mean?

The roof rises 6 in for every 12 in it runs across. That is an angle of arctan(6 ÷ 12) = 26.57°. The roof pitch calculator converts between pitch, angle and percent.

### Is this a structural design?

No. It counts trusses and works out their outside dimensions for ordering and budgeting. The truss maker designs each truss for your loads and building code.

## Sources

- Fonthill Lumber, Roof Truss Spacing Guide for Ontario Builders (a custom truss manufacturer; residential trusses 16 in or 24 in on center, 12 in for high loads). https://fonthilllumber.ca/roof-truss-spacing-explained-for-ontario-builders.html (retrieved 2026-10-02)
- OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem (a² + b² = c²). https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-02)
- NIST Handbook 44 (2026), Appendix C, General Tables of Units of Measurement: 1 ft = 12 in = 0.3048 m. https://www.nist.gov/document/2026-nist-handbook-44-appendix-c (retrieved 2026-10-01)