# Roof Truss Calculator

> Design roof truss dimensions from span, pitch, and loading requirements

**Category:** Utility
**Keywords:** calculator, tool
**URL:** https://complete.tools/roof-truss-calculator

## How the calculations work

The calculator follows a three-step process: geometry, loading, and member sizing.

**Geometry**

The half span and rise define a right triangle. Given a span of S feet and a pitch of P/12:

```
Half span (a) = S / 2
Rise (h)      = a x P / 12
Rafter length = sqrt(a^2 + h^2)
Roof angle    = atan(h / a)  [in degrees]
```

**Loading**

Each truss carries the roof area between adjacent trusses:

```
Tributary area = span x truss spacing
Total load     = (dead load + snow load) x tributary area
Reaction R     = total load / 2  [each support]
```

**Member forces (king-post truss)**

Resolving forces at the peak joint:

```
Top chord (compression): F_top    = R / sin(angle)
Bottom chord (tension):  F_bottom = R / tan(angle)
Vertical king post:      F_web    = total load / 2
```

**Lumber sizing**

Required cross-section area is compared against standard dimensional lumber (2x4 through 2x12):

```
Top chord:    A_req = F_top    / (Fc x 0.8)   [compression with slenderness factor]
Bottom chord: A_req = F_bottom / Ft             [tension]
King post:    A_req = F_web    / (Fc x 0.6)   [slender web member]
```

The tool selects the smallest standard size whose actual area meets or exceeds the required area.

## Understanding roof truss components

A king-post truss is the simplest common truss type and is well suited to spans up to about 30 feet.

**Top chord** — The pair of inclined members that follow the roof slope. They carry the roof sheathing and experience compression from downward loads. This is the longest member and often drives the lumber size.

**Bottom chord** — The horizontal tie at ceiling level. It resists the outward thrust produced by the sloping top chords. Because it is in pure tension it can often be a smaller size than the top chord despite carrying a similar force magnitude.

**King post** — The single vertical member at the center of the truss connecting the ridge to the bottom chord midpoint. It transfers the weight of the bottom chord upward and carries a compression or tension force depending on loading. In a king-post truss this is the only interior web member.

**Heel joint** — Where the top chord meets the bottom chord at each wall plate. This is a critical connection point and must be detailed carefully in practice.

For spans over 30 feet a queen-post truss (two verticals) or a Fink W-truss (diagonal webs) is more appropriate. The forces computed here still give useful guidance for preliminary planning on those configurations.

## Common roof pitches and their uses

Roof pitch controls drainage, snow shedding, attic space, and the visual character of a building.

- **3/12 (14 degrees)** — Minimum recommended for asphalt shingles. Low visual profile; common on garages and shallow additions.
- **4/12 (18 degrees)** — Popular residential pitch. Good balance of attic space and wind resistance.
- **5/12 to 6/12 (23 to 27 degrees)** — The most common range for North American homes. Sheds snow well and provides usable attic storage.
- **7/12 to 9/12 (30 to 37 degrees)** — Steeper slopes typical of colonial and craftsman styles. Excellent for heavy snowfall regions.
- **10/12 to 12/12 (40 to 45 degrees)** — Very steep. Common in Victorian and Gothic Revival architecture. Significant structural forces; lumber sizes increase noticeably.

Higher pitches increase the top chord force because the rafter is longer and more steeply inclined, but they reduce the horizontal thrust on the bottom chord. Steeper roofs also mean more roofing material and more complex construction.

## Load considerations

Accurate load inputs are essential for reliable results.

**Dead load** covers the permanent weight of roofing materials: sheathing (typically 3 psf for 3/4-inch plywood), roofing felt (0.5 psf), and the finish material. Asphalt shingles add about 2 to 4 psf; wood shakes 3 to 5 psf; clay tile 10 to 15 psf. A default of 15 psf is conservative for most light residential roofs.

**Snow load** depends on geographic location and roof slope. The International Building Code uses ground snow load maps to establish design values. Flat-roof snow loads typically range from 20 psf in mild climates to 50 psf or more in mountain regions. Roof snow load is somewhat less than ground snow load due to wind scour and heat loss, but code reduction factors require a licensed engineer to apply correctly.

**Live load** for uninhabited roofs is typically 20 psf per building codes, applied to account for workers and maintenance equipment during construction and repairs.

When in doubt, use a higher load value. It only increases the required lumber size by one step, which is a small cost compared to an under-designed structure.

## FAQs

**Q:** What span range is this calculator designed for?


**A:** The calculator works for spans from 8 to 60 feet. For spans above about 30 feet a simple king-post truss may not be the most efficient choice structurally, but the forces calculated here still provide a useful starting point for more complex truss configurations.


**Q:** Why does the bottom chord force sometimes exceed the top chord force?


**A:** At low pitches (shallow angles) the horizontal component of the top chord reaction is very large. The bottom chord must resist this outward thrust, so its tension force can exceed the top chord compression force. This is normal and is one reason shallow-pitch roofs are more demanding on connections than steep-pitch roofs.


**Q:** Can I use this for engineered wood products like LVL or I-joists?


**A:** The calculator uses allowable stresses for sawn lumber only. Engineered wood products (LVL, PSL, LSL) have higher allowable stresses and would result in smaller required sizes. You would need to use the manufacturer's published design values and consult an engineer.


**Q:** What does the 0.8 compression factor represent?


**A:** The top chord is a slender compression member and is subject to buckling. The factor of 0.8 applied to the tabulated compression stress (Fc) is a simplified conservative adjustment for column stability. A full NDS column stability calculation requires knowing the unbraced length and slenderness ratio, which is beyond the scope of a preliminary calculator.


**Q:** Is this calculator appropriate for building permit submissions?


**A:** No. Permit submissions require stamped engineering drawings prepared by a licensed structural engineer. This tool is for preliminary design and educational purposes only.

## How to use

1. Enter the total building span — the horizontal distance from outside wall to outside wall.
2. Select the roof pitch from the dropdown. If you know the angle in degrees, choose the closest pitch listed.
3. Enter the dead load for your roofing assembly. Use 15 psf if unsure; increase to 20 psf for heavier materials.
4. Enter the snow or live load for your location. Check your local building code or use the IBC ground snow load maps as a starting point.
5. Select the truss spacing. Residential construction most commonly uses 2 feet on center.
6. Choose the lumber species and grade available in your area. Douglas Fir-Larch and Southern Pine are among the strongest common species.
7. Click Calculate Truss. Review the rafter length, member forces, and minimum lumber sizes.
8. Have a licensed structural engineer review the design before purchasing materials or beginning construction.

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