Roof Truss Calculator - Design, Materials & Cost Estimates

Roof Truss Calculator

A roof truss calculator estimates the lumber length, joint count, carried load, and material cost of a roof truss from its span, pitch, spacing, and material. This tool covers five common truss designs: king post, queen post, fink, howe, and pratt.

What is a roof truss?

A roof truss is a prefabricated frame, usually made of wood or steel, that holds up a roof. It is built from straight members joined in triangles. A triangle keeps its shape under load, so the frame carries weight through simple pushing (compression) and pulling (tension) forces instead of bending. This lets a truss span the width of a building without posts or load-bearing walls underneath it.

The top two members of a truss are called the top chords, or rafters. They form the sloped roof line. The bottom member is the bottom chord. It usually runs level and often doubles as a ceiling joist. The members that connect the top and bottom chords inside the triangle are called web members.

Truss types

• King post: one vertical post runs from the peak to the center of the bottom chord. It is the simplest design and is common on small spans such as sheds and single garages.
• Queen post: two vertical posts and two diagonals replace the single king post, spreading the load across a wider middle section. It suits somewhat longer spans than a king post truss.
• Fink: web members form a W shape between the top and bottom chords. It is the most common shape in residential construction because it uses lumber efficiently across a wide range of spans.
• Howe: named after William Howe, who patented the design in 1840. Vertical members and diagonal members form a pattern that was originally built with iron rods for the verticals and timber for the diagonals.
• Pratt: named after Thomas and Caleb Pratt, who patented the design in 1844. It is close to a mirror image of the Howe truss.

How to calculate a roof truss

Rise formula

Rise is the height of the truss at its peak, measured above the bottom chord. Pitch is expressed as inches of rise per 12 inches of horizontal run, written as x/12.

$\text{Rise} = \frac{\text{Span}}{2} \times \frac{\text{Pitch}}{12}$

A 4/12 pitch on a 24-foot span gives a rise of (24 ÷ 2) × (4 ÷ 12) = 4 feet.

Rafter length formula

Half the span and the rise form the two shorter sides of a right triangle. The rafter is the long side, found with the Pythagorean theorem.

$\text{Rafter Length} = \sqrt{\left(\frac{\text{Span}}{2}\right)^2 + \text{Rise}^2}$

Total lumber formula

Total lumber is the combined length of both rafters, the bottom chord, and the web members. The web member formula depends on the truss type.

King post: web length equals the rise, since the post runs straight from the peak to the bottom chord.

$\text{Total Lumber} = (2 \times \text{Rafter Length}) + \text{Span} + \text{Rise}$

Queen post: web length is the center post (equal to the rise) plus two diagonals running from the quarter points of the bottom chord to the peak.

$\text{Total Lumber} = (2 \times \text{Rafter Length}) + \text{Span} + \text{Rise} + 2\sqrt{\left(\frac{\text{Span}}{4}\right)^2 + \text{Rise}^2}$

Fink: the W-shaped web has four pieces. Two run from the quarter points of the top chord down to the third points of the bottom chord. Two more continue from those bottom points up to the peak.

$\text{Web Members} = 2\left[\sqrt{\left(\frac{\text{Span}}{4}-\frac{\text{Span}}{3}\right)^2+\left(\frac{\text{Rise}}{2}\right)^2} + \sqrt{\left(\frac{\text{Span}}{2}-\frac{\text{Span}}{3}\right)^2+\text{Rise}^2}\right]$

$\text{Total Lumber} = (2 \times \text{Rafter Length}) + \text{Span} + \text{Web Members}$

Howe and pratt: two short verticals meet the top chord at half the rise, and two diagonals run from there to the peak.

$\text{Web Members} = \text{Rise} + 2\sqrt{\left(\frac{\text{Span}}{4}\right)^2 + \left(\frac{\text{Rise}}{2}\right)^2}$

$\text{Total Lumber} = (2 \times \text{Rafter Length}) + \text{Span} + \text{Web Members}$

Each truss type also has a fixed number of joints, the points where members meet: king post has 4, queen post has 6, and fink, howe, and pratt each have 7.

Design load carried per truss formula

This figure is the load one truss must support, not the maximum load it can safely hold. A truss picks up the roof load from a strip that reaches halfway to the next truss on each side. That strip's width is the truss spacing, converted from inches to feet.

$\text{Design Load per Truss} = \text{Design Load} \times \frac{\text{Spacing}}{12} \times \text{Span}$

Design load is entered in pounds per square foot (psf) and covers the combined top-chord live load, top-chord dead load, and bottom-chord dead load. The calculator defaults to 50 psf, matching a common residential 30-10-10 truss: 30 psf live load plus 10 psf top-chord dead load plus 10 psf bottom-chord dead load. Building codes set a minimum roof live load, and local snow load can raise that minimum.

The load figure is not the truss's weight capacity. Actual capacity depends on lumber species and grade, member size, and the metal connector plates at each joint, none of which this calculator computes. In the United States, IRC section R802.10.2 requires trusses to be engineered to the ANSI/TPI 1 standard. A truss designer or licensed engineer should approve any truss design before it is built or loaded.

Cost estimate formula

$\text{Cost Estimate} = \text{Total Lumber} \times \text{Material Cost per Foot}$

The calculator uses approximate costs per linear foot: $2.50 for wood,$5.75 for steel, and $4.25 for engineered wood (laminated veneer lumber or similar products). These figures cover raw material only, not connector plates, labor, delivery, or engineering fees.

Example calculations

Example 1: king post truss

Inputs: king post, 24-foot span, 4/12 pitch, 24-inch spacing, 50 psf design load, wood.

1. Rise = (24 ÷ 2) × (4 ÷ 12) = 4.00 ft
2. Rafter length = √(12² + 4²) = √160 = 12.65 ft
3. Total lumber = (2 × 12.65) + 24 + 4 = 53.30 ft
4. Joints = 4
5. Design load per truss = 50 × (24 ÷ 12) × 24 = 2,400.00 lbs
6. Cost estimate = 53.30 × $2.50 =$133.25

Example 2: fink truss

Inputs: fink, 40-foot span, 5/12 pitch, 16-inch spacing, 50 psf design load, steel.

1. Rise = (40 ÷ 2) × (5 ÷ 12) = 8.33 ft
2. Rafter length = √(20² + 8.33²) = √469.44 = 21.67 ft
3. Web members = 2 × [√((10−13.33)² + 4.17²) + √((20−13.33)² + 8.33²)] = 2 × (5.34 + 10.67) = 32.02 ft
4. Total lumber = (2 × 21.67) + 40 + 32.02 = 115.35 ft
5. Joints = 7
6. Design load per truss = 50 × (16 ÷ 12) × 40 = 2,666.67 lbs
7. Cost estimate = 115.35 × $5.75 =$663.26

Using the calculator

1. Choose a truss type: king post, queen post, fink, howe, or pratt.
2. Enter the span, the horizontal distance between the outside walls, in feet.
3. Enter the pitch as x/12, where x is the inches of rise per foot of run. The calculator accepts values up to 12/12.
4. Enter the spacing between trusses in inches. Common values are 16, 19.2, and 24 inches.
5. Enter the design load in pounds per square foot, or use the 50 psf default.
6. Choose a material: wood, steel, or engineered wood.
7. Read the results: rise, total lumber per truss, number of joints, design load carried per truss, and cost estimate per truss.

Frequently asked questions

What does this calculator not do?

It does not check whether a truss can safely carry its load. It only reports geometry, lumber length, joint count, the load a truss must carry, and a rough material cost. Verifying that a truss can hold that load requires engineering software or a licensed truss designer working to the ANSI/TPI 1 standard.

Why is the default design load 50 psf?

Fifty psf is a common combined figure for residential roofs: 30 psf top-chord live load, 10 psf top-chord dead load, and 10 psf bottom-chord dead load. A higher local snow load or a heavier roof covering can raise the number that should be used.

How many joints does each truss type have?

King post has 4 joints. Queen post has 6. Fink, howe, and pratt each have 7: two heels, the peak, two top-chord panel points, and two bottom-chord panel points.

Why does design load per truss go down when trusses are spaced closer together?

Each truss carries the load from a strip of roof equal to the spacing. Narrower spacing means a narrower strip per truss, so each truss carries less, even though the roof needs more trusses in total.

What is the difference between a king post and a queen post truss?

A king post truss uses a single central post and works for shorter spans. A queen post truss uses two posts and two diagonals spread across the middle of the span, which lets it cover a somewhat wider span for the same rise.

Do the cost estimates include labor and installation?

No. The cost estimate covers raw material only, based on cost per linear foot of lumber. Connector plates, labor, delivery, crane rental, and engineering fees are separate and are not included.

References

1. American Wood Council. National Design Specification for Wood Construction. Leesburg, VA.
2. International Code Council. International Residential Code, Section R802.10.2.
3. Truss Plate Institute. ANSI/TPI 1: National Design Standard for Metal Plate Connected Wood Truss Construction. Alexandria, VA.
4. Structural Building Components Association. BCSI: Guide to Good Practice for Handling, Installing, Restraining & Bracing of Metal Plate Connected Wood Trusses. Madison, WI.