Roof Truss Calculator — Calculate Truss Dimensions Instantly

Free roof truss calculator computes rafter length, rise, run, pitch, and roof angle. Enter span and rise or pitch for step-by-step truss geometry results with verified formulas.

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Roof Truss Calculator

Enter the total span and either the rise or roof pitch to compute all truss dimensions for a symmetric gable truss.

Enter truss parameters and click Calculate Truss to see all dimensions.

Roof Truss Formula Explained

The roof truss geometry for a symmetric gable truss is governed by the Pythagorean theorem and basic trigonometric relationships. All calculations assume a centered ridge with equal spans on both sides.

Run = Span ÷ 2
Rafter Length = √(Run² + Rise²)
Pitch = (Rise ÷ Run) × 12  (inches per 12 in. run)
Roof Angle = arctan(Rise ÷ Run)  (in degrees)

Variable Definitions

  • Span — Total horizontal distance from outer wall to outer wall (the full width of the truss)
  • Run — Half the span; the horizontal distance from the outer wall to the ridge centerline
  • Rise — Vertical height from the top plate to the peak of the ridge
  • Rafter Length — The diagonal length of the top chord from ridge to outer wall
  • Pitch — Roof steepness expressed as inches of rise per 12 inches of run (e.g., 6/12)
  • Roof Angle — The angle of inclination of the rafter measured from horizontal, in degrees

How to Calculate Roof Truss Dimensions

Follow these steps to determine all key dimensions for a symmetric gable roof truss:

  1. Measure the total span — Determine the horizontal distance between the two outer walls where the truss will sit.
  2. Calculate the run — Divide the span by 2. For a 24-foot span, run = 12 feet.
  3. Determine the rise — Either measure the desired rise directly or use the target pitch: Rise = (Pitch ÷ 12) × Run.
  4. Compute rafter length — Use the Pythagorean theorem: Rafter = √(Run² + Rise²).
  5. Calculate pitch and angle — Pitch = (Rise ÷ Run) × 12; Angle = arctan(Rise ÷ Run) in degrees.
  6. Verify results — Cross-check all values to ensure geometric consistency.

For a truss with a 24-foot span and 6-foot rise: Run = 12 ft, Rafter = √(12² + 6²) = √180 ≈ 13.42 ft, Pitch = (6/12)×12 = 6/12, Angle ≈ 26.57°.

Roof Truss Calculator Examples

Example 1: Standard Gable Truss by Rise

A truss with a 30-foot span and 7.5-foot rise:

Run = 30 ÷ 2 = 15 ft
Rafter = √(15² + 7.5²) = √(225 + 56.25) = √281.25 ≈ 16.77 ft
Pitch = (7.5 ÷ 15) × 12 = 6/12
Angle = arctan(7.5/15) ≈ 26.57°

Example 2: Steep Pitch Truss by Pitch

A truss with a 20-foot span and 10/12 pitch:

Run = 20 ÷ 2 = 10 ft
Rise = (10 ÷ 12) × 10 ≈ 8.33 ft
Rafter = √(10² + 8.33²) = √(100 + 69.44) = √169.44 ≈ 13.02 ft
Angle = arctan(8.33/10) ≈ 39.81°

Example 3: Low-Slope Shed Truss by Rise

A truss with a 16-foot span and 2-foot rise:

Run = 16 ÷ 2 = 8 ft
Rafter = √(8² + 2²) = √(64 + 4) = √68 ≈ 8.25 ft
Pitch = (2 ÷ 8) × 12 = 3/12
Angle = arctan(2/8) ≈ 14.04°

Real-World Roof Truss Applications

  • Residential Construction: Determining rafter lengths for gable, hip, and shed roof designs before ordering lumber.
  • Truss Manufacturing: Calculating top chord lengths and peak heights for prefabricated truss production.
  • Remodeling & Additions: Matching existing roof pitches when extending or modifying rooflines.
  • Estimating Materials: Computing total rafter linear footage and roof surface area for material takeoffs.
  • Architectural Design: Visualizing roof proportions and ensuring aesthetic pitch-to-span ratios.
  • DIY Shed & Outbuilding Plans: Designing simple gable roofs for backyard structures with accurate cut lists.
  • Solar Panel Installation: Determining roof angle for optimal solar panel tilt calculations.

People Also Ask

Rafter length is calculated using the Pythagorean theorem: Rafter Length = √(run² + rise²), where run is half the total span and rise is the vertical height from the top plate to the ridge peak. For a truss with a 24-foot span and 6-foot rise, run = 12 ft, so rafter length = √(12² + 6²) = √(144 + 36) = √180 ≈ 13.42 feet.
Roof pitch is expressed as inches of rise per 12 inches of run. The formula is: Pitch = (Rise ÷ Run) × 12. For example, if the rise is 6 feet and the run is 12 feet, pitch = (6 ÷ 12) × 12 = 6, so the roof has a 6/12 pitch. This means the roof rises 6 inches for every 12 inches of horizontal run.
The most common roof pitches for residential homes range from 4/12 to 9/12. A 4/12 pitch is common in ranch-style homes and warmer climates, while 6/12 to 8/12 pitches are typical for colonial and traditional homes. Steeper pitches of 10/12 and above are often found in Cape Cod, Victorian, and mountain-style architecture.
The roof angle is found using the arctangent function: Angle = arctan(rise ÷ run). For a 6/12 pitch roof, rise = 6, run = 12, so angle = arctan(6/12) = arctan(0.5) ≈ 26.57°. This angle represents the inclination of the rafter from horizontal and is useful for cutting rafter ends.
This calculator is designed for symmetric gable-style roof trusses where the ridge is centered and both sides are equal. For asymmetrical trusses with different pitches on each side or off-center ridges, separate calculations for each side are required using the individual run and rise values for each roof plane.

Frequently Asked Questions

This calculator is optimized for symmetric gable roof trusses where the ridge is centered. It provides accurate rafter length, rise, run, pitch, and angle for any symmetric design. For hip roofs, gambrel trusses, or scissor trusses, specialized calculators or manual adjustments are recommended.
The calculator works with any consistent unit of measurement. If you enter span and rise in feet, all outputs will be in feet. You can also use inches, meters, or any other unit as long as all inputs use the same unit. Pitch is always expressed as inches of rise per 12 inches of run regardless of the input unit.
The calculator uses precise mathematical formulas including the Pythagorean theorem and arctangent function. Results are computed to high precision and displayed with up to 6 decimal places. For construction purposes, rounding to the nearest 1/8 inch or 0.01 feet is recommended.
Roof pitch is typically expressed as a ratio of rise to run in inches per 12 inches (e.g., 6/12). Roof slope is often expressed as a percentage or decimal (e.g., 50% or 0.5 for a 6/12 pitch). Both describe roof steepness, but pitch is the standard convention in US residential construction.
The rafter length from this calculator can be used to estimate roof area. Multiply the rafter length by the total length of the roof (along the ridge) and then by 2 (for both sides) to get the total roof surface area. Remember to account for overhangs separately.
A 4/12 pitch means the roof rises 4 inches for every 12 inches (1 foot) of horizontal run. This is considered a low to moderate slope, common in ranch-style homes. The corresponding roof angle is approximately 18.43°, and it provides a balance between water drainage and ease of construction.

Roof Truss Glossary

Roof Truss

A prefabricated structural framework of triangular units used to support a roof, transferring loads from the roof to the building's walls.

Rafter

The sloping structural member that extends from the ridge to the wall plate, forming the top chord of a truss.

Span

The total horizontal distance between the outer supports of a truss, measured from wall to wall.

Rise

The vertical distance from the top of the wall plate to the peak of the ridge, determining roof height.

Run

Half the span; the horizontal distance from the outer wall to a point directly beneath the ridge.

Pitch

Roof steepness expressed as inches of rise per 12 inches of run (e.g., 6/12 pitch means 6 inches of rise per foot).

Gable Roof

A classic roof style with two sloping sides that meet at a central ridge, forming a triangular end wall.

Top Chord

The upper member of a truss that follows the roof slope, typically functioning as the rafter.

Editorial Review & Methodology

This roof truss calculator was built and reviewed by the NumbrWiz Editorial Team. The truss geometry formulas are based on the Pythagorean theorem and fundamental trigonometric relationships, verified against standard construction references, carpentry textbooks, and architectural geometry principles.

  • Formula verification: Cross-checked against multiple authoritative construction math and carpentry sources.
  • Edge case testing: Tested with very small spans, steep pitches up to 24/12, and fractional inputs for precision.
  • UX review: Designed for intuitive input with clear error messaging and step-by-step breakdown showing all intermediate calculations.

Transparency note: All calculations run client-side in your browser. No data is ever collected, stored, or transmitted. Results are for educational and planning purposes; always verify critical measurements with a qualified professional before construction.

Page last reviewed: May 2026 · NumbrWiz Editorial Team