Truss Calculator
Calculate truss dimensions, member lengths, and angles from span and pitch. Enter values for instant results with step-by-step formulas.
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Where span is the total width of the building, pitch is expressed as rise per 12 inches of run, rise is the vertical height at the peak, and rafter length is the hypotenuse of the right triangle formed by half the span and the rise.
Last reviewed: December 2025
Worked Examples
Example 1: Standard Residential Roof Truss
Example 2: Steep Pitch Garage Truss
Background & Theory
The Truss Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads — the permanent self-weight of structural elements, finishes, and fixed equipment — and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40–0.45 typically yields concrete with 28-day compressive strengths of 30–40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5–2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250–350 MPa for mild steel) and ultimate tensile strength (typically 400–500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by δ = FL³ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of m²·K/W (SI) or ft²·°F·h/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1–2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Truss Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete — a mixture of volcanic ash, lime, and seawater — enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including François Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes — including the 1971 San Fernando and 1994 Northridge events — drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Frequently Asked Questions
Formula
Rafter = sqrt((span/2)^2 + rise^2) | Rise = (pitch/12) x (span/2) | Angle = arctan(pitch/12)
Where span is the total width of the building, pitch is expressed as rise per 12 inches of run, rise is the vertical height at the peak, and rafter length is the hypotenuse of the right triangle formed by half the span and the rise.
Worked Examples
Example 1: Standard Residential Roof Truss
Problem: Calculate truss dimensions for a 24-foot span with a 6/12 pitch and 12-inch overhang for a 40-foot long building with 24-inch spacing.
Solution: Half span = 24 / 2 = 12 feet\nRise = (6/12) x 12 = 6 feet\nRoof angle = arctan(6/12) = 26.6 degrees\nRafter length = sqrt(12^2 + 6^2) = sqrt(180) = 13.42 feet\nRafter with overhang = 13.42 + 1 = 14.42 feet\nNumber of trusses = (40 x 12) / 24 + 1 = 21 trusses
Result: Rise: 6 ft | Rafter: 13.42 ft | Angle: 26.6 deg | 21 trusses needed
Example 2: Steep Pitch Garage Truss
Problem: Calculate truss dimensions for a 20-foot span with a 10/12 pitch and 18-inch overhang for a 24-foot garage with 24-inch spacing.
Solution: Half span = 20 / 2 = 10 feet\nRise = (10/12) x 10 = 8.33 feet\nRoof angle = arctan(10/12) = 39.8 degrees\nRafter length = sqrt(10^2 + 8.33^2) = sqrt(169.39) = 13.01 feet\nRafter with overhang = 13.01 + 1.5 = 14.51 feet\nNumber of trusses = (24 x 12) / 24 + 1 = 13 trusses
Result: Rise: 8.33 ft | Rafter: 13.01 ft | Angle: 39.8 deg | 13 trusses needed
Frequently Asked Questions
What is a truss and how does it differ from conventional rafters?
A truss is a pre-engineered structural framework made of triangulated members that supports a roof load and transfers it to the walls below. Unlike conventional stick-built rafters that rely on ridge boards and ceiling joists for structural integrity, trusses use a web of interconnected triangles to distribute weight efficiently. Trusses are typically manufactured in a factory and delivered to the job site ready for installation, which speeds up construction time significantly. They can span greater distances without interior load-bearing walls, giving builders more flexibility in floor plan design. Most residential construction today uses prefabricated trusses because they are cost-effective and engineered for specific load requirements.
What loads must a truss be designed to support?
Trusses must be designed for several types of loads including dead load, live load, wind load, and in some regions, snow load and seismic load. Dead load includes the weight of the roofing materials, sheathing, insulation, and the truss itself, typically ranging from 10 to 20 pounds per square foot. Live load accounts for maintenance workers, equipment, and temporary loads, usually 20 pounds per square foot for residential roofs. Snow load varies dramatically by region, from zero in southern climates to over 80 pounds per square foot in mountainous areas. Wind uplift can be a critical factor in hurricane-prone regions where trusses must resist being lifted off the walls. All loads must comply with the International Residential Code or local building code requirements.
Can I modify or cut into a prefabricated truss on site?
You should never cut, drill, or modify a prefabricated truss without written approval from a licensed structural engineer. Every member and connector plate in a truss is engineered to carry specific loads, and removing or weakening any component can cause catastrophic failure. Even drilling a single hole through a chord member can reduce its load-carrying capacity by 20 percent or more. If you need to run plumbing, electrical, or HVAC through a truss, consult the truss manufacturer for approved penetration locations or request trusses with pre-designed openings called chases. Some builders mistakenly cut web members to accommodate ductwork, which is extremely dangerous and often violates building codes. Always work with the truss engineer to accommodate mechanical systems during the design phase.
How do I verify Truss Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy