Roof Truss Calculator: Rafter Length, Count, and Cost
Enter your roof span, pitch, and length to get the common rafter length, ridge board length, roof sheathing area, and the number of trusses you need. Add truss price and optional labor cost for a full project estimate. Every formula is shown step by step so you can verify the math.
Formula
Worked example
A 28 ft wide house with a 6/12 pitch, 1 ft overhang, and 40 ft roof length: run = 14 ft, rise = (6/12) x 14 = 7 ft, rafter = sqrt(7^2 + 14^2) = 15.65 ft. Overhang adds sqrt(0.5^2 + 1^2) = 1.12 ft, giving a total rafter of 16.77 ft. At 24 in on-center spacing: floor(40 / 2) + 1 = 21 trusses. At $250 per truss: material cost = $5,250.
How roof truss geometry works
A standard gable roof truss is a triangular frame. The two top chords (rafters) slope upward from the outside walls to the ridge, while the bottom chord ties them together at ceiling level. Web members inside the triangle carry the load between chords.
The horizontal distance from the wall plate to the center line of the roof is the run, which is exactly half the building span. The rise is the vertical height from the top of the wall to the ridge. The pitch describes this slope as a ratio of rise-per-12-units of run: a 6/12 pitch rises 6 inches for every 12 inches of horizontal travel.
The actual rafter length follows directly from the Pythagorean theorem applied to rise and run. Add the overhang slant at the same pitch to get the full cut length to order from a truss manufacturer.
How to use this calculator
Fill in the building span (total wall-to-wall width), roof pitch (rise per 12 units of run), and any eave overhang. Then add the roof length (ridge-to-gable dimension) and choose your truss spacing. The calculator gives you:
- Common rafter length - what to specify when ordering manufactured trusses
- Ridge board length - equal to the roof length for a standard gable
- Roof area for one slope - use to order sheathing and roofing material
- Truss count at your chosen spacing
- Project cost with optional labor breakdown
Switch between imperial (feet/inches) and metric (metres) at the top. The step-by-step panel shows the arithmetic so you can cross-check your own takeoff sheet.
Choosing the right roof pitch
Pitch affects drainage, structural load, attic space, and cost. Low pitches (under 4/12) require special low-slope roofing materials and shed water slowly. They are common on commercial buildings and shed extensions but need careful flashing details to prevent leaks.
The most common residential pitch in North America falls between 4/12 and 8/12. This range is compatible with asphalt shingles, wood shakes, and metal panels, and gives a useful attic space. Pitches above 8/12 add dramatic curb appeal and clear snow efficiently but increase the cut length of rafters, sheathing area, and labor time.
The slope multiplier in the reference table below tells you how much longer the rafter is compared to the horizontal run. A 6/12 pitch has a multiplier of 1.118, meaning each linear foot of run becomes 1.118 ft of rafter. Use this to do quick mental checks on material quantities.
Estimating truss count and project cost
The standard formula for truss count is:
count = floor(roof length / on-center spacing) + 1
The extra truss accounts for the starting piece at one end. At 24-inch (2 ft) spacing on a 40 ft roof, that gives floor(40/2) + 1 = 21 trusses. Always order 1-2 spares for field cuts at hip returns or damaged pieces.
Manufactured truss prices vary widely by span, pitch, and region. Small simple trusses for a 20 ft span may run $75 each; large complex trusses for a 50 ft span can exceed $500 each. Installation (crane or hand-setting, bracing, fastening) adds $40-$80 per labor-hour for a crew, and a typical residential gable roof takes 8-24 hours depending on size and site access.
Get at least three quotes from local truss manufacturers. Prices depend heavily on wood species, local lumber markets, and lead time. Some manufacturers require engineered drawings stamped by a licensed structural engineer; factor that into your timeline.
Common roof pitches and their typical uses
| Pitch (rise/run) | Slope angle | Slope multiplier | Typical use |
|---|---|---|---|
| 1/12 | 4.8° | 1.003 | Nearly flat - commercial/industrial |
| 2/12 | 9.5° | 1.014 | Low-slope - sheds, extensions |
| 3/12 | 14.0° | 1.031 | Low-slope - modern residential |
| 4/12 | 18.4° | 1.054 | Standard - most common residential |
| 5/12 | 22.6° | 1.083 | Medium slope - good drainage |
| 6/12 | 26.6° | 1.118 | Moderate - traditional residential |
| 7/12 | 30.3° | 1.158 | Medium-high - ranch/cottage style |
| 8/12 | 33.7° | 1.202 | Steep - Cape Cod, colonial |
| 9/12 | 36.9° | 1.250 | Steep - Victorian, attic clearance |
| 10/12 | 39.8° | 1.302 | Very steep - traditional steep gable |
| 12/12 | 45.0° | 1.414 | Extreme - dramatic design, snow country |
Rise-per-12-run values with approximate slope angle and typical application. Pitch also affects the slope multiplier used to convert horizontal run to rafter length.
Frequently asked questions
What is a roof truss and how does it differ from stick framing?
A roof truss is a pre-engineered triangular frame made from dimensional lumber and metal connector plates, fabricated off-site to exact specifications. Stick framing cuts and assembles each rafter, ridge board, and ceiling joist on-site. Trusses are faster to install, often cheaper for simple spans, and engineered for specific loads; stick framing offers more on-site flexibility for complex roof shapes and is preferred when attic access or living space is needed above the ceiling.
How do I calculate rafter length from pitch and span?
Divide the building span by 2 to get the run. Multiply the run by the pitch (rise-per-12) divided by 12 to get the rise. Then apply the Pythagorean theorem: rafter length = sqrt(rise squared + run squared). Add the overhang by calculating its slant length at the same pitch and adding it to the basic rafter length. This calculator shows all three steps in the "Show your work" panel.
How many trusses do I need for my roof?
The standard formula is: truss count = floor(roof length divided by on-center spacing) + 1. For example, a 40 ft roof at 24 in (2 ft) spacing needs floor(40/2) + 1 = 21 trusses. Order 1-2 extras as spares for cuts, damage, or hip returns. The spacing is typically 16 in or 24 in for residential construction, with 24 in being the most common for roof trusses.
What is the most common roof pitch for houses?
In North America, pitches between 4/12 and 8/12 are most common for residential construction. A 6/12 pitch (26.6 degrees) is often considered the standard moderate slope: it drains well, suits most roofing materials including asphalt shingles and metal panels, and provides good attic clearance. Pitches below 4/12 require special low-slope materials; pitches above 12/12 are steep and require extra safety measures during installation.
How much do roof trusses cost?
Manufactured roof truss prices range from roughly $75 for a small 20 ft span simple gable truss to $500 or more for large complex trusses spanning 50+ ft. For a typical 28 ft wide, 40 ft long residential roof at 24-inch spacing (21 trusses), material cost is commonly $3,000-$8,000. Add $1,500-$3,000 for crane rental and installation labor. Always get local quotes because lumber prices and regional labor rates vary significantly.
What is roof area used for in this calculator?
The one-slope roof area equals the rafter length multiplied by the roof length. Double it to get the total deck area for a gable roof with two equal slopes. You need this figure to order roof sheathing (plywood or OSB panels) and roofing material (shingles, metal sheets). Add 10-15% for waste and cuts. The ridge board runs the full length of the roof, and gable-end framing adds additional materials not included here.
What is a slope multiplier and why does it matter?
The slope multiplier is the ratio of rafter length to horizontal run for a given pitch. For a 6/12 pitch it is sqrt(6^2 + 12^2) / 12 = approximately 1.118. This means every foot of horizontal distance on the roof plan corresponds to 1.118 ft of actual rafter. Roofers and estimators use it to quickly convert plan dimensions to material quantities: multiply the plan area by the slope multiplier to get the actual sloped roof area for material ordering.