Roof Truss Calculator — truss geometry, member lengths and count

A roof truss is not a stick of lumber you can size from a chart. It is a manufactured, engineered assembly: a fabricator's engineer takes the span, the pitch, the spacing, the loads and the bearing conditions for one specific building, runs the analysis, picks the chord and web sizes, specifies every plate, and seals the drawing. That sealed drawing is the design. Everything this page does sits underneath that — it is the geometry of the assembly, which is genuinely useful for planning, take-offs and understanding what you are being quoted, and which is a completely different thing from sizing a truss.

So this roof truss calculator answers geometric questions and only geometric questions. How many trusses does a forty-foot building take at two feet on centre? How long is each top chord once the overhang is included? How much web material is in a Fink compared with a king post at the same span? Arb Digital builds these estimating tools for trades and self-builders who want to arrive at a supplier conversation already knowing the shape of the answer, so the quote can be checked rather than simply accepted.

What This Roof Truss Calculator Does

Give it a clear span, a pitch expressed as rise per twelve of run, an overhang, a spacing and a building length, and it returns the truss count, the rise at the ridge, the length of each top chord including the tail, the bottom chord length, the total web length for the layout you chose, and the total lineal feet of material across every truss with your cutting allowance added. The breakdown bars show how that material divides between top chords, bottom chord and webs, which is the quickest way to see why a steeper roof costs more in lumber than the plan area suggests.

It handles three classical symmetrical configurations. The king post has a single vertical web from the apex down to the centre of the bottom chord. The queen post has two verticals rising to the top chords at the quarter points with a horizontal straining piece between them. The Fink, the familiar W truss that dominates residential roofs, has four webs running from the bottom chord third points up to the apex and out to the mid-points of each rafter.

What it does not do, and will not do: it publishes no span table, no allowable load table and no member sizes. It never tells you that a span, a spacing or a configuration is adequate. Those are outputs of an engineering analysis against loads that vary by site, and they belong on a sealed drawing.

How to Use It

1. Pick the configuration. Fink is the default because it is what most residential suppliers ship. King and queen post are common in garages, porches, barns and traditional timber work.
2. Enter the clear span and the pitch. Span is out to out of the bearing walls. If you only know the roof angle in degrees, convert it first with our roof pitch calculator, which moves between x/12, degrees, percentage grade and the slope multiplier.
3. Set the overhang and the spacing. Overhang is the horizontal projection past the wall, not the length of the tail along the slope — the calculator converts it. Spacing is whatever you are being quoted or whatever the designer has specified.
4. Enter the building length and any extra end trusses. Gable-end trusses and girder trusses are usually different products with different prices, so they are counted separately.
5. Read the geometry, then take it to a supplier. The lineal-foot figure is a material take-off for pricing conversations, not a bill of materials you can cut from.

The Formula and How It Is Calculated

Everything here comes from one right triangle. For a pitch of p rise per twelve of run, the slope multiplier is √(1 + (p/12)²). That single number converts any horizontal distance into the sloping distance above it. The rise at the ridge is half the span multiplied by p/12. The rafter, or top chord, from the heel to the apex is half the span multiplied by the slope multiplier, and the overhang tail is the horizontal overhang multiplied by the same figure. The roof angle in degrees is the arctangent of p/12.

Web lengths follow from the panel points. In the Fink layout the bottom chord carries nodes at one third and two thirds of the span, and each top chord carries a node at its mid-point, which sits at a quarter of the span horizontally and half the rise vertically. The short web runs from the third point to that mid-point, a horizontal step of span ÷ 12 against a vertical step of half the rise. The long web runs from the same third point up to the apex, a horizontal step of span ÷ 6 against the full rise. Both are solved with Pythagoras and doubled for symmetry. The king post web is simply the rise. The queen post gives two verticals of half the rise plus a straining piece of half the span.

Truss count is the building length divided by the spacing, rounded up, plus one for the closing end, plus any extra end or girder trusses you entered. That plus-one exists because a run of bays needs one more member than it has bays — the classic off-by-one that shows up on every fence, joist and stud take-off.

Worked example, so you can check the page against arithmetic you can do yourself: a 24 ft span at 6/12 with a 12 in overhang, Fink, at 24 in centres along a 40 ft building. Rise is 12 × 0.5 = 6.00 ft. The slope multiplier is √1.25 = 1.1180. Each rafter is 12 × 1.1180 = 13.42 ft, plus a tail of 1 × 1.1180 = 1.12 ft, giving 14.53 ft per top chord and 29.07 ft for the pair. The bottom chord is 24.00 ft. The short webs are √(2² + 3²) = 3.61 ft each and the long webs √(4² + 6²) = 7.21 ft each, so the four webs total 21.63 ft. That is 74.70 ft of material per truss. The count is 40 × 12 ÷ 24 = 20 bays, plus one, so 21 trusses, and 21 × 74.70 = 1,568.7 lineal feet before any allowance.

Why a Truss Cannot Be Sized From a Table

Stick framing has span tables because a rafter is a single member carrying a load in bending, and the relationship between species, grade, depth, spacing and span can be tabulated. A truss is a statically determinate frame in which every member carries axial force, tension or compression, and the plated joints are themselves designed elements. Change the pitch by one increment and the force in every web changes. Add a girder point load from an intersecting roof and the whole analysis changes. Put a storage floor or a solar array on it and the load case changes again.

This is why the truss industry works to the Structural Building Components Association's published practice and to the ANSI/TPI 1 design standard rather than to charts in a builder's handbook, and why every truss arrives with a sealed drawing specific to that job. Getting your loads is a separate step: ground snow, wind and seismic values are site-specific and come from your building department or from the ASCE 7 Hazard Tool. If you want to see how a ground snow load turns into a design roof load, our snow load calculator applies the published ASCE 7 method to values you supply — it also publishes no map and no table, for the same reason.

Field Modification Voids a Truss

This is the single most important sentence on the page. Cutting, notching, drilling or removing any chord or web of a truss voids the engineering behind it. A truss is not a beam with spare capacity; it is a frame in equilibrium, and a web you cut because it was in the way of a duct was carrying a force that now has nowhere to go. The same applies to a plate that has been knocked loose in handling, a truss that has been stored flat and taken a set, or a bearing that has been shimmed differently from the drawing.

If something has to change, the fix is a repair detail from the truss designer, not a decision on site. Suppliers issue these routinely and they are usually straightforward. The expensive outcome is the one where nobody asks.

Where the Boundary Sits Against Our Other Roof Tools

Four Arb Digital tools touch a roof and they answer four different questions, so it is worth being explicit. The roof pitch calculator converts a slope between x/12, degrees, grade and the slope multiplier, and gives the true surface area of a sloping plane. The rafter length calculator is for stick framing: it returns common, hip and jack rafter lengths with the plumb and seat cut angles you actually mark on the timber. That is a different construction method from trusses — you cut rafters on site, you do not cut trusses at all. The roofing calculator is about the covering: squares, bundles, underlayment and ridge cap. And for a curved or multi-slope profile, the gambrel roof calculator handles the two-pitch barn form. This page is the only one of the five concerned with the truss assembly itself, and it stops at geometry.

Spacing, Count and the Things Spacing Cannot Tell You

Twenty-four inches on centre is the common residential spacing, but the number is an output of design, not a default you can assume. Heavier snow, a longer span, a heavier covering such as tile or slate, or a ceiling that has to carry storage will all push a designer toward closer spacing or a heavier truss. Engineered trusses at wider spacings are normal in agricultural buildings, with purlins to suit.

What the spacing does control, arithmetically, is the count and therefore the price and the crane time. Moving from 24 in to 16 in centres on a 40 ft building takes you from 21 trusses to 31, a 48 per cent increase in units and in lineal feet of material. Seeing that trade-off in numbers before you ask for a re-quote is most of the value of a geometry tool.

Reading a Truss Quote With the Geometry in Front of You

A supplier's quote lists a profile name, an overall span, an overall height, an overhang and a quantity, often with a girder or two priced separately. With the geometry on this page you can sanity-check three things immediately. Does the quoted overall height match the rise your pitch implies, allowing for the heel height? Does the quantity match your building length and the stated spacing, including the end truss? And is the overhang quoted horizontally or along the slope, because the two differ by the slope multiplier and on a steep roof that is a real length difference.

The take-off also tells you roughly how much timber is in the assembly, which makes an outlier quote visible. The board foot calculator converts lineal feet into board feet and cost.

Common Mistakes to Avoid

• Treating the lineal-foot figure as a cut list. It is a take-off for pricing. Real trusses are cut with plate allowances, bevels and heel details this page knows nothing about.
• Entering the overhang along the slope. The field expects the horizontal projection past the wall face; the slope conversion is applied for you, so entering a sloping length double-counts the pitch.
• Forgetting the plus-one truss. Twenty bays need twenty-one trusses. Ordering by bays alone leaves the last one short every time.
• Assuming span means the room width. Truss span is out to out of bearing, which includes the wall thickness on both sides and is larger than the clear internal dimension.
• Reading a spacing here as approval to use it. Nothing on this page evaluates capacity. Spacing is an input you supply and the truss designer confirms.

Related Free Tools From Arb Digital

Convert the slope itself with the roof pitch calculator, cut a stick-framed roof with the rafter length calculator, price the covering with the roofing calculator, handle a barn profile with the gambrel roof calculator, turn the load map into a design load with the snow load calculator, and price the timber with the board foot calculator. Everything else is in the free tools hub.

Frequently Asked Questions

This tool computes roof truss geometry and material quantity from inputs you supply. It is a planning and estimating aid for education and preliminary work only. It performs no structural analysis, applies no load, evaluates no capacity, and is not a design. Roof trusses must be designed and sealed by a licensed engineer, supplied against that sealed drawing, and approved by the building department having jurisdiction over your site.