Framing & structure
Wood beam & header size calculator
Size a built-up 2x beam or header from its span and the floor or roof it carries, with moment, shear, reactions and every size and ply count checked.
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What a beam and header size calculator does
A beam and header size calculator works out what a beam has to carry and which sawn-lumber sizes can carry it. Enter the clear span, the tributary width of floor or roof it supports, the loads and the species and grade, and it returns the uniform load, the bending moment, the shear, each end reaction and the section properties the beam needs, then checks every 2x depth with one to four plies and recommends the lightest one that passes.
Each option is checked for bending, shear and deflection under both live and total load, with the load duration factor for floors, snow or roof live load and the repetitive-member factor for beams of three or more plies. The reactions are the loads the posts, jack studs and footings below must carry.
It is a preliminary sizing for a simple span with a uniform load and a braced top edge. Point loads from posts or girder trusses, bearing length, connections and self-weight are left out, so confirm the final header with the code tables your jurisdiction adopts or an engineer.
How to use the wood beam & header size calculator
- Choose Imperial or Metric. Imperial is the default, and your choice carries across the free tools.
- Enter the Clear span between supports and the Tributary width: half the joist or rafter span on each side the beam supports, added together.
- Choose the Load case (floor, roof snow or roof live), then enter the Live or snow load and the Dead load. Set the Live-load deflection limit and Total-load deflection limit (L/360 and L/240 are usual for floors).
- Pick the Species and grade, the Member size and the number of Plies you plan to use, then read the utilisation and result for that beam.
- Read the Lightest passing option and scan the table for every size and ply count. Pass the end reactions to the post and footing design, and download the result as PDF or CSV.
Worked example
Imperial: A 10 ft span carrying 8 ft of 40 psf live and 10 psf dead (400 plf) has a 5,000 ft·lb moment and 2,000 lb reactions; three Douglas Fir-Larch No.2 2x10 plies are the lightest passing option at 82% utilisation.
Metric: A 3 m span carrying 2.4 m of 1.5 kPa live and 0.5 kPa dead (4.8 kN/m) has a 5.4 kN·m moment and 7.2 kN reactions; two 45 × 240 mm C24 plies are 59% utilised.
Built-up beam sizes by span (floor beam)
The table shows the lightest passing built-up Douglas Fir-Larch No.2 beam for a floor beam carrying 8 ft of floor at 40 psf live and 10 psf dead (400 lb per foot), with L/360 live and L/240 total deflection limits. Load and reaction rise in step with the span, and the moment rises with its square, which is why each extra 2 ft of span needs a deeper beam or another ply.
Lightest means the smallest cross-section. In a wall, the header also has to fill the wall thickness, so a 2x4 wall usually takes two plies and a 2x6 wall three, with spacers where needed.
| Clear span | Moment | Reaction each end | Lightest option |
|---|---|---|---|
| 4 ft | 800 ft·lb | 800 lb | 1 × 2x8 |
| 6 ft | 1,800 ft·lb | 1,200 lb | 1 × 2x12 |
| 8 ft | 3,200 ft·lb | 1,600 lb | 2 × 2x10 |
| 10 ft | 5,000 ft·lb | 2,000 lb | 3 × 2x10 |
| 12 ft | 7,200 ft·lb | 2,400 lb | 3 × 2x12 |
| 14 ft | 9,800 ft·lb | 2,800 lb | 4 × 2x12 |
Tributary width: how much load reaches the beam
A beam carries the strip of floor or roof halfway to the next support on each side. A beam in the middle of a house with 12 ft joists on one side and 14 ft joists on the other has a tributary width of 6 + 7 = 13 ft. A header over a window in an exterior wall carries half the joist or rafter span on the inside only, plus any wall, floor or roof stacked above it.
Multiply the tributary width by the load per square foot to get the load per foot of beam. At 40 psf live and 10 psf dead, every foot of tributary width adds 50 plf. Loads from more than one level add together; enter the total as the live and dead loads, or run the calculator once per level and combine the reactions.
Roof headers and load duration
Wood carries a short load better than a permanent one, so the allowable stresses go up with the load duration factor: 1.0 for floor live load, 1.15 for snow and 1.25 for roof live (construction) load. That is why a roof header can be smaller than a floor beam at the same load.
The table uses 30 psf snow and 15 psf dead load over 8 ft of roof, with L/240 live and L/180 total deflection. Use the design snow load for your site; heavy-snow regions can need far deeper headers.
| Clear span | Reaction each end | Lightest option |
|---|---|---|
| 3 ft | 540 lb | 1 × 2x6 |
| 4 ft | 720 lb | 1 × 2x6 |
| 6 ft | 1,080 lb | 1 × 2x10 |
| 8 ft | 1,440 lb | 3 × 2x6 |
Worked example: a 10 ft floor beam
A 10 ft clear span carrying 8 ft of floor at 40 psf live and 10 psf dead takes 400 plf. The moment is 400 × 10² ÷ 8 = 5,000 ft·lb, the shear and each reaction are 400 × 10 ÷ 2 = 2,000 lb. Two Douglas Fir-Larch No.2 2x10s have Fb′ = 900 × 1.1 = 990 psi and a section modulus of 42.8 in³, so they are 142% utilised in bending and fail.
Three plies add capacity twice over: the section modulus rises to 64.2 in³ and the repetitive-member factor raises Fb′ to 1,138.5 psi, so bending utilisation drops to 82%. Shear is 40% and deflection 45%, so three 2x10s pass and are the lightest option for this beam. Each post or jack stud stack below must carry 2,000 lb.
Metric built-up beams
Metric grades are converted from characteristic values to an allowable-stress equivalent, so the method is the same. For a C24 beam carrying 2.4 m of floor at 1.5 kPa live and 0.5 kPa dead (4.8 kN/m), the lightest passing options are shown below.
| Clear span | Lightest option |
|---|---|
| 2 m | 1 × 47 × 175 mm |
| 3 m | 1 × 45 × 290 mm |
| 4 m | 2 × 45 × 290 mm |
| 5 m | 3 × 45 × 290 mm |
Who it is for and when to use it
Opening up a wall
Estimate the beam that replaces a wall you want to remove, and the load each new post will take, before asking an engineer to confirm it.
Sizing window and door headers
Check headers over wider openings in exterior walls, including roof headers under snow.
Deck and porch beams
Get a first size for a dropped beam under joists, then confirm treated-lumber values and wet-service factors.
Comparing with LVL
When no sawn option passes, or the beam gets too deep, move to the LVL and glulam calculator with the same loads.
Method, formulas & assumptions
Uniform load w = (live or snow + dead) × tributary width. Moment M = wL²/8; shear and each end reaction V = wL/2. Fb′ = Fb × CD (1.0 floor, 1.15 snow, 1.25 roof live) × CF × Cr (1.15 for three or more plies, otherwise 1.0); Fv′ = Fv × CD. Utilisation is the largest of M ÷ (Fb′ S), 1.5V ÷ (Fv′ A) and the live- and total-load deflections 5wL⁴/(384EI) against L/360 and L/240 (or the limits you choose). Required S, I and shear area are reported for the selected member, and the table checks 1–4 plies of each depth to find the lightest passing option.
Imperial inputs are converted with exact factors (1 ft = 0.3048 m, 1 lb = 0.45359237 kg, 1 US gal = 3.785411784 L) before the calculation runs in SI, then results are converted back.
Common mistakes to avoid
- Using the full joist span instead of half of it on each side for the tributary width.
- Forgetting loads from above: a header under a bearing wall and a second floor carries both.
- Assuming plies share load without proper nailing or screwing. Built-up beams need a fastening schedule.
- Ignoring the posts. The reaction has to travel through jack studs, posts and footings to the ground.
- Sizing a beam that carries a post or girder truss with a uniform load. Concentrated loads need a separate check.
- Leaving out beam self-weight on long or heavy beams; add it to the dead load.
Scope & limits
A preliminary estimate for a simply supported beam with a uniform load, the compression edge braced along its length and plies fastened to act together. Beam self-weight, point loads from posts or girder trusses, bearing length, jack studs, notches, connections, wet service and fire are not included. Confirm header sizes with the adopted code tables or an engineer.
Frequently asked questions
What size header do I need for a 6 ft opening?
It depends on what the header carries. Under 8 ft of floor at 40 psf live and 10 psf dead, a single Douglas Fir-Larch No.2 2x12 passes on paper, and two plies fill a 2x4 wall. Under 8 ft of roof at 30 psf snow and 15 psf dead, a 2x10 passes.
How far can a triple 2x10 beam span?
Carrying 8 ft of floor at 40 psf live and 10 psf dead, three Douglas Fir-Larch No.2 2x10s pass at 10 ft with 82% utilisation. Lighter loads allow more span, heavier loads less.
What is tributary width?
The width of floor or roof whose load reaches the beam: half the span of the joists or rafters on each side, added together.
Why do three plies help more than you would expect?
Three or more members fastened together qualify for the 1.15 repetitive-member factor, so the third ply adds both section and allowable stress.
What are the end reactions used for?
They are the loads the posts, jack studs and footings at each end of the beam must carry and the bearing the supports must provide.
Does the calculator include the weight of the beam?
No. Add the beam's self-weight to the dead load for long or heavy beams.
Can I use this for a beam carrying a point load?
No. It models a uniform load only. Posts, girder trusses and point loads from above need an engineered check.
Do I need an account to download the result?
No. All calculations, local file processing and exports on this page are free, without an account.
Where are my inputs stored?
The tool keeps inputs in this browser tab. It does not upload them or create a cloud copy. Save or download anything you want to keep before leaving the page. Standard site analytics may operate independently of the tool.
Can I work in metric instead of imperial?
Yes. Use the Imperial / Metric switch above the inputs. Imperial (feet, inches, pounds, gallons) is the default; switching converts every dimensional field and result, and your choice is remembered across the free tools in this browser.
Further reading
- Ground snow load explained
- Renovations and extensions
- Building permit process explained
- All framing & structure tools
- All free architecture & construction tools
- Harth resource library
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