Wood Beam Span Calculator

Background.

"How far can a 2x12 span?" has no single answer, and the reason is worth understanding before you use any number on this page. A beam is stopped by three completely independent things: it can break in bending, it can sag past what the finishes tolerate, or it can split along the grain in horizontal shear. Each of those limits produces its own span, they respond to different properties, and the beam can only go as far as the shortest of them. This calculator computes all three and tells you which one is doing the stopping, because that is what tells you what to change.

Bending is governed by the section modulus, which is breadth times depth squared over six, and by the adjusted bending design value of the wood. Deflection is governed by the moment of inertia, breadth times depth cubed over twelve, and by the modulus of elasticity — a stiffness property that barely improves when you buy a better grade. Shear is governed by the cross-sectional area and the shear design value. The practical consequence is that the three limits move in different directions when you change something: upgrading Douglas Fir-Larch No.2 to Select Structural lifts the bending value by 67 percent but the stiffness by only 19 percent, so a beam that was bending-limited may become deflection-limited without spanning much further. Going one size deeper improves all three at once, and improves deflection most of all.

The design values here are the real ones. Reference bending and modulus-of-elasticity figures come from the NDS 2018 Supplement, Table 4A for Douglas Fir-Larch, Hem-Fir and Spruce-Pine-Fir, and Table 4B for Southern Pine, which is published separately because its values are size-specific rather than adjusted by a size factor. Douglas Fir-Larch No.2 is 900 psi in bending with a 1,600,000 psi modulus; Hem-Fir No.2 is 850 and 1,300,000; Spruce-Pine-Fir publishes a single combined No.1/No.2 row at 875 and 1,400,000; Southern Pine No.2 falls from 1,100 psi at 4 inches wide to 750 psi at 12 inches, all at 1,400,000. Shear values are 180, 150, 135 and 175 psi respectively. Those numbers are quoted, not estimated, and the tests assert them against the published table.

Two adjustment factors are applied and named. The load duration factor CD comes from NDS Table 2.3.2 and is chosen by you: 0.9 for permanent load, 1.0 for ten-year occupancy live load, 1.15 for snow, 1.25 for seven-day construction and roof live load, 1.6 for wind or seismic. It raises bending and shear capacity but never stiffness, so it can lengthen a bending-governed span and can never lengthen a deflection-governed one — a fact the calculator will show you directly if you switch it. The size factor CF comes from the Table 4A adjustment table and depends on depth: 1.5 at 4 inches, 1.3 at 6, 1.2 at 8, 1.1 at 10 and 1.0 at 12. Southern Pine gets CF = 1.0 because Table 4B has the adjustment baked in already.

One factor is deliberately left out, and this is the most important judgement call on the page. The repetitive member factor Cr of 1.15 applies, in the words of Table 4A, to members "in contact or spaced not more than 24 inches on center, not less than 3 in number, and joined by floor, roof or other load distributing elements adequate to support the design load". A three-ply built-up girder is three members in contact, but it is not joined by a load-distributing element in the sense the provision describes, and practice among designers is genuinely divided. This page takes the conservative reading and omits Cr for beams and girders. The repetitive case, where the provision applies without argument, is handled on the floor joist page instead, and the difference is worth about 15 percent of bending capacity.

The worked example is a three-ply 2x12 in Douglas Fir-Larch No.2 carrying a living-area floor: joists span 8 feet to a wall on each side so the tributary width is 8 feet, live load is 40 pounds per square foot and dead load is 10, giving 400 pounds per lineal foot. Bending allows 11.93 feet, deflection at L/360 on the live load allows 15.81 feet, and shear allows 32.25 feet. Bending is the binding constraint, so the answer is 11 feet 11 inches, and if you want more span the useful move is a deeper or stronger member rather than a stiffer one. That pattern — bending governing a beam while deflection governs a joist — is the normal one, and it is exactly what you would expect from a member carrying a wide tributary strip without the repetitive-member bonus.

The scope is narrow on purpose. This page covers nominal 2-inch visually graded dimension lumber, single or built up, in four species and three grades. It does not cover solid sawn timbers 5 inches and thicker, whose design values live in NDS Table 4D with a different size factor; it does not cover glulam, which is Table 5A; and it does not cover LVL, PSL, LSL or I-joists, whose values are product-specific and come from the manufacturer's evaluation report. It assumes dry service at 19 percent moisture content or less, normal temperature, no incising, and a compression edge held in line by sheathing or blocking so that lateral-torsional buckling does not govern. It does not check bearing at the supports, connections, notches, holes, point loads, cantilevers, continuity over multiple supports, or anything below the beam. Span requirements are set by the code your jurisdiction has adopted — IRC 2021 Tables R502.5(1) and R502.5(2) for girders and headers, Table R301.7 for deflection — local amendments govern, adopted editions differ, and a licensed structural engineer or architect must sign off before work proceeds.

What is wood beam span calculator?

The allowable span of a wood beam is the greatest distance it can bridge between supports while satisfying every applicable limit state at once. There are three that matter for a simply supported, uniformly loaded sawn member, and the allowable span is the smallest of the three.

Bending capacity comes from the adjusted bending design value Fb' multiplied by the section modulus S. Setting the demand wL²/8 equal to that capacity and solving gives the bending-limited span. Deflection capacity comes from the modulus of elasticity E and the moment of inertia I: setting 5wL⁴/(384EI) equal to L divided by the code denominator and solving gives the deflection-limited span. Shear capacity comes from the adjusted shear design value Fv' and the cross-sectional area, with the peak stress in a rectangular section being 1.5 times the average; NDS 3.4.3.1(a) permits uniform load within a distance d of each support to be ignored, and solving that relation gives the shear-limited span.

Design values are not properties of a species alone. A reference value from the NDS Supplement has to be multiplied by adjustment factors for load duration, wet service, temperature, size, flat use, incising, repetitive use and beam stability before it becomes an allowable stress. This page applies the load duration factor and the size factor, states which ones it assumes to be 1.0 and why, and deliberately omits the repetitive member factor for beams.

The calculator handles a simply supported beam of nominal 2-inch dimension lumber, single or multi-ply, under a uniform load derived from a tributary width. It does not handle continuous or cantilevered beams, point loads, notches and holes, bearing checks, connection design, timbers 5 inches and thicker, engineered lumber, or fire-resistance requirements.

How to use this calculator.

1. 01Read the species and grade off the grade stamp on the lumber. If there is no stamp the material has no design value and cannot be used structurally.
2. 02Choose the nominal depth and the number of plies. Each ply is 1.5 inches of dressed thickness; plies must be fastened together to act as one member.
3. 03Enter the tributary width — half the joist span on each side of the beam, added together, not the full width of the room.
4. 04Enter the live load from IRC Table R301.5 for the occupancy, and estimate the dead load from the actual assembly. For a roof beam, put the design roof snow load in the live field.
5. 05Pick the deflection limit that matches what the beam supports, and decide whether it is checked against live load alone (the AWC and IRC span-table convention) or dead plus live (the IBC column).
6. 06Set the load duration factor for the shortest-duration load in the combination: 1.0 for floor occupancy, 1.15 for snow, 1.25 for roof live load.
7. 07Read the allowable span, then read which criterion governs. If deflection governs, go deeper. If bending governs, go deeper, add a ply or buy a better grade. If shear governs, add a ply.
8. 08Check what this page does not: bearing at the supports, the posts and footings under it, connections, notches and any concentrated loads — and have a licensed engineer or architect sign off before work proceeds.

The formula.

Three limits are computed independently, all in inches with the uniform load converted to pounds per inch, and the smallest is reported. Bending: the demand wL²/8 must not exceed Fb'·S, so L = √(8·Fb'·S ⁄ w). Deflection: 5wL⁴/(384EI) must not exceed L divided by the limit denominator, and the L on both sides cancels to first order, leaving L = ∛(384·E·I ⁄ (5·w·denominator)). Shear: the peak horizontal shear stress in a rectangular member is 3V/(2bd), and NDS 3.4.3.1(a) allows uniform load within a distance d of the supports to be neglected, so V = w(L/2 − d) and solving gives L = 2·(2·Fv'·b·d ⁄ (3w) + d). Working the example: a three-ply 2x12 is 4.5 by 11.25 inches dressed, so S = 4.5 × 11.25² ⁄ 6 = 94.921875 in³ and I = 4.5 × 11.25³ ⁄ 12 = 533.935547 in⁴. Douglas Fir-Larch No.2 has a reference Fb of 900 psi and, at a 12-inch nominal depth, a size factor of 1.0; with CD = 1.0 the adjusted value is Fb' = 900 psi, and Fv' = 180 psi. The load is (40 + 10) × 8 = 400 plf total, of which 320 plf is live; in pounds per inch those are 33.333 and 26.667. Bending gives √(8 × 900 × 94.921875 ⁄ 33.333) = √20,503.125 = 143.189 in = 11.9324 ft. Deflection at L/360 on the live load gives ∛(384 × 1,600,000 × 533.935547 ⁄ (5 × 26.667 × 360)) = ∛6,834,375 = 189.772 in = 15.8144 ft. Shear gives 2 × (2 × 180 × 4.5 × 11.25 ⁄ (3 × 33.333) + 11.25) = 2 × 193.5 = 387 in = 32.25 ft. Bending is smallest, so the allowable span is 11.9324 feet, displayed as 11 ft 11 in — truncated downward to the whole inch, never rounded up. Every intermediate value including the square and cube roots is carried at twenty significant digits and rounded only at the final result.

A worked example.

Frequently asked questions.

References& sources.

1. [1]American Wood Council — NDS 2018 Supplement, Table 4A, Reference Design Values for Visually Graded Dimension Lumber (2"–4" thick), all species except Southern Pine. Source of Fb, E, Fv and Fc⊥ for Douglas Fir-Larch (1500/1000/900 psi Fb; 1.9/1.7/1.6 million psi E; Fv 180; Fc⊥ 625), Hem-Fir (1400/975/850; 1.6/1.5/1.3 million; Fv 150; Fc⊥ 405) and Spruce-Pine-Fir (1250 Select Structural, 875 combined No.1/No.2; 1.5/1.4 million; Fv 135; Fc⊥ 425).
2. [2]American Wood Council — NDS 2018 Supplement, Table 4A adjustment factors: the size factor CF for Fb at 2" and 3" breadth (1.5 at 2–4" depth, 1.4 at 5", 1.3 at 6", 1.2 at 8", 1.1 at 10", 1.0 at 12", 0.9 at 14" and wider) and the repetitive member factor Cr = 1.15 with its three conditions.
3. [3]American Wood Council — NDS 2018 Supplement, Table 4B, Reference Design Values for Visually Graded Southern Pine Dimension Lumber, whose size factors are already incorporated. Fb by nominal width for No.2: 1100 at 4", 1000 at 5–6", 925 at 8", 800 at 10", 750 at 12"; E 1,800,000 / 1,600,000 / 1,400,000 psi for Select Structural / No.1 / No.2; Fv 175; Fc⊥ 565.
4. [4]American Wood Council — Span Tables for Joists and Rafters, 2021 edition. Table F-2 (40 psf live plus 10 psf dead, L/360) is used as the independent check on this calculator's deflection branch, and "Explanation of Tables" section 3 gives the PS 20-20 dressed sizes and section 9 the bearing requirements.
5. [5]American Wood Council — Span Tables for Joists and Rafters, 2024 edition, the current printing of the same document, confirming that the tabulated spans and the design basis are unchanged.
6. [6]International Code Council — IRC 2021 Table R301.7, Allowable Deflection of Structural Members (L/360 floors, L/240 all other members, L/180 rafters over 3:12 with no ceiling attached, L/600 lintels supporting masonry veneer), and Tables R502.5(1) and R502.5(2) for girder and header spans. Adopted editions and local amendments govern.
7. [7]International Code Council — IRC 2021 Table R301.5, Minimum Uniformly Distributed Live Loads, the source of the live-load figures quoted in the field hint.