Wood Beam Span Calculator

A wood beam passes only when all four checks pass. Each check gives a ratio of actual to allowed. A ratio above 100 percent fails. The longest span is the shortest of the four spans, and the check that sets it is the controlling check.

In the example above, bending controls at 9.7 ft. Shear allows 22.2 ft, so shear rarely decides a beam of this size.

The calculator treats the beam as a simple span with a uniform load. It finds the section properties, adjusts the published design values, then compares the actual stress and sag with what the lumber allows. Then it solves each check for the longest span.

Bending, shear and deflection formulas

1. Bending: M = wL² / 8, then fb = M / S. The beam passes when fb is at or below Fb′.
2. Shear: V = wL / 2, then fv = 3V / (2A) for a rectangular section. The beam passes when fv is at or below Fv′.
3. Deflection: δ = 5wL⁴ / (384EI). The beam passes when δ is at or below L divided by the limit ratio.

S = n x b x d² / 6      I = n x b x d³ / 12      A = n x b x d
Longest span, bending:  L = √(8 x Fb′ x S / (12 x w))
Longest span, shear:    L = 4 x Fv′ x A / (3 x w)
Longest span, sag:      L = ∛( (12 / ratio) x 384 x E′ x I / (5 x (w / 12) x 12⁴) )
w in plf, L in ft, b and d in inches, stresses in psi

In plain words, the beam gets stiffer and stronger fast as it gets deeper, and weaker fast as it gets longer. Bending span grows with the square root of strength. Sag span grows only with the cube root of stiffness.

The shear formula uses the rectangular-section form 3V / (2A), which is 50 percent higher than the average stress V / A. A formula that uses V / A reads low. Shear is taken at the support face, which is the conservative choice.

Design values and adjustment factors used

Base values come from the WWPA Western Lumber Product Use Manual, Table 1. The tool multiplies Fb by the size factor CF for the member depth, and by the wet service factors when wet service is on. Load duration is 1.0 for every case. That is conservative for snow loads.

Wet service applies when the lumber stays above 19 percent moisture content. It multiplies Fv by 0.97 and E by 0.9. It multiplies Fb by 0.85 only when the size-adjusted Fb is over 1,150 psi.

A double 2x10 in Douglas Fir-Larch No. 2 spans 8 ft and carries a floor strip 6 ft wide. The load is 40 psf live and 10 psf dead. That gives 240 plf live and 60 plf dead, or 300 plf total. Every check passes and bending controls.

1. Section: two plies of 1.5 x 9.25 in. S = 42.78 in³, I = 197.86 in⁴, A = 27.75 in².
2. Allowed bending: Fb′ = 900 x 1.1 = 990 psi. E = 1,600,000 psi. Fv′ = 180 psi.
3. Moment: M = 300 x 8² / 8 = 2,400 lb-ft, or 28,800 lb-in. Bending stress fb = 28,800 / 42.78 = 673 psi, which is 68 percent of allowed.
4. Shear: V = 300 x 8 / 2 = 1,200 lb. fv = 1.5 x 1,200 / 27.75 = 64.9 psi, which is 36 percent of allowed.
5. Sag: live-load deflection is 0.070 in against a limit of 0.267 in. Total-load deflection is 0.087 in against 0.400 in.
6. Longest span: bending 9.70 ft, shear 22.2 ft, live sag 12.5 ft, total sag 13.29 ft. Bending sets 9.7 ft.

Under 300 plf in Douglas Fir-Larch No. 2, dry service, the sections below reach 7.9 to 15.9 ft. Bending controls every row. The table uses a 6 ft tributary width, 40 psf live load, 10 psf dead load, L/360 for live load and L/240 for total load.

Values come from the same math as the calculator. Change the load and the table no longer applies. Use the calculator for your own load, species and grade.

Start with the span and the load, then pick the smallest member that passes all four checks. Enter your span, set the tributary width, and try deeper members or more plies until the result passes. The calculator names the smallest listed member that passes when yours fails.

• Bending usually decides spans under about 16 ft in this list. A deeper member helps most, because section strength grows with the square of the depth.
• Plies add strength in direct proportion. A triple 2x10 reaches 11.9 ft where a double 2x10 reaches 9.7 ft under the same load.
• Grade matters. Select Structural lifts Fb from 900 to 1,500 psi in Douglas Fir-Larch before the size factor.

To order the lumber, count the pieces and use the lumber calculator for board feet. For the posts and footings under a deck beam, see the deck calculator.

Most wrong answers come from the inputs, not the math. These five mistakes show up most often, and each one changes the result by a measurable amount.

1. Using the wrong tributary width. A double 2x10 reaches 11.9 ft at a 4 ft tributary width and 8.4 ft at 8 ft. Measure to the midpoint of the next support on each side.
2. Counting plies that are not tied together. The math assumes the plies act as one member. Fasten them with the pattern your inspector requires.
3. Checking only bending. Deeper, higher-grade beams can fail on sag first. Four plies of 2x12 Select Structural reach 20.5 ft in bending but only 20.3 ft on live sag.
4. Using dry values outdoors. Wet service cuts the live sag span of the example beam from 12.5 ft to 12.1 ft.
5. Reading a planning check as a design. The tool does not check bearing length, notches, holes or point loads.

Call a licensed engineer or your building department when the beam leaves the simple case this tool covers. The calculator is a planning check. It is not a stamped design and it does not replace the plan review.

• The beam carries a post, a wall, a stair or any point load.
• The beam cantilevers past a support or runs over more than two supports.
• The span is 20 ft or more, or no listed member passes.
• The beam has notches or holes, or the bearing is short.
• The roof load in your area is set by snow. This tool uses a load duration factor of 1.0, so confirm the roof load and the duration factor with your jurisdiction.
• You want LVL, glulam or steel. Use the manufacturer's tables or an engineer.

Your local building department sets the design loads and the deflection limits that apply. Take the numbers from this page to that conversation.

Published November 2026. Last reviewed November 2026. Next review May 2027. This is a planning estimate, not a stamped design.

Alex Rivera, PEPE

Reviews: volume calculators · 38 calculators reviewed

Alex Rivera is a Licensed Professional Engineer (PE) with 18 years of structural and civil engineering experience. He holds PE licenses in California (#C-89412) and Texas (#P.E.-98765). He previously served as Engineer of Record on 250+ residential foundation designs at Thornton Tomasetti. At CalcSummit, he writes and personally reviews every structural, concrete, rebar, deck, and framing calculator against current IRC and ACI 318 standards.

Full profile →