2×6 Deflection Calculator: Beam Sag vs L/360 and L/240

This 2×6 deflection calculator shows how far a simply supported 2×6 joist or beam sags at midspan under a uniform load, a point load at the center, or both, and compares the result with the L/360 and L/240 limits. A selector switches the member to a 2×4, 2×8, 2×10 or 2×12, boards can be doubled, and the modulus of elasticity comes from the American Wood Council’s published design values. It is a planning check for sag only.

Press Calculate to see the math with your numbers.

How the 2×6 deflection calculator works

The calculator treats the board as a simply supported beam, which means it rests on a support at each end and carries the load between them. Midspan deflection is the sum of two standard results from Table 9-1 of the USDA Wood Handbook:

• Uniform load: δ = 5wL⁴ ÷ (384EI)
• Point load at midspan: δ = PL³ ÷ (48EI)

Here w is the uniform load in pounds per inch (the lb-per-foot input divided by 12), P is the point load in pounds, L is the span in inches, E is the modulus of elasticity in psi, and I is the moment of inertia of the cross-section, I = b × d³ ÷ 12, with b the total thickness and d the depth in inches. When both loads are entered, the two deflections add. Doubling the boards (the plies box) doubles b, so I doubles.

Depth is cubed in I, which is why a 2×8 is far stiffer than a 2×6: its I is 47.6 in.⁴ against 20.8 in.⁴, about 2.3 times as stiff.

Modulus of elasticity values

The E list comes from Table W-1 of the American Wood Council’s Design Values for Joists and Rafters (2024). Every row below has the same E for 2×4 through 2×12, which is why the list needs no size adjustment. These are the averages the table assigns to each grade, adjusted for shear deflection (Wood Handbook Chapter 7), so the bending-only formulas above are the right ones to pair with them.

The Southern pine rows are for the plain grade; the dense and non-dense variants of No.2 have their own E (1,600,000 and 1,300,000 psi), so use the custom box for those. Hem-fir has an E that changes with member size (1,200,000 to 1,300,000 psi in the same table), so the list leaves it out. For hem-fir or any other lumber, type the E value into the custom box, which overrides the list.

Actual sizes used

The calculator uses dressed dry sizes from Wood Handbook Table 6-6: 1-1/2 in. thick, and 3-1/2, 5-1/2, 7-1/4, 9-1/4 or 11-1/4 in. deep for 2×4, 2×6, 2×8, 2×10 and 2×12.

Deflection limits: L/360 and L/240

Limits are written as the span divided by a number. At 10 feet (120 in.) the L/360 limit is 0.333 in. and the L/240 limit is 0.500 in. The values below are from International Building Code Table 1604.3. The bar under the calculator reads your result against them.

The limits apply to the load named in the column, so check the live load on its own against the live-load limit. Local codes and the project’s engineer decide which row applies.

Worked example: 2×6 joist over 10 feet

Take a Douglas fir-larch No.2 2×6 spanning 10 feet and carrying 50 lb per foot, which is 37.5 psf on a joist spaced 16 in. apart (50 ÷ (16/12)).

• I = 1.5 × 5.5³ ÷ 12 = 20.797 in.⁴
• δ = 5 × (50/12) × 120⁴ ÷ (384 × 1,600,000 × 20.797) = 0.338 in.
• L/δ = 120 ÷ 0.338 = 355, just short of L/360 (0.333 in.) but inside L/240 (0.500 in.)

Moving up to a 2×8 cuts the sag to 0.148 in. (L/813). Staying with the 2×6 but using SPF No.1/No.2 at E = 1,400,000 psi raises it to 0.386 in. (L/311), because deflection is inversely proportional to E. A 2×8 on a 12-foot span with a 300 lb point load at center and E = 1,400,000 psi sags 0.280 in. (L/515).

What this calculator does not check

• Strength. Deflection is a stiffness check. Bending strength, shear and bearing need design values and adjustment factors that this page does not apply.
• Long-term sag. Wood creeps under constant load. The NDS applies a creep factor of 1.5 to the dead-load part of seasoned lumber (NDS Section 3.5.2), so a floor that is close to a limit today can exceed it later.
• Self-weight and other loads. Add the weight of the board itself, flooring and fixtures to the uniform load. The wood weight calculator gives pounds per foot for the board.
• Conditions. E values apply to dry service at 19% moisture or less. Notches, holes, wet service and floor vibration are outside the formulas.

For permits and real floors or roofs, use the AWC span tables or an engineer.

Related tools

The wood load capacity calculator adds bending stress and a shelf check, the how much weight can wood hold calculator compares breaking load with sag for a single board, and the plywood load capacity calculator handles panels.

Frequently asked questions

How much deflection is acceptable for a 2×6?

It depends on the use. For floor members the building code limit is L/360 for live load and L/240 for total load, and for roof members with a non-plaster ceiling it is L/240 and L/180. On a 10-foot 2×6 span, L/360 is 0.333 in. and L/240 is 0.500 in.

How much does the modulus of elasticity change the result?

Deflection is inversely proportional to E. Going from a 1,600,000 psi grade to a 1,400,000 psi grade raises the sag by about 14% (1.6 ÷ 1.4). Depth matters more, since stiffness rises with the cube of the depth: a 2×8 is about 2.3 times as stiff as a 2×6.

Does this calculator check whether the 2×6 will break?

No. It reports sag only. Breaking depends on bending strength, shear, bearing and adjustment factors for load duration and moisture. A member that passes the deflection check still has to pass those checks, so use span tables or an engineer for anything that carries people.