Beam Span Calculator
Estimate how far a built-up dimensional-lumber beam can span. Pick the beam size (2- or 3-ply 2×6 through 2×12) and species grade, enter design load in psf and tributary width in feet, and get bending- and deflection-limited spans.
Example: with Beam (plies × size) 2-ply 2×10 (3 × 9.25 in) · Species & grade (Fb, E) Douglas fir-larch #2 (900 psi, 1.6M) · Total design load (psf) 50 · Tributary width (ft) 8 → Estimated allowable span: 8 ft 5 in (bending governs, w = 400 plf).
- Bending-limited span8.40 ft
- Deflection-limited span (L/360)10.54 ft
Computed by the calculator below using its default values. Change any input to see your own numbers.
Simply supported beam under uniform load: span limited by bending (Fb × S) and deflection (L/360). A planning estimate — final sizing belongs to code span tables or an engineer.
What limits a beam span
Two checks size most simple wood beams. Bending strength: the maximum moment of a uniformly loaded, simply supported beam is wL²/8, and it cannot exceed the lumber's allowable bending stress (Fb) times the section modulus (S = bd²/6). Stiffness: total sag is held to span/360, the customary limit for floors, using the deflection formula 5wL⁴/384EI. The shorter of the two answers governs — deeper beams are usually bending-limited, long shallow ones deflection-limited.
Load comes from tributary width: a center girder carries half the joist span on each side. A house 16 ft deep loads its center beam with 8 ft of tributary width; at 50 psf total (40 live + 10 dead) that is 400 lb on every foot of beam.
How it’s calculated
w (plf) = load (psf) × tributary width (ft). Bending span: L = sqrt(8 × Fb′ × S ÷ (w/12)) with S = bd²/6 and Fb′ = base Fb × NDS-style size factor (1.3 for 2×6, 1.2 for 2×8, 1.1 for 2×10, 1.0 for 2×12). Deflection span: L = cbrt(384 × E × I ÷ (1800 × w/12)) from 5wL⁴/384EI ≤ L/360, I = bd³/12. Base Fb/E are NDS No.2 reference values; no duration, wet-service, or repetitive-member adjustments are applied.
A simplified guidance model: simply supported, uniform load, total load checked against L/360, no shear or bearing checks, and Southern pine values approximated with one size. Size actual construction from IRC span tables or a licensed engineer.
Estimated spans, DF-L #2 at 50 psf and 8 ft tributary
| Beam | Estimated span | Limited by |
|---|---|---|
| 2-ply 2×6 | ≈ 5.4 ft | Bending |
| 2-ply 2×8 | ≈ 6.9 ft | Bending |
| 2-ply 2×10 | ≈ 8.4 ft | Bending |
| 2-ply 2×12 | ≈ 9.7 ft | Bending |
| 3-ply 2×10 | ≈ 10.3 ft | Bending |
| 3-ply 2×12 | ≈ 11.9 ft | Bending |
Computed with this page's formulas (Fb 900 psi × size factor, E 1.6M psi); for planning comparison only.
Common mistakes
- Treating this as a code check — IRC girder tables and engineers account for shear, bearing, load duration, and lamination nailing that this estimate omits.
- Using live load only: the beam carries dead load too, so check totals (e.g., 40 + 10 = 50 psf for floors).
- Forgetting tributary width — a beam under 12 ft of floor carries 50% more load per foot than one under 8 ft.
- Assuming two 2×10s equal a 4×10: built-up plies must be properly nailed or bolted to act together.
Frequently asked questions
What formula does a beam span calculator use?
Two: bending, L = sqrt(8 × Fb × S ÷ w), and deflection, from 5wL⁴/384EI ≤ L/360. S = bd²/6 and I = bd³/12 for rectangular sections, with w as load per inch of beam. The smaller span governs.
How far can a double 2×10 span as a beam?
Under 50 psf total load with 8 ft of tributary width, a 2-ply 2×10 in #2 Douglas fir estimates to about 8 ft 4 in, limited by bending. More tributary width or heavier loads shorten that quickly.
What is the L/360 deflection limit?
A stiffness rule: the beam may sag no more than its span divided by 360 — about 1/3 inch over 10 ft. It keeps floors from feeling bouncy and finishes from cracking, and it often governs long, shallow beams.
Can I use this to size a beam for my house?
Use it to shortlist candidates, not to build. Real girder sizing must follow your code's span tables or a licensed engineer's design, which also cover shear, bearing length, and connections this estimate leaves out.
Does species really matter?
Yes. Douglas fir-larch #2 (Fb 900 psi, E 1.6M) spans several inches to a foot farther than hem-fir or southern pine #2 in the same size, because both strength and stiffness values differ.