How this instrument works
Every beam has a maximum bending stress its material can safely withstand before it's considered overstressed — called the allowable bending stress, Fb. Working backward from that allowable stress, a beam's section size, and its span, you can calculate the maximum uniform load (in pounds per linear foot) the beam can carry before it exceeds that stress limit.
The math works in two steps. First, a beam's section modulus S (a measure of how efficiently its cross-section resists bending) is calculated from its width b and depth d: S = b x d²/6. Then, starting from the standard uniform-load bending moment formula M = w x L²/8 and the stress relationship Fb = M/S, the formula is rearranged to solve directly for the maximum allowable uniform load w.
This is a strength check, not a deflection check — a beam can pass this bending-stress test and still sag more than acceptable under the same load, which is what the companion beam-deflection calculator checks instead. Real beam design always verifies both, and uses whichever gives the more restrictive result. The default allowable stress (875 psi) matches Spruce-Pine-Fir No.2 lumber's published reference value, but you should replace it with the correct value for your actual species, grade, and application before relying on any result — this is a preliminary estimate only, not a substitute for review by a licensed structural engineer or your local building department.
- Enter the allowable bending stress Fb for your material (psi) — the default is a common lumber reference value, but confirm the correct figure for your species/grade or material.
- Enter the beam's section width and depth in inches (actual dimensions).
- Enter the span between supports in feet.
- Read the maximum allowable uniform load in pounds per linear foot and the resulting maximum total load.
A single 2x10 at SPF No.2's reference bending stress
A single 2x10 (actual 1.5 in x 9.25 in) spans 10 ft and is being checked at Spruce-Pine-Fir No.2's published reference allowable bending stress of 875 psi. Section modulus: S = 1.5 x 9.25² / 6 = 21.3906 in³. Applying the load formula: w_max = 8 x 875 x 21.3906 / (12 x 10²) = 149,734.4 / 1,200 = 124.779 lb/ft, giving a maximum total uniform load of 124.779 x 10 = 1,247.79 lb across the full span.
Swap in a beefier double 2x8 header (3 in x 7.25 in) at Douglas Fir-Larch No.2's slightly higher 900 psi allowable stress over a shorter 6 ft span, and the picture changes: section modulus jumps to 26.28125 in³, and the shorter span concentrates capacity, yielding w_max = 438.02 lb/ft — over three times the first example's per-foot capacity, driven mostly by the larger section and shorter span rather than the small stress increase. This is a preliminary estimate only; confirm the correct allowable stress for your actual material and have the final design reviewed by a licensed structural engineer.
Questions
What allowable bending stress (Fb) should I use for my lumber?
Fb depends on your specific wood species and grade, and is published in tables like the American Wood Council's NDS Supplement Table 4A — common softwood framing lumber (No.2 grade) typically falls in the 875-900 psi range, but always verify against the correct table entry for your exact species and grade rather than assuming a default applies.
Does passing this check mean my beam is safe to use?
It means the beam clears one specific strength check (bending stress) at the load and span you entered. A complete design also needs a deflection check (see the beam-deflection calculator), a shear check near the supports, and confirmation that the beam is properly supported and connected — this calculator only addresses bending strength, and is a preliminary estimate, not a stamped design.
Why does the formula use the number 12 in the denominator?
The bending moment formula M = wL²/8 naturally produces foot-pounds when w is in lb/ft and L is in feet, but the stress relationship Fb = M/S works in inch-pounds. The 12 converts the moment capacity (Fb x S, in inch-pounds) into foot-pounds before solving algebraically for w, keeping every term in consistent units.
What's the difference between total load and uniform load in the result?
Maximum uniform load (lb/ft) is the per-foot capacity along the beam's length — the number to compare against your actual applied load per foot. Maximum total load (lb) is simply that per-foot figure multiplied by the span, representing the full load the entire beam could carry if it were spread evenly along its length.