Beam Load Capacity Calculator

How much load can a beam carry in bending?

A beam load capacity calculator gives the allowable bending moment: section modulus (S) × yield strength (Fy) ÷ safety factor, divided by 12 to turn inch-pounds into foot-pounds. A steel section with S = 21.4 in³ in 50 ksi steel, with the ASD factor of 1.67, can carry about 53,393 ft-lb of bending moment.

That moment is not a load in pounds yet. It is the bending a section can take. To know what that means for your beam, compare it with the moment the real loads create, which depends on span and on how the load is spread.

The formula in plain words

When a beam bends, its top edge squeezes and its bottom edge stretches. The section modulus measures how well the shape resists that. Deeper beams have a much bigger S, because depth is squared in it.

1. Moment at yield = S × Fy, in inch-pounds. This is the bending that would push the outer fibers to yield.
2. Allowable moment = that ÷ safety factor.
3. Convert to foot-pounds by dividing by 12.

The result is only the bending-strength check. Long beams are often limited by sag instead, and short heavy beams by shear.

Worked examples

1. Calculator defaults: S = 21.4 in³, Fy = 50,000 psi, factor 1.67

• Moment at yield: 21.4 × 50,000 = 1,070,000 in-lb
• Allowable: 1,070,000 ÷ 1.67 = 640,719 in-lb
• Allowable moment: 640,719 ÷ 12 = 53,393 ft-lb

What that means on a 20 ft simply supported span with an even load: w = 8 × M ÷ L² = 8 × 53,393 ÷ 400 = 1,068 lb per foot, before the beam’s own weight. On a 16 ft span the same section allows 8 × 53,393 ÷ 256 = 1,669 lb per foot.

2. The same shape in A36 steel

• Allowable: 21.4 × 36,000 ÷ 1.67 ÷ 12 = 38,443 ft-lb

That is 28% less, purely from the lower yield strength.

Wood beam (illustration only): a 3.5 × 9.25 in solid beam has S = 3.5 × 9.25² ÷ 6 = 49.9 in³. If its adjusted allowable bending stress were 1,000 psi, you would enter Fy = 1,000 and a factor of 1, giving 4,159 ft-lb. Real Fb values depend on species, grade, size, moisture, and load duration, so take them from the NDS tables for your lumber.

Allowable moment for common wide-flange shapes

Shape	Sx (in³)	50 ksi, Ω 1.67	A36, Ω 1.67
W8x10	7.81	19,486 ft-lb	14,030 ft-lb
W10x12	10.9	27,196 ft-lb	19,581 ft-lb
W12x14	14.9	37,176 ft-lb	26,766 ft-lb
W8x18	15.2	37,924 ft-lb	27,305 ft-lb
W10x22	23.2	57,884 ft-lb	41,677 ft-lb
W14x22	29.0	72,355 ft-lb	52,096 ft-lb
W12x26	33.4	83,333 ft-lb	60,000 ft-lb

These assume the compression flange is braced so the beam cannot twist sideways. A long unbraced beam can buckle laterally well below these values. The W14x22 carries more than the W10x22 at the same weight per foot, because depth is what buys bending strength.

Where the inputs come from

• Section modulus: steel tables list Sx for each shape. For a rectangle, S = b × d² ÷ 6. For built-up or odd shapes, find I with the moment of inertia calculator and divide by the distance from the neutral axis to the outer edge.
• Yield strength: from the steel grade on the mill certificate or drawings.
• Safety factor: follow the design standard you are working to.

Common mistakes

• Treating moment as load. 53,393 ft-lb does not mean the beam holds 53,393 lb. Convert with span and load pattern first.
• Using Sy instead of Sx. Wide-flange beams are many times weaker bent about their weak axis.
• Skipping deflection. A floor beam that is strong enough can still bounce or crack finishes. Check sag with the beam deflection calculator.
• Ignoring self-weight. A steel beam’s own weight per foot uses up part of the capacity. Look it up with the I-beam weight calculator.

To go the other way, from a known moment to the stress in the beam, use the bending stress calculator. This tool is a planning estimate. Beam sizing is safety-critical, so have the final member and its connections designed by a licensed structural engineer.