Beam Load Calculator

Beam load calculator: reactions, shear, and moment

This beam load calculator takes a span in feet and a uniform load in pounds per foot and returns the three numbers every beam check starts from: each end reaction = w × L ÷ 2, maximum shear = the reaction, and maximum bending moment = w × L² ÷ 8 in lb-ft. It covers one case only, a single simple span carrying an even load along its full length.

The reaction tells you what each post or footing must hold up. The moment tells you how hard the beam is bending at its middle.

What the formulas mean

Picture the total load as w × L pounds sitting on the beam. Because it is spread evenly, the two supports share it equally, so each end pushes up with half: w × L ÷ 2.

Shear is the force trying to slice the beam vertically. It is largest right at the supports and falls to zero at mid-span.

Moment is the bending effect. It is zero at the supports, where the beam is free to rotate, and peaks at the center. The ÷ 8 comes from the area under the shear diagram, which is a triangle from each end to the middle.

Worked examples

1. The default: 12 ft span, 200 lb/ft

• Total load: 200 × 12 = 2,400 lb
• Each end reaction: 2,400 ÷ 2 = 1,200 lb
• Max shear: 1,200 lb
• Max moment: 200 × 12² ÷ 8 = 200 × 144 ÷ 8 = 3,600 lb-ft

2. Deck beam: 8 ft between posts, joists span 12 ft

The beam carries half the joist span, so its tributary width is 6 ft. At a 40 psf live load plus 10 psf dead load, w = 6 × 50 = 300 lb/ft.

• Each end reaction: 300 × 8 ÷ 2 = 1,200 lb
• Max moment: 300 × 64 ÷ 8 = 2,400 lb-ft, which is 28,800 lb-in

To see what that means for sizing, divide lb-in by the allowable bending stress. If a lumber grade allowed 1,000 psi, the beam would need a section modulus of 28,800 ÷ 1,000 = 28.8 in³. A single 2×10 has about 21.4 in³, so it falls short; two 2×10s give about 42.8 in³. The real allowable stress depends on species, grade, size, and load duration, so treat this as an illustration of the method, not a sizing.

Common design loads

Use	Live load	Typical dead load	Notes
Residential floor (living areas)	40 psf	10–15 psf	Widely used in US residential codes
Sleeping rooms	30 psf	10–15 psf	Check local code
Residential deck	40 psf	10 psf	Hot tubs need a separate analysis
Roof snow	Varies by location	10–15 psf	See the snow load calculator

Check your local building department for the loads that apply where you build.

How moment grows with span

Span	Moment at 200 lb/ft	Moment at 300 lb/ft
6 ft	900 lb-ft	1,350 lb-ft
8 ft	1,600 lb-ft	2,400 lb-ft
10 ft	2,500 lb-ft	3,750 lb-ft
12 ft	3,600 lb-ft	5,400 lb-ft
16 ft	6,400 lb-ft	9,600 lb-ft

How to measure the inputs

• Span: measure center to center of the supports, or the clear distance between them for a conservative check.
• Load per foot: add live and dead loads in psf, then multiply by the tributary width in feet.
• Self-weight: heavy beams add their own weight. A doubled 2×10 adds only a few pounds per foot; a steel or glulam beam can add more.

Mistakes to avoid

• Using the full joist span as tributary width. A beam at the end of joists supports only half their span. An interior beam with joists on both sides supports half of each.
• Ignoring point loads. A post from the floor above, or a hot tub, concentrates weight. This calculator does not handle those cases.
• Checking only bending. Long beams often fail the deflection check first. Run the beam deflection calculator as well.
• Forgetting the footing. Each 1,200 lb reaction travels down a post into soil. Size the footing with the footing size calculator.

For a complete deck load path, start with the deck load calculator.

This is a planning estimate, not an engineered design. Beam sizing is safety-critical and code-governed, so confirm members, connections, and footings with a licensed structural engineer and your local building department.