Beam Load Calculator
Find the reactions, shear, and maximum bending moment on a simply supported beam with a uniform load: enter span and load per foot.
How this calculator works
When a beam spans between two supports and carries an even load, engineers use a few standard formulas to find how hard it is working. This calculator takes the span length and the load per foot you enter, then returns the support reactions, the maximum shear, and the maximum bending moment for a simply supported beam.
The load per foot is spread evenly across the span. Half of the total goes down to each support, which sets the reactions and the peak shear. The bending moment peaks at the center of the span, where the beam resists sagging the most.
Formula: For a simply supported beam under a uniform load w (lb/ft) over span L (ft): each end reaction = w × L ÷ 2; maximum shear = the reaction; maximum bending moment = w × L² ÷ 8 (lb-ft).
Worked example
A 12 ft span carrying a 200 lb/ft uniform load:
- Span: 12 ft, load: 200 lb/ft
- Each end reaction: 200 × 12 ÷ 2 = 1,200 lb
- Maximum shear: ≈ 1,200 lb
- Maximum moment: 200 × 144 ÷ 8 = 3,600 lb-ft
Notes
This calculator covers one specific case: a single simply supported span carrying an even load across its full length. That is a common and useful starting point, but real structures are not always so simple.
Point loads change the picture, since a concentrated weight at one spot shifts where the shear and moment peak. Cantilevers, where a beam extends past its support with no support at the free end, follow different formulas entirely. Continuous spans, where one beam runs across three or more supports, also behave differently from the single-span case shown here. For any of those, this single-span estimate does not apply.
How to use
Enter the clear span of your beam in feet and the uniform load it carries in pounds per foot. Read off the reaction at each end, the maximum shear, and the maximum bending moment. Use the reactions to check the supports and the moment to check the beam, keeping in mind this covers the even, single-span case only.
This is a planning estimate, not an engineered design. Structural sizing is safety-critical and code-governed — confirm all members, connections, and footings with a licensed structural engineer and your local building code.
Frequently asked questions
What is a simply supported beam?
A simply supported beam rests on a support at each end, with nothing holding it down in between. One end can be thought of as pinned and the other as free to slide slightly, so the beam is free to bend under load without fixed corners. It is the most common and most basic beam case, which is why it makes a clean starting point for hand estimates.
What does a uniform load mean here?
A uniform load is weight spread evenly across the entire span, measured in pounds per foot. Decking that carries an even layer of people and furniture across a beam is often treated this way. It contrasts with a point load, where a single heavy item sits at one spot, which produces different reaction, shear, and moment results.
Why is the maximum moment at the middle of the span?
For a simply supported beam under a uniform load, the bending is greatest at the center and drops to zero at the supports. The middle is where the beam has to work hardest to resist sagging, so that is where the maximum bending moment occurs. Sizing the beam for this peak keeps the whole span within its limits.
What are reactions and shear used for?
The reactions are the upward forces the supports provide, and they tell you how much load each post or footing beneath the beam must carry. The maximum shear equals the end reaction and shows the strongest cutting force near the supports. Together they help you size both the beam and the supports it rests on.
Estimates only. Verify quantities with your supplier before purchasing.