Enter the span and load of a simply supported beam (resting on two end supports) to find the maximum bending moment and reaction force at each support.
Beam Load Calculator
LiveThe formulas
A 10 ft simply supported beam with a uniform 500 lb/ft load: max moment = 500 x 100 / 8 = 6,250 lb-ft, and each support carries 2,500 lb. The same 5,000 lb total applied instead as a single centered point load would produce a max moment of PL/4 = 5,000 x 10 / 4 = 12,500 lb-ft -- exactly double, even though the total force is identical.
How support type changes everything
This calculator handles the simply supported case specifically -- a beam resting freely on two end supports, like a joist or header. That's the most common residential framing case, but far from the only one. Changing how a beam is held changes the maximum moment dramatically, even for the identical span and load:
| Configuration | Max moment (uniform load) | For w=500 lb/ft, L=10 ft |
|---|---|---|
| Simply supported (this calculator) | wL² ÷ 8 | 6,250 lb-ft |
| Fixed at both ends | wL² ÷ 12 | 4,167 lb-ft |
| Cantilever (fixed one end, free other) | wL² ÷ 2 | 25,000 lb-ft |
A cantilever carries four times the moment of a simply supported beam for the identical span and load, because there's no opposing support to share the bending -- this is why cantilevered decks, balconies, and overhangs need noticeably larger or more closely spaced framing than a beam supported on both ends. A fully fixed beam, by contrast, carries less moment than simply supported, since rigidly restraining the ends resists some of the rotation that causes bending -- but achieving a genuinely fixed (not just supported) connection in real construction is harder than it sounds, so simply supported is the conservative, commonly used assumption for hand calculations.
What bending moment tells you
Maximum bending moment is a key input for checking whether a specific beam (of a given material and cross-section) is strong enough for a load -- engineers compare it against the beam's section modulus and material strength to verify it won't fail or deflect excessively. This calculator gives you the moment and reactions; translating that into "is this exact beam strong enough" requires the beam's specific material properties and cross-sectional shape, which varies by product. Once you have a candidate beam size, the Beam Deflection Calculator checks the next question: how much it will actually sag under that load, which matters even for a beam strong enough not to break.
Common mistakes
Frequently asked questions
What does "simply supported" mean?
It means the beam rests freely on two end supports (like a beam sitting on two posts), free to rotate slightly at each end, as opposed to being rigidly fixed or continuous across multiple spans -- those other configurations use different formulas, shown in the comparison table above.
Why does a point load create twice the moment of an equal total uniform load?
Concentrating the same total weight at a single center point creates more bending stress than spreading it evenly along the beam, which is why the point-load formula (PL/4) gives a larger moment than the uniform-load formula (wL²/8) for the same total force -- exactly double, as the diagram above shows.
Do I need to know the beam's material to use this calculator?
Not for the moment and reaction figures shown here -- those depend only on span and load. Material and cross-section matter for the next step: checking whether a specific beam can actually handle that moment without failing or deflecting too much.
Why does a cantilever carry so much more moment than a simply supported beam?
A cantilever has only one support resisting the load, with the entire span acting like a lever arm against that single fixed point. A simply supported beam splits the load between two supports, which is why the cantilever formula (wL²/2) gives four times the moment of the simply supported formula (wL²/8) for the identical span and load.
What's the difference between moment and reaction?
Reaction is simply how much weight each support physically carries -- it always adds up to the total load. Moment is a measure of bending stress at a point along the beam, which depends on both the load and how far it is from the supports -- a beam can have small reactions but a large moment if the span is long.
Where does the maximum moment occur on a simply supported beam?
At the center of the span for both a uniform load and a centered point load -- that's why both formulas in this calculator compute the value at midspan. An off-center point load would peak at a different location, which this calculator doesn't cover.
Can I use this for a deck beam or floor joist?
It's a reasonable starting point for understanding the loads involved, but sizing an actual joist or beam requires matching the resulting moment against your specific lumber species, grade, and cross-section span tables -- or local building code prescriptive tables -- not just this calculator alone. For anything load-bearing, verify against your jurisdiction's adopted code.
Is a fixed-end beam always better than simply supported?
It carries less maximum moment for the same load, which is favorable, but achieving a genuinely fixed connection (one that fully resists rotation, not just vertical movement) is harder to build reliably than a simple support. Most residential framing is designed and analyzed as simply supported even when the real connection has some partial fixity, as a conservative simplification.
Does beam length matter more than load amount?
Span matters more, because it enters the moment formula squared (L²) for a uniform load, while load enters only linearly. Doubling the span quadruples the moment for the same load per foot; doubling the load only doubles it -- which is why beams get disproportionately stronger sizing requirements as spans increase.
Sources
- Bending moment and reaction formulas. Standard mechanics of materials / structural engineering beam formulas for statically determinate beams -- consistent across engineering references (e.g., AISC Steel Construction Manual beam diagrams and formulas tables, and standard mechanics of materials textbooks).
- Real-world beam sizing. For actual construction, prescriptive span tables in your jurisdiction's adopted building code (commonly based on the International Residential Code, IRC) or manufacturer engineered-lumber span tables should be used rather than hand calculations alone.
Related calculators
See the full list of Engineering calculators, or try:
- Beam Deflection Calculator — check how much a beam will sag under this load
- Material Weight Calculator — estimate a beam's own self-weight
- Stair Calculator
- Board Feet Calculator