Beam Load Calculator
Find bending moment, shear and reactions on a beam.
Results update as you type.
How it works
This beam load calculator finds the key structural quantities for a simply supported beam carrying a uniformly distributed load, the most common textbook and design case. You enter the load per unit length and the span between supports, and it returns the maximum bending moment, the maximum shear force, and the reaction at each support. These three values are the starting point for sizing a beam: the bending moment governs whether the beam will fail in flexure and drives the choice of section and material, while the shear force and reactions determine the connections and the supports. For a uniformly distributed load, the reactions and maximum shear each equal half the total load, and the bending moment peaks at the centre with the classic w-L-squared-over-eight formula. Engineers, builders, and students use these results to check joists, lintels, and simple spans against allowable stresses, though a full design must also consider the beam's own weight, deflection limits, load factors, and applicable building codes. This tool provides the fundamental statics for a preliminary check and learning; it is not a substitute for a qualified structural engineer's design. Enter the load and span to see the results.
M = wL²/8; R = V = wL/2
For a simply supported beam carrying a uniformly distributed load, the two supports share the total load equally, so each reaction is half the load times the span. The maximum shear force at the supports equals that same reaction. The bending moment is greatest at midspan and equals the distributed load times the span squared, divided by eight, which is the standard result derived by integrating the shear along the beam.
Source:Structural engineering (simply supported beam statics)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter distributed load (w) and span (l).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Max bending moment updates instantly as you type — no button to press.
Frequently asked questions
What is a simply supported beam?
A simply supported beam rests on two supports, one at each end, with one typically a pin and the other a roller so the beam can expand freely. It carries loads by bending between the supports. This is the most basic and common structural arrangement, used for floor joists, lintels over openings, and many bridge spans, and it is the case this calculator analyses.
Why is the maximum moment wL²/8?
For a uniformly distributed load on a simply supported beam, the bending moment is zero at the supports and rises to a maximum at midspan. Integrating the shear force along the beam gives a parabolic moment diagram peaking at the centre, and the algebra works out to the load per unit length times the span squared divided by eight. It is one of the most-used formulas in structural engineering.
What are the support reactions?
The support reactions are the upward forces the supports exert to hold the beam in equilibrium against the downward load. For a symmetric uniformly distributed load, each of the two supports carries exactly half the total load, so each reaction equals the load per unit length times the span, divided by two. These reactions size the supports and connections.
Does this account for the beam's own weight?
No. The calculator uses only the distributed load you enter. In a real design you should add the beam's self-weight to the applied load, since a heavy steel or concrete beam contributes meaningfully to the total. You would also apply load factors and check deflection and shear capacity. Treat this result as the applied-load statics, then combine it with self-weight and code requirements.
Can I use it for point loads?
Not directly. This calculator is built for a uniformly distributed load spread evenly along the span. A single concentrated point load produces different formulas: for a central point load, the maximum moment is the load times the span divided by four. For point loads or combinations, use the appropriate formulas or a structural analysis tool rather than this uniformly-distributed-load calculator.