Beam Load Calculator
Before you can size a beam you need to know the forces it carries. This calculator handles the standard textbook case of a simply supported beam with a single point load at the centre of the span. From the load and span you enter, it computes the reactions at each support, the maximum shear force, and the maximum bending moment at midspan using basic statics. These are the quantities a designer feeds into the next step, the stress check. Enter the load in newtons and the span in metres for results in newtons and newton-metres.
Beam load formulas
Reaction at A = P / 2
Reaction at B = P / 2
Max shear = P / 2
Max bending moment = (P * L) / 4
By symmetry of a central point load, each support carries half the load, and the shear force on either side of midspan equals that reaction. The bending moment is zero at the supports, rises linearly, and peaks at midspan at P times L over 4. These are exact results from static equilibrium.
Statics context
- Support reactions are found from two equilibrium conditions: the sum of vertical forces is zero and the sum of moments is zero.
- For a central point load the reactions are equal; for an off-centre load they differ in inverse proportion to the distance from each support.
- The maximum bending moment governs bending stress and so the required section size.
- Shear force is constant in magnitude between a support and the load point for this case.
- This educational tool covers a single point load only; combine with self-weight and verify with a licensed engineer for real designs.
Beam load: frequently asked questions
What does this beam load calculator find?
For a simply supported beam carrying a single point load P at the centre of its span, it finds the two support reactions, the maximum shear force, and the maximum bending moment. By symmetry each support carries half the load, the shear equals that reaction, and the maximum moment at midspan is P times L divided by 4.
Why are both reactions equal?
When a single load sits exactly at midspan of a beam supported at both ends, the geometry is symmetric, so each support must carry the same share. Static equilibrium requires the upward reactions to sum to the downward load, so each reaction is P divided by 2. Off-centre loads give unequal reactions.
What is the maximum bending moment used for?
The maximum bending moment drives the bending stress in the beam and therefore the size of section you need. Once you know the maximum moment, you divide it by the section modulus to get the maximum bending stress, which you compare against the material's allowable stress to confirm the beam is adequate.
Does this include the beam's self-weight?
No. This case is a single concentrated point load at midspan. A beam's own weight acts as a uniformly distributed load and produces a maximum moment of w L squared over 8. For a real design you superpose the point-load and self-weight effects, or use software, and have a structural engineer verify the result.
What units should I use?
Enter the load in newtons and the span in metres. Reactions and shear come out in newtons, and the bending moment in newton-metres. Keep your units consistent: if you prefer kilonewtons and metres, the moment will be in kilonewton-metres. The calculator simply applies the formulas to whatever consistent units you provide.
Official sources
- NASA Glenn Research Center: Beam bending fundamentals.
- NIST: SI units reference.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.