Simply Supported Beam Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the span length L.
- Add a point load (and its distance from the left support) and/or a uniform load across the span.
- Read the maximum bending moment, where it occurs, the maximum shear force and the support reactions.
How it works
The Simply Supported Beam Calculator finds the maximum bending moment and shear force for a beam on two supports carrying a point load, a uniform load, or both.
It first solves the support reactions, then walks the bending-moment diagram along the span — M(x) = R₁·x − w·x²/2 − P·(x − a) past the load — and reports the largest value and its position. Maximum shear occurs at the more heavily loaded support.
Worked example
6 m span, 5 kN/m uniform load. Reactions are 15 kN each. Maximum moment is at mid-span: wL²/8 = 5×6²/8 = 22.5 kN·m. Maximum shear equals the reaction, 15 kN.
Tips
- Bending stress = maximum moment ÷ section modulus (Z). Keep units consistent.
- Leave the point-load position blank to centre it.
Frequently asked questions
Where is the maximum bending moment?
For a single central point load it's at mid-span (PL/4). For a uniform load it's also at mid-span (wL²/8). With combined or off-centre loads the tool samples the whole span and reports the actual peak and its location.
Why do I need the maximum moment?
You divide it by the section modulus (Z) to get the bending stress, which you then compare against the material's allowable stress. Pair this with the Section Modulus Calculator.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.