Moment Calculator
Peak bending moment for the four classic cases — the one number every other beam check consumes, priced per case with the constant shown.
Moment Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Four idealised cases; peak values only
- Single spans — no continuity
In short: The default case — 10 kN/m across a 6 m simply supported span — peaks at 45.000000 kN·m at midspan: wL² over 8, the quiet eighth that starts every beam sizing. Run the same load as a cantilever and the peak climbs to 180.000000 kN·m at the fixed end — fourfold for identical steel and identical load, which is the whole economics of simply supported framing in one comparison.
Formula
M = wL²/8 · PL/4 · PL · wL²/2 — by case
The peak moment is where the shear diagram crosses zero, and each classic case parks that crossing in a known place with a known constant: an eighth for the simply supported distributed case, a quarter for the central point load, the whole PL at a cantilever's root. The constants are the lever arms' autobiography — the same load, four architectures, four verdicts.
Worked Example
- Pick the case that matches the real supports.
- Enter the load and the span.
- Read the peak moment and where it sits.
- Compare the cross-case map before choosing a framing scheme.
Defaults: case 1, 10 kN/m, 6 m → 45.000000 kN·m midspan. The point-load check: 20 kN centred on the same span → 30.000000. The cantilever penalty: case 4 → 180.000000 at the root, four times the simply supported verdict.
Strengths & Limits Of This Model
Where this engine is strong
- Case constant shown in the arithmetic
- Cross-case comparison card built in
Where it stops
- No moment diagrams plotted
- No off-centre point loads
Practical Use Cases
Member sizing
the number the stress check eats
Framing studies
simply supported vs cantilever
Teaching
one load, four architectures
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Moment Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the same load give four different moments?
Because moment is load times lever arm, and the four cases are four different lever-arm architectures. A simply supported beam shares each load particle's leverage between two supports approaching from both sides; a cantilever lets every particle hang at full reach from one fixed end. The constants — 1/8, 1/4, 1, 1/2 — are the compressed geometry of where the load sits relative to restraint.
Where exactly is the peak?
Midspan for the two simply supported cases (where the shear diagram crosses zero), the fixed end for both cantilevers. The page names the location beside the number because two checks hang off it: the bending check happens at the peak-moment section, the shear check at the peak-shear section, and for these cases they are different places.
Is the peak moment all the beam feels?
It is the worst, not the whole — the moment diagram rises smoothly from zero at the pins to the peak, and every section between carries its own share. That distribution is why real beams can be tapered or lightened away from the peak. For sizing, the peak is the number; for understanding the member, the diagram is.
Can I add cases — UDL plus a point load?
Superposition says the moments add — but the peaks may not sit in the same place, so adding peaks is conservative and adding diagrams is correct. A common quick check: compute each case's peak here, sum them, and treat the sum as an upper bracket. The page prices one case at a time so the arithmetic stays visible; the bracket is your subtraction.
The load is not centred. Which case is closest?
For a simply supported point load off centre, the peak is Pab/L at the load — always larger than the centred PL/4 when the load is off centre, peaking as it approaches a support. The centred case is the mildest point-load story, which makes it a poor conservative choice for off-centre reality; the honest bracket is PL/4 up to PL/4·(something under 4) as the load walks.
Why do codes care about pattern loading?
Because live loads can sit exactly where they hurt most — alternate spans loaded to maximize midspan moment, adjacent spans to maximize support moment. The classic cases are the atoms; pattern loading is the chemistry. This page's cantilever and point-load cases are literally the patterns a code checker worries about, isolated for study.
Does the moment change along a cantilever?
Linearly for a point load, parabolically for a UDL — always maximum at the root and zero at the free tip. That is why cantilever roots get the deeper haunch and the tip gets the light connection: the member knows its own diagram. Balconies and canopies fail at the building face, never at the railing, for exactly this arithmetic reason.
What is the relationship to the deflection page?
Curvature — the moment's second cousin — integrated twice gives deflection, which is why the deflection formulas carry the same case constants in different powers. The moment page answers 'what is the worst request' and the deflection page answers 'how much does the member comply'; between them sits the stiffness EI that turns one into the other.