Bending Moment Calculator
Work out bending moment instantly with clear inputs, formula shown and shareable results.
About Bending Moment Calculator
Maximum bending moment depends on how the load is arranged. A central point load gives PL/4, a uniformly distributed total load gives WL/8, and a cantilever tip load gives PL - four times the simply supported point case for the same load and length. 12 kN centrally on 6 m gives 18 kN m at mid-span.
Formulas
Central point load
M = P L / 4
Uniform load
M = W L / 8
Cantilever tip load
M = P L
Worked example
With the default values below, Bending Moment Calculator returns Maximum Bending Moment of 18,000.0. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Load magnitudeminimum 0 N
- 12,000 N
- Spanminimum 0 m
- 6 m
- Load arrangementone of Central point load (PL/4), Uniformly distributed total load (WL/8), Cantilever tip load (PL)
- Central point load (PL/4)
Results
- Maximum Bending Moment
- 18,000.0 N m
- Same Moment In kN m
- 18.0000
- Support Reaction
- 6,000.0 N
- Where The Maximum Occurs
- At mid-span
Step by step
- 1Values used
- 2Central point load
- 3Uniform load
- 4Cantilever tip load
- 5Maximum Bending Moment= 18,000.0 N m
- 6Same Moment In kN m= 18.0000
- 7Support Reaction= 6,000.0 N
- 8Where The Maximum Occurs= At mid-span
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is a cantilever so much worse?
The whole load acts at full lever arm from the single support, with no second reaction to share it. That is four times the simply supported point-load moment.
How do I turn a moment into a stress?
Divide by the section modulus: sigma = M/Z. That is the pairing that sizes a beam.