Beam bending stress calculator
The Beam bending stress calculator computes beam bending stress from the relation sigma = M c / I. It takes 3 inputs (bending moment in N m, distance to neutral axis in m, moment of inertia in m^4) and returns the bending stress in Pa. These tools are written for engineering students, technicians, draftspeople and practising engineers who need a quick quantitative answer part-way through a larger piece of work, whether the question in front of them is structural, mechanical, fluid, thermal, electrical or a matter of site quantities, and who want to see how the numbers behave before committing more effort to a given arrangement. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Keep every input in one consistent unit system before you enter it, since a mismatched length, area, pressure, flow or electrical unit is the usual reason a result lands orders of magnitude away from expectation; be explicit about the assumptions behind each figure, whether those are geometry and material properties or flow, thermal and operating conditions; and carry no more precision into the next step than the least certain input justifies. For example, with bending moment = 500 N m, distance to neutral axis = 0.05 m, moment of inertia = 0.0001 m^4, the bending stress works out to 250000 Pa, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. This is a standard formula rather than a jurisdiction-specific rule, so it does not depend on an external rate or schedule, and the figure above each result carries the date it was last verified. These are working calculations that model one idealised condition at a time, so they carry none of the safety margin, the full range of loads and operating states, or the real material, fabrication and installation behaviour that a finished structure, machine or system has to tolerate, and the qualified engineer responsible for the project still has to make the call.
With Bending moment = 500 N m, Distance to neutral axis = 0.05 m, Moment of inertia = 0.0001 m^4, the result is 250000 Pa.
Applies to: any numeric inputs. Method: a standard formula, not a jurisdiction-specific rule. How we document and test our methods, checked 2026-07-09.
The formula
sigma = M c / I
Worked example
With Bending moment = 500 N m, Distance to neutral axis = 0.05 m, Moment of inertia = 0.0001 m^4:
- sigma = M c / I
- Bending stress = 250000 Pa
This worked example is one of the automated golden-value tests this calculator must pass before it can publish.
What this assumes
- Inputs are real numbers in the units shown.
- The result is the exact value of sigma = M c / I; general information, not professional advice.
Frequently asked questions
What formula does this use?
sigma = M c / I. This is a standard formula rather than a jurisdiction-specific rule.
Does the result ever change over time?
No. This is a pure formula with no external rate, so the same inputs always give the same result.
Official sources and verification
- Method: a standard formula rather than a jurisdiction-specific rule; how we document and test our methods, checked 2026-07-09.
Reviewed by the CalculatorHub team, edited by James Graham, 2026-07-09. See our methodology. General information, not professional advice.