Beam Stress Calculator
Bending stress is the internal stress a beam develops when it bends under load, and it decides whether the beam is strong enough. The flexure formula relates that stress to the bending moment, the cross-section geometry, and how far the material sits from the neutral axis. This calculator applies it directly: enter the maximum bending moment, the extreme-fibre distance c, and the second moment of area I, and it returns the maximum bending stress in pascals and megapascals along with the section modulus. Compare the result against your material's allowable stress to check the design.
Bending stress (flexure) formula
Max bending stress = (M * c) / I
Section modulus = I / c
Bending stress (MPa) = stress (Pa) / 1,000,000
Equivalently, bending stress = M / section modulus
This is the Euler-Bernoulli flexure formula. Stress varies linearly across the section, from zero at the neutral axis to its maximum at the extreme fibre a distance c away. The section modulus packages I and c into one property, so stress reduces to moment divided by section modulus.
Materials context
- The flexure formula assumes linear-elastic material, plane sections remaining plane, and pure bending.
- Stress is tensile on one face of the beam and compressive on the other; the magnitudes are equal for a symmetric section.
- Compare the computed stress against the material's allowable or yield stress, applying the appropriate factor of safety.
- Steel design handbooks tabulate the section modulus for standard rolled shapes, removing the need to compute I and c separately.
- This educational tool does not check shear, buckling, or fatigue; a licensed engineer must verify a real design.
Beam stress: frequently asked questions
What is the bending stress formula?
The flexure formula gives bending stress as sigma equals M times c divided by I, where M is the bending moment, c is the distance from the neutral axis to the extreme fibre, and I is the second moment of area of the cross section. The stress is largest at the fibre farthest from the neutral axis.
What is c in the flexure formula?
c is the perpendicular distance from the neutral axis (which passes through the centroid for a symmetric section) to the outermost fibre of the cross section. For a rectangle of height h bent about its horizontal axis, c equals h divided by 2. The maximum stress occurs at this extreme fibre.
How do I get the bending moment to enter here?
The bending moment comes from the loads and supports on your beam. For a simply supported beam with a central point load it is P times L over 4; for a uniform load it is w L squared over 8. Use a beam load calculator or hand statics to find M, then enter it here in newton-metres.
What does the section modulus output mean?
The section modulus S equals I divided by c. It is a single geometric property that combines the moment of inertia and the extreme-fibre distance. Bending stress can be written simply as M divided by S, which is why S is tabulated for standard steel sections in design handbooks.
What units should I use?
Enter the moment in newton-metres, c in metres, and I in metres to the fourth power. The resulting stress is in pascals. Divide by 1,000,000 to read it in megapascals, the unit usually quoted for material strength. The calculator also shows the result in megapascals for convenience.
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.