Bending Stress Calculator
Find bending stress from moment, distance and inertia.
Results update as you type.
How it works
When a beam bends under load, it develops internal stress, and this calculator finds that bending stress using the flexure formula. You enter the bending moment, the distance from the neutral axis to the point of interest (usually the outer fiber), and the moment of inertia of the cross-section, and it returns the bending stress in pascals and megapascals. The formula, sigma equals M times c over I, is one of the most important in structural and mechanical engineering. The bending moment measures how strongly the load tries to bend the beam, the distance c locates where in the cross-section you are checking the stress, and the moment of inertia captures how the material is distributed about the neutral axis, with more material far from the axis giving a larger inertia and lower stress. Bending stress is greatest at the top and bottom surfaces, farthest from the neutral axis, where one side is in tension and the other in compression, which is why beams often fail there first. Engineers compare the maximum bending stress to the material's allowable stress to size beams safely, and the formula shows why deeper beams and shapes like I-beams, which put material far from the axis, resist bending so efficiently. Keep units consistent for a correct result. Enter the bending moment, distance, and moment of inertia to find the bending stress.
σ = M·c / I
The bending (flexural) stress in a beam equals the bending moment times the distance from the neutral axis to the point of interest, divided by the moment of inertia of the cross-section. Stress is highest at the outer fibers, farthest from the neutral axis, where c is largest.
Source:Mechanics of materials
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter bending moment (m), distance to outer fiber (c) and moment of inertia (i).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Bending stress updates instantly as you type — no button to press.
Frequently asked questions
What is bending stress?
Bending stress, or flexural stress, is the internal stress in a beam caused by a bending moment. It equals the moment times the distance from the neutral axis, divided by the moment of inertia. One side of the beam is in tension and the other in compression, with the greatest stress at the outer surfaces.
What is the flexure formula?
The flexure formula, sigma equals M times c over I, gives the bending stress at a distance c from the neutral axis, where M is the bending moment and I is the moment of inertia of the cross-section. It is a cornerstone of beam design, letting engineers find the stress at any point in a bent beam.
Why is stress highest at the outer fibers?
In bending, the stress varies linearly with distance from the neutral axis, which runs through the centroid and experiences no bending stress. The farther a point is from this axis, the more it stretches or compresses, so the outer fibers, at the greatest distance c, carry the highest tensile and compressive stress and are where failure typically begins.
What is the moment of inertia's role?
The moment of inertia measures how a cross-section's area is distributed about the neutral axis. A larger moment of inertia means the beam resists bending better and develops lower stress for the same moment. This is why shapes like I-beams, which concentrate material far from the axis, are so efficient at resisting bending.
How do engineers use bending stress?
Engineers calculate the maximum bending stress in a beam under its expected loads and compare it to the material's allowable stress, including a safety factor, to ensure the beam will not fail. If the stress is too high, they choose a stronger material, a larger or deeper section, or reduce the span or load.