Beam Deflection Calculator
Calculate the maximum deflection of simply supported and cantilever beams under point or uniform loads.
This uses idealized linear-elastic, small-deflection beam theory and ignores shear deformation, self-weight, and real end conditions. Verify critical structural designs with a qualified engineer.
How it works
- 1Choose the beam support and load case, the material, and the cross-section.
- 2Enter the load, span, and section dimensions to set the second moment of area I.
- 3Read the maximum elastic deflection, see the labeled diagram, and review the assumptions.
Use cases
- Checking that a shelf, joist, or beam will not sag beyond an acceptable limit.
- Comparing how span, material, and section depth affect stiffness.
- Teaching the standard beam deflection formulas with live numbers and a diagram.
Frequently asked questions
What are the standard deflection formulas?
Simply supported with a central point load: δ = PL³/48EI. Simply supported with a uniform load: δ = 5wL⁴/384EI. Cantilever with an end load: δ = PL³/3EI. Cantilever with a uniform load: δ = wL⁴/8EI.
Why does span matter so much?
Deflection grows with the cube or fourth power of span (L³ or L⁴), so doubling the span increases deflection roughly 8 to 16 times. Increasing section depth, which raises I, is the most effective way to stiffen a beam.
Is this calculator suitable for structural design?
It is an educational estimate using idealized linear-elastic theory. It ignores shear deformation, self-weight, and real end fixity. Verify any load-bearing design with a qualified structural engineer and the governing code.
Related tools
See all →Find the gear ratio, output speed, torque, and mechanical advantage of a gear pair, in metric or imperial.
Calculate the overall ratio and output speed of a multi-stage compound gear train.
Calculate shaft torque from power and rotational speed in metric or imperial units.
Calculate the mechanical power transmitted by a rotating shaft from torque and shaft speed.