What is the Beam Deflection Calculator?

Calculate maximum beam deflection and bending moment with this free beam deflection calculator. Choose simply supported, cantilever, or fixed–fixed beams under a center point load or uniform distributed load. Enter span length L, elastic modulus E, moment of inertia I, and load — get δ_max in mm or inches, M_max, deflection/span ratio, and checks against L/360 and L/250 limits. Metric (m, kN, GPa, cm⁴) and imperial (ft, lbf, psi, in⁴) units with steel, aluminum, wood, and concrete E presets. Runs instantly in your browser.

How to use the Beam Deflection Calculator

Select a loading case (simply supported, cantilever, or fixed–fixed).
Choose metric or imperial units.
Enter span L, elastic modulus E, and moment of inertia I.
Enter point load P or uniform load w as required by the case.
Review maximum deflection, bending moment, serviceability limits, and steps.

Common use cases

Checking midspan deflection of a steel beam under a point load
Sizing floor joists with uniform live load on a simply supported span
Estimating cantilever balcony deflection at the free end
Comparing fixed-end vs simply supported deflection for the same load
Structural homework on δ = PL³/(48EI) and related beam formulas

Frequently asked questions

What is beam deflection?: Beam deflection (δ) is the vertical displacement of a beam under load. It depends on span L, load, Young's modulus E, and second moment of area I. Stiffer beams (higher EI) deflect less.
What formula is used for a simply supported beam with a center load?: Maximum deflection at midspan: δ = PL³/(48EI). Maximum bending moment: M = PL/4. This assumes elastic behavior and a point load at the center.
What units should I use for I?: Metric: cm⁴ (common in section tables). Imperial: in⁴. The calculator converts internally to SI (m⁴) for the formula.
What are L/360 and L/250 limits?: These are common serviceability limits for floor and roof beams — maximum deflection should not exceed span/360 or span/250 depending on building code and usage. The tool compares your result to both.
Does this include shear deflection?: No. Standard Euler–Bernoulli formulas for bending deflection only. For very short deep beams, shear deformation may matter; use FEA or advanced methods for those cases.

More Scientific Tools

What is the Beam Deflection Calculator?

Common use cases

Checking midspan deflection of a steel beam under a point load

Sizing floor joists with uniform live load on a simply supported span

Estimating cantilever balcony deflection at the free end

Comparing fixed-end vs simply supported deflection for the same load

Structural homework on δ = PL³/(48EI) and related beam formulas

Frequently asked questions

What is beam deflection?

Beam deflection (δ) is the vertical displacement of a beam under load. It depends on span L, load, Young's modulus E, and second moment of area I. Stiffer beams (higher EI) deflect less.

What formula is used for a simply supported beam with a center load?

Maximum deflection at midspan: δ = PL³/(48EI). Maximum bending moment: M = PL/4. This assumes elastic behavior and a point load at the center.

What units should I use for I?

Metric: cm⁴ (common in section tables). Imperial: in⁴. The calculator converts internally to SI (m⁴) for the formula.

What are L/360 and L/250 limits?

These are common serviceability limits for floor and roof beams — maximum deflection should not exceed span/360 or span/250 depending on building code and usage. The tool compares your result to both.

Does this include shear deflection?

No. Standard Euler–Bernoulli formulas for bending deflection only. For very short deep beams, shear deformation may matter; use FEA or advanced methods for those cases.