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Beam Deflection Calculator

Select the beam type, load type, and enter the necessary values. The tool will instantly calculate the beam deflection for you.

Beam Type:

Midspan Load:

Span Length, L:

m ▾

Moment Load, M:

N/m ▾

Moment Load, M:

N.m ▾

Modulus of Elasticity, E:

kN ▾

Point Load, P:

kPa ▾

Moment of Inertia, Ix:

m⁴ ▾

Deflection At:

m ▾

Distance:

Related

Beam Deflection Calculator

Use our beam deflection calculator to determine the maximum bending or deflection of a beam, whether it is simply-supported or cantilevered. The calculator considers the load magnitude, its location, and beam properties such as elasticity and moment of inertia.

How to Calculate Beam Deflection

The maximum deflection of a beam depends on its support type and the nature of the applied load. Below are commonly used formulas:

Simply-Supported Beam

Midspan Point Load

Simply-supported beam midspan load

\( \delta_{max} = \dfrac{PL^3}{48EI} \)

Point Load at Any Position

Point load at any position

\( \delta_{max} = \dfrac{Pb(3L^2 - 4b^2)}{48EI} \)

Uniformly Distributed Load

Uniform load

\( \delta_{max} = \dfrac{5wL^4}{384EI} \)

Uniformly Varying Load

Uniformly varying load

\( \delta_{max} = \dfrac{0.00652 w L^4}{EI} \)

Triangular Load

Triangular load

\( \delta_{max} = \dfrac{w L^4}{120EI} \)

Moment at Support

Moment at support

\( \delta_{max} = \dfrac{M L^2}{9 \sqrt{3} EI} \)

Cantilever Beam

End Point Load

Cantilever end load

\( \delta_{max} = \dfrac{P L^3}{3 EI} \)

Point Load at Any Location

Point load anywhere

\( \delta_{max} = \dfrac{P a^2 (3L - a)}{6 EI} \)

Uniform Load

\( \delta_{max} = \dfrac{w L^4}{30 EI} \)

Uniformly Varying Load (Triangular)

Case 1: \( \delta_{max} = \dfrac{w L^4}{30 EI} \)

Case 2: \( \delta_{max} = \dfrac{11 w L^4}{120 EI} \)

Moment at Free End

Moment at cantilever end

\( \delta_{max} = \dfrac{M L^2}{2 EI} \)

How to Use the Beam Deflection Calculator

Select the type of beam: Simply-Supported or Cantilever.
Choose the type of load applied (point load, uniform load, moment, etc.).
Enter the beam span length and applied load values.
Provide the material properties: Modulus of Elasticity (E) and Moment of Inertia (I).
Click Calculate to get the maximum deflection.

References

From Wikipedia: Deflection (Engineering) – Beam deflection under various loading and support conditions. From Lumen Learning: Stress, Strain, and Elastic Modulus – Tensile and compressive stress concepts.

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