Beam Deflection Calculator

Formula and method

Simply supported centre point load: δ=P L³/(48EI); simply supported full UDL: δ=5w L⁴/(384EI); cantilever tip point load: δ=P L³/(3EI); cantilever full UDL: δ=w L⁴/(8EI). Convert E from GPa to N/mm² by multiplying by 1000; use L in mm and I in mm⁴.

Worked example

For a simply supported centre point load, L=2000 mm, E=200 GPa, I=8,000,000 mm⁴ and P=1000 N give about 0.104167 mm maximum downward deflection at x=1000 mm.

Assumptions and limits

Supply E and I for the actual material, section and bending axis. 200 GPa is an example; no material or section-name preset is inferred. I is the second moment of area, not section modulus, area or mass moment of inertia.
The simply supported point load must be at midspan; the cantilever point load must be at the free end. A uniform load covers all of L. w is load per length: 1 N/mm = 1 kN/m, not total load. Self-weight is included only if you add it to w.
Only deflection magnitude and the standard location are reported. For nonzero loads, the maximum is at L/2 for simple supports and L for a cantilever. At zero load the whole beam has zero deflection, so its maximum location is not unique.
Strength, stability, shear deflection, dynamics, connection flexibility and code limits are not checked; no capacity or safety conclusion is made. Large deformation, varying EI, multiple loads and other supports require an appropriate model.

Frequently asked questions

How do I select the four cases?

Choose simple supports or a cantilever, then a point load or full-span uniform load. The point-load position is fixed at midspan or the free end; arbitrary positions are not supported.

Why is there no automatic section or allowable-load selection?

I depends on the actual section and bending axis. Allowable load also requires strength, stability, support, connection and code checks. This tool only calculates linear deflection for the stated cases.

Does a finite result validate the small-deflection assumption?

No. The model does not verify deformation size, material linearity or actual support stiffness, and applies no universal L/240 or L/360 acceptance rule.

References

Beam Deflection Calculator practical guide and common questions

What does Beam Deflection Calculator calculate?

Four fixed cases only: a simply supported beam with a centre point load or full-span uniform load, and a cantilever with a free-end point load or full-span uniform load. The model assumes constant EI, a prismatic beam, ideal supports, linear-elastic static small deflection and negligible shear deformation. Simply supported centre point load: δ=P L³/(48EI); simply supported full UDL: δ=5w L⁴/(384EI); cantilever tip point load: δ=P L³/(3EI); cantilever full UDL: δ=w L⁴/(8EI). Convert E from GPa to N/mm² by multiplying by 1000; use L in mm and I in mm⁴.

When is this useful?

For a simply supported centre point load, L=2000 mm, E=200 GPa, I=8,000,000 mm⁴ and P=1000 N give about 0.104167 mm maximum downward deflection at x=1000 mm.

How do I enter the inputs?

Enter the inputs for Beam Deflection Calculator: Support condition, Load type and position, Span or cantilever length L, Elastic modulus E (replace example as needed), Second moment of area I about the bending axis, Downward point load P at the stated position, Full-span downward uniform line load w. Calculate, check the units and assumptions, then copy or download the results.

How should I interpret the results?

Supply E and I for the actual material, section and bending axis. 200 GPa is an example; no material or section-name preset is inferred. I is the second moment of area, not section modulus, area or mass moment of inertia. The simply supported point load must be at midspan; the cantilever point load must be at the free end. A uniform load covers all of L. w is load per length: 1 N/mm = 1 kN/m, not total load. Self-weight is included only if you add it to w. Only deflection magnitude and the standard location are reported. For nonzero loads, the maximum is at L/2 for simple supports and L for a cantilever. At zero load the whole beam has zero deflection, so its maximum location is not unique. Strength, stability, shear deflection, dynamics, connection flexibility and code limits are not checked; no capacity or safety conclusion is made. Large deformation, varying EI, multiple loads and other supports require an appropriate model.

Where are my inputs processed?

Beam Deflection Calculator runs in this browser. Inputs are not uploaded to a calculation server; copying and CSV download require your action. The existing site analytics and advertising still load.