Beam Deflection Calculator

Enter your beam span, load type, load magnitude, and modulus of elasticity with moment of inertia to calculate the maximum beam deflection. Select from common support conditions like simply supported or cantilever beams, and get back the maximum deflection (δ), deflection ratio (L/δ), and a visual breakdown of how load and span interact.

m

Total length of the beam between supports

kN or kN/m

Point load in kN, or distributed load intensity in kN/m

GPa

Steel ≈ 200 GPa, Concrete ≈ 30 GPa, Wood ≈ 12 GPa

cm⁴

Second moment of area of the beam cross-section

Results

Maximum Deflection (δ)

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Deflection Ratio (L/δ)

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Maximum Deflection (m)

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Flexural Rigidity (EI)

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Serviceability (L/300 limit)

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Deflection vs Span Sensitivity

Results Table

Frequently Asked Questions

What is beam deflection and why does it matter?

Beam deflection is the displacement a structural beam undergoes when subjected to an applied load. It matters because excessive deflection can cause structural damage, cracking in finishes, and serviceability problems even if the beam has adequate strength. Most design codes limit deflection to L/300 or L/360 of the span.

What is the formula for maximum deflection of a simply supported beam with a central point load?

For a simply supported beam with a central point load P, the maximum deflection is δ = PL³ / (48EI), occurring at mid-span. Here L is the beam span, E is the modulus of elasticity, and I is the second moment of area of the cross-section.

How does a cantilever beam deflection formula differ from a simply supported beam?

A cantilever beam with a point load at its free end deflects by δ = PL³ / (3EI), which is 16 times greater than an equivalent simply supported beam under the same load. This is because only one end is restrained, making cantilevers significantly more flexible.

What is the modulus of elasticity (E) for common materials?

Steel has E ≈ 200 GPa, making it the stiffest common structural material. Concrete ranges from 25–35 GPa depending on strength grade, timber is typically 8–14 GPa, and aluminium is around 70 GPa. Using the correct E value is critical for accurate deflection results.

What is the moment of inertia (I) and how do I find it for my beam?

The moment of inertia (also called second moment of area) measures a cross-section's resistance to bending. For a rectangular section it is I = bh³/12 where b is width and h is height. Standard steel I-beams have I values listed in manufacturer tables and design handbooks.

What deflection limit should I design to?

Common serviceability limits are L/300 for floors, L/360 for floors supporting brittle finishes, and L/200 for roofs. For example, a 6 m floor beam should not deflect more than 20 mm under live load if using an L/300 criterion. Always verify against your local design code.

How does span length affect beam deflection?

Deflection is proportional to the cube of the span (L³), meaning doubling the span increases deflection by 8 times, all else equal. This is why long-span beams require significantly deeper or stiffer sections to remain within acceptable serviceability limits.

Can I use this calculator for steel I-beams, timber, and concrete beams?

Yes. Simply enter the appropriate modulus of elasticity (E) and moment of inertia (I) for your specific material and cross-section. For steel I-beams look up I in steel section tables; for timber use the species E value; for concrete use the effective I accounting for cracking if required by code.

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