Beam Deflection Calculator

Calculate deflection, slope, moment, and shear

Formula

Cantilever point load: δ = PL³/3EI, M = PL. Simply supported center load: δ = PL³/48EI, M = PL/4. Fixed-fixed center: δ = PL³/192EI, M = PL/8. UDL: δ = wL⁴/8EI (cantilever), 5wL⁴/384EI (simply supported).

Beam deflection formulas derived from double integration of moment equation: EI(d²y/dx²) = M(x). Boundary conditions determine constants. E = modulus of elasticity, I = moment of inertia.

How to Calculate Manually

1
Select beam type and load type
2
Enter span, load, E, and I
3
Choose units
4
Calculator shows deflection, moment, shear, and L/δ ratio

Reference Table

Beam Type	Load	Max Deflection	Max Moment	Max Shear
Cantilever	P at end	PL³/3EI	PL	P
Cantilever	UDL w	wL⁴/8EI	wL²/2	wL
Simply Supported	P at center	PL³/48EI	PL/4	P/2
Simply Supported	UDL w	5wL⁴/384EI	wL²/8	wL/2
Fixed-Fixed	P at center	PL³/192EI	PL/8	P/2
Fixed-Fixed	UDL w	wL⁴/384EI	wL²/12	wL/2
Fixed-Pinned	P at center	PL³/76.8EI	3PL/16	3P/8
Fixed-Pinned	UDL w	wL⁴/185EI	wL²/8	3wL/8

Beam Deflection Calculator: Cantilever, Simply Supported, Fixed Beams

Beam deflection is a critical check in structural design. Excessive deflection can cause cracking in finishes, misalignment of equipment, ponding on roofs, and uncomfortable vibrations. Building codes specify maximum allowable deflections typically as a fraction of the span (L/360 for floors, L/240 for roofs, L/180 for non-structural elements)...

Frequently Asked Questions

What are the common beam types? Cantilever (fixed-free), Simply Supported (pin-roller), Fixed-Fixed, Fixed-Pinned, Overhanging. Each has different deflection formulas.: Cantilever (fixed-free), Simply Supported (pin-roller), Fixed-Fixed, Fixed-Pinned, Overhanging. Each has different deflection formulas.
What is the max allowable deflection? Typical limits: L/360 for floors, L/240 for roofs, L/180 for non-structural. L = span length. Check local building codes.: Typical limits: L/360 for floors, L/240 for roofs, L/180 for non-structural. L = span length. Check local building codes.
What do I need for calculation? Span (L), Load (P or w), Modulus of Elasticity (E), Moment of Inertia (I). For steel: E ≈ 29,000 ksi. For concrete: E ≈ 3,000-5,000 ksi.: Span (L), Load (P or w), Modulus of Elasticity (E), Moment of Inertia (I). For steel: E ≈ 29,000 ksi. For concrete: E ≈ 3,000-5,000 ksi.

Calculator

Formula

Formula

How to Calculate Manually

Reference Table

Beam Deflection Calculator: Cantilever, Simply Supported, Fixed Beams

Frequently Asked Questions

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