What formulas are used to calculate deflection?

For a point load at the free end, deflection is calculated as PL³/(3EI). For a uniformly distributed load, it is qL⁴/(8EI).

What units should I use for the inputs?

Use Newtons (N) for point load, N/mm for UDL, millimeters (mm) for span length, MPa (N/mm²) for Young's Modulus, and mm⁴ for the second moment of area.

Where do the maximum bending moment and shear force occur?

For both load types, the maximum bending moment and maximum shear force occur at the fixed end of the cantilever beam.

How do I find the second moment of area (I) for my beam?

You can calculate it based on the beam's cross-sectional shape (such as bh³/12 for a solid rectangle) or look it up in standard structural steel section tables.

Can this calculator handle multiple combined loads?

No, this calculator is designed for a single load type at a time: either a single free-end point load or a full-span uniformly distributed load.

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Cantilever Beam Calculator

Calculate the maximum bending moment M_max, maximum shear force V_max and free-end deflection δ_max of a cantilever beam under a free-end point load P or a uniformly distributed load q. Point load: δ = PL³/(3EI); UDL: δ = qL⁴/(8EI).

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Point load: P=2000 N, L=2000 mm, E=210000 MPa, I=1.5×10⁷ mm⁴

M_max = P·L = 4.0×10⁶ N·mm at the fixed end. V_max = P = 2000 N. δ = P·L³/(3·E·I) = 2000·2000³/(3·210000·1.5×10⁷) ≈ 1.6931 mm at the free end.

{"result":"Cantilever beam, point load P=2000 N at free end, L=2000 mm. M_max = P·L = 4000000 N·mm (4000 N·m) at the fixed end. V_max = P = 2000 N. δ_max = P·L³/(3·E·I) = 1.6931 mm at the free end.","metadata":{"input":{"loadType":"pointEnd","P":2000,"L":2000,"E":210000,"I":15000000},"result":{"loadType":"pointEnd","M_max":4000000,"M_max_Nm":4000,"V_max":2000,"deflection":1.6931,"deflectionUnit":"mm","E":210000,"I":15000000}}}

UDL: q=5 N/mm, L=2000 mm, E=210000 MPa, I=1.5×10⁷ mm⁴

M_max = q·L²/2 = 1.0×10⁷ N·mm at the fixed end. V_max = q·L = 10000 N. δ = q·L⁴/(8·E·I) = 5·2000⁴/(8·210000·1.5×10⁷) ≈ 3.1746 mm at the free end.

{"result":"Cantilever beam, UDL q=5 N/mm over L=2000 mm. M_max = q·L²/2 = 10000000 N·mm (10000 N·m) at the fixed end. V_max = q·L = 10000 N. δ_max = q·L⁴/(8·E·I) = 3.1746 mm at the free end.","metadata":{"input":{"loadType":"udl","q":5,"L":2000,"E":210000,"I":15000000},"result":{"loadType":"udl","M_max":10000000,"M_max_Nm":10000,"V_max":10000,"deflection":3.1746,"deflectionUnit":"mm","E":210000,"I":15000000}}}

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Load TypeselectOptionalPoint Load P at Free End (N)numberOptionalUsed in 'Point Load at Free End' mode.Uniformly Distributed Load q (N/mm)numberOptionalUsed in 'Uniformly Distributed Load' mode.Span Length L (mm)numberRequiredYoung's Modulus E (MPa)numberRequiredModulus of elasticity in MPa (= N/mm²). Steel ≈ 210000, aluminum ≈ 70000.Second Moment of Area I (mm⁴)numberRequiredArea moment of inertia of the cross-section about the bending axis, in mm⁴.Decimal PlacesnumberOptional

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Cantilever Beam Calculator

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Examples

1. Verifying Deflection of a Steel Cantilever Bracket

2. Calculating Balcony Joist Deflection Under Uniform Load

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