What units should I use for the inputs?

Use Newtons (N) for point loads, Newtons per millimeter (N/mm) for UDLs, millimeters (mm) for span length, Megapascals (MPa or N/mm²) for Young's Modulus, and mm⁴ for the second moment of area.

Which beam configurations are supported?

The calculator supports cantilever beams with end point loads or UDLs, and simply supported beams with mid-span point loads or UDLs.

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

You can look up the second moment of area (I) in standard steel section tables for standard profiles, or calculate it using geometric formulas for simple shapes like rectangles (bh³/12).

What formula is used for a simply supported beam under a UDL?

The calculator uses the classic formula: δ = 5qL⁴ / (384EI) to find the maximum deflection at the mid-span.

Can I adjust the precision of the calculated deflection?

Yes, you can specify the number of decimal places (from 0 to 8) in the settings before running the calculation.

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Beam Deflection Calculator

Look up and compute the maximum deflection for four classic beam cases: cantilever with end point load (δ=PL³/3EI), cantilever with UDL (δ=qL⁴/8EI), simply supported with mid-span point load (δ=PL³/48EI), and simply supported with UDL (δ=5qL⁴/384EI).

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2 examples

Simply supported + UDL: q=10 N/mm, L=4000 mm, E=210000, I=8.36×10⁷ mm⁴

δ = 5·q·L⁴/(384·E·I) = 5·10·4000⁴/(384·210000·8.36×10⁷) ≈ 1.8987 mm at mid-span.

{"result":"Simply supported beam + UDL, q=10 N/mm, L=4000 mm, E=210000 MPa, I=83600000 mm⁴. δ_max = 5·q·L⁴/(384·E·I) = 1.8987 mm at mid-span.","metadata":{"input":{"supportCase":"simplySupportedUDL","q":10,"L":4000,"E":210000,"I":83600000},"result":{"supportCase":"simplySupportedUDL","load":"q","deflection":1.8987,"deflectionUnit":"mm","formula":"δ = 5·q·L⁴ / (384·E·I)","location":"mid-span"}}}

Cantilever + end point load: P=5000 N, L=2000 mm, E=210000, I=8.36×10⁷ mm⁴

δ = P·L³/(3·E·I) = 5000·2000³/(3·210000·8.36×10⁷) ≈ 0.7595 mm at the free end.

{"result":"Cantilever beam + end point load, P=5000 N, L=2000 mm, E=210000 MPa, I=83600000 mm⁴. δ_max = P·L³/(3·E·I) = 0.7595 mm at the free end.","metadata":{"input":{"supportCase":"cantileverPoint","P":5000,"L":2000,"E":210000,"I":83600000},"result":{"supportCase":"cantileverPoint","load":"P","deflection":0.7595,"deflectionUnit":"mm","formula":"δ = P·L³ / (3·E·I)","location":"free end"}}}

Inputs

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7 options

SettingsAdjust formats, ranges, numbers, and modes.7

Support & Load CaseselectOptionalPoint Load P (N)numberOptionalRequired for point-load cases.Uniformly Distributed Load q (N/mm)numberOptionalRequired for UDL cases.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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Beam Deflection Calculator

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Use cases

Examples

1. Simply Supported Steel Beam Under Uniform Load

2. Cantilever Bracket Tip Deflection

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