Beam Deflection Calculator Simply Supported with Uniform Load

This calculator covers a simply supported beam carrying a uniformly distributed load (UDL) along its full span — the standard model for a floor or roof beam supporting an evenly spread load such as flooring, snow, or a uniformly loaded panel. Both support reactions are equal (each carrying half the total load), and maximum deflection and maximum bending stress both occur at mid-span, just as with a centre point load, but at lower magnitude for the same total applied load.

For a load concentrated at a single point instead, see our Simple Centre Point Load calculator; for a UDL over only part of the span, see Simply Supported, Partial Load.

This calculator calculates the End Slopes, Support Reactions, Maximum Deflection and Maximum Stress in a Cantilever beam with a point load at its free end.

Enter your values as required and press SOLVE, your results will be displayed. If you change any unit types or values please press SOLVE again.

CLEAR ALL clears all fields.

SIMPLY SUPPORTED BEAM - UNIFORM LOAD

MATERIAL: Aluminium 2024-T4Aluminium 6061-T6Aluminium 7075-T3BrassCast IronCopperLeadMagnesiumPhosphur BronzeStainless Steel, 304Stainless Steel, 316Steel, S235Steel, S275Steel, S355Steel, 4130Steel, ASTM A36Steel, ASTM A441Titanium, Grade 2Titanium, Grade 5

MOMENT OF INERTIA:

mm4cm4m4Inch4

TOTAL LENGTH: (L)

MetresCentimetresMillimetresInches

DISTANCE TO NEUTRAL PLANE: (Z)

MetresCentimetresMillimetresInches

UNIFORM LOAD: (w)

N/mmkN/mlb/inlb/ft

END SLOPE A: (A°)

DegreesRadians

END SLOPE: (B°)

DegreesRadians

SUPPORT REACTION: (WA)

NewtonsKgflbf

SUPPORT REACTION: (WB)

NewtonsKgflbf

MAXIMUM DEFLECTION: (y)

MetresCentimetresMillimetresInches

MAXIMUM STRESS:

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RELATED PAGES

• Simply Supported, Partial Load
• Simply Supported, Centre Point Load
• Simple Overhanging, Uniform Load

FREQUENTLY ASKED QUESTIONS

Does a UDL cause more or less deflection than the same total load as a centre point load?

Less — for the same total load, a uniform load produces 5/8 of the deflection a centre point load would cause, since much of the UDL's weight acts closer to the supports where it has less effect on mid-span deflection.

What units should the distributed load be entered in?

As a load per unit length (e.g. N/m or lb/ft), not a total load — double-check the calculator's input labels, since mixing up a total load with a per-length value is a common source of error.