Simply Supported Beam Deflection Calculator
Estimate maximum deflection, reactions and bending moment for a simply supported constant-section beam under a centered point load or full-span uniform load.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use Euler–Bernoulli small-deflection formulas for a prismatic beam with ideal simple supports. The uniform-load option takes total load over the span, then divides it by span length for load intensity.
Centered point: δmax=PL³/(48EI), Mmax=PL/4. Uniform total W: δmax=5WL³/(384EI), Mmax=WL/8.
Worked example
A 3 m steel beam with E=200 GPa, I=8.0×10⁷ mm⁴ and a centered 5 kN load deflects about 0.1758 mm at midspan. Each reaction is 2.5 kN.
Assumptions and input details
Euler–Bernoulli linear elasticity, small deflection, ideal pin/roller supports, constant E and I, and static vertical loading are assumed. Enter the entire uniform load, not force per length. Self-weight is included only if added to that total. Shear deformation, local effects, lateral-torsional buckling, residual stress, connection flexibility, strength, vibration and code limits are not checked.
References: NASA Structures Manual: beam formulas
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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