Structural Beam Bending Equations / Calculation Cantilevered Beam with One Load Applied at End

Beam Deflection and Stress Formula and Calculators

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Stress at specific point

Stress at the support (must be constant cross section)

Deflection at specified point

Deflection at the unsupported end


E =  Modulus of Elasticity psi


I = Moment of Inertia in4 (m4)
W =  Load lbs (N)
s =  Stress at the cross-section being evaluated lbs/in2 (N/m2)
y = Deflection inches (m)
Some distance as indicated inches (m)
x = Some distance as indicated inches (m)
Z = section modulus of the cross-section of the beam    
Z = I distance from neutral axis to extreme fiber (edge)    
  • Please note letter "" (lower case "L") is different than "I" (Moment of Inertia).
  • Deflections apply only to constant cross sections along entire length.


  • Any Machinery's Handbook published since 1931 or,
  • Machinery's Handbook, 21st Edition, Page 408 or,
  • Machinery's Handbook, 23st Edition, Page 264 or,
  • Machinery's Handbook, 27st Edition, Page 265

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