`theta = (32* "L" * "T" )/( "G" *pi* "D" ^4)`

Enter a value for all fields

The Angular Deflection of a Torsion Solid Shaft calculator computes the deflection based on the twisting moment, length and outer diameter of the shaft and the modulus of rigidity.

INSTRUCTIONS: Choose units and enter the following:

• (T) Twist Moment in Newton millimeters (N⋅mm)
• (L) Length of Shaft
• (D) Outer Diameter of Shaft
• (G) Modulus of Rigidity

Angular Deflection of Torsion Solid Shaft (θ): The parameter is returned as a real number.

The Math / Science

The formula for  angular deflection of a torsion solid shaft is:

θ = (32 ⋅L⋅ T) / (G ⋅ π ⋅ D⁴)

where:

• θ = angular deflection as a real number
• T = twisting moment (N⋅mm)
• L = length of shaft
• G = modulus of rigidity
• D = shaft outside diameter