The torsion formula for circular shafts relates the shear stress ($\tau$) experienced by a shaft to the applied torque ($T$), the radial distance from the center of the shaft ($r$), and the polar moment of inertia ($J$) of the cross-sectional area of the shaft. This formula is fundamental for analyzing the behavior of circular shafts under torsional loading. The torsion formula for circular shafts is given by:

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Where:

• $\tau$ is the shear stress induced by torsion,
• $T$ is the applied torque,
• $r$ is the radial distance from the center to the point where the shear stress is calculated, 
• $J$ is the polar moment of inertia of the cross-sectional area of the shaft.