🔩 Torsional Constant Calculator

Torsional Constant (Polar Moment of Inertia)

The torsional constant J describes a shaft’s cross-sectional resistance to twisting, used in the twist-angle formula θ = TL/(GJ). For a solid circular shaft, J = πd⁴/32. For a hollow shaft with outer diameter D_o and inner diameter D_i, J = π(D_o⁴ − D_i⁴)/32.

Because J depends on diameter to the fourth power, small increases in shaft diameter dramatically increase torsional stiffness and strength — which is why hollow shafts can be nearly as stiff as solid ones while using much less material, since removing material near the center (where it contributes least to J) has little effect.