# Shaft Torque Calculator, Formula, Shaft Torque Calculation

## Shaft Torque Calculator:

Enter the values of shear stress, ss(Pa), moment of inertia, J(m2) and the shaft’s radius r(m) to generate the value of Shaft Torque, Ts(N.m).

 Enter The Shear Stress: Pa Enter Shaft Radius: m Enter Polar Moment of Ratio: m2 Result – Shaft Torque: N.m

## Shaft Torque Formula:

Shaft torque refers to the rotational force applied on or transmitted by a shaft, crucial for understanding the dynamics of power transmission in machinery, such as in gearboxes, motors, and turbines. This measurement helps in designing shafts that can withstand operational stresses without failing.

Shaft Torque, Ts(N.m) in Newton metres, is determined by the multiplication of shear stress ss(Pa) in the material in Pascal, the polar moment of inertia J(m2) of the shaft cross-section in square metres, and divided by the shaft’s radius r(m) in metres.

Shaft Torque, Ts(N.m) = ss(Pa) * J(m2) /  r(m)

Ts(N.m) = Shaft Torque in Newton metre, N.m

ss(Pa) = the shear stress in Pascal, Pa

r(m) = shaft radius in metre, m.

J(m2) = polar moment of ratio in square metre, m2.

### Shaft Torque Calculation:

1. A shaft is subjected to a shear stress of 120 MPa. It has a polar moment of inertia of 0.0001 2 and a radius of 0.05 m. Determine the torque that this shaft can transmit.

Given: ss(Pa) = 120 * 106 (since 1 MPa = 106 Pa), J(m2) = 0.0001m2 and r(m) = 0.05m.

Shaft Torque, Ts(N.m) = ss(Pa) * J(m2) /  r(m)

Ts(N.m) = 120 * 106 * 0.0001 / 0.05

Ts(N.m) = 240N.m.

2. A mechanical engineer needs to design a shaft that must transmit a torque of 500 N.m. If the shaft has a polar moment of inertia of 0.0002 m2 and a radius of 0.04 m, what must be the minimum shear stress in the shaft material?

Given: Ts(N.m) = 500N.m, J(m2) = 0.0002m2 and r(m) = 0.04m.

Shaft Torque, Ts(N.m) = ss(Pa) * J(m2) /  r(m)

ss(Pa) = Ts(N.m) * r(m) / J(m2)

ss(Pa) = 500 * 0.04 / 0.0002