EngineerBenchCalculating the engaged length of a shaft key
A key transmits torque through a tangential force at the shaft radius. The required engaged length is checked against both key shear and bearing stress. The larger length from those two checks controls within this simple model; using only a shear check can miss a bearing limitation.
Measure the length that carries load
Use the effective engagement between the key, shaft, and hub rather than assuming the entire nominal key length is active. End geometry and incomplete contact can reduce the working length. Enter the shaft diameter and the actual key width and height.
Check the shaft and hub too
The model uses the entered shear and bearing allowances; it does not select a standard key or verify a catalog rating. The keyway also changes the shaft's local stress, and the hub can have its own strength limit. Shock, reversing loads, and fatigue require additional consideration.
Converting shaft torque to key force
Tangential force at a shaft surface is twice torque divided by shaft diameter when compatible units are used. A 100 N·m torque on a 50 mm shaft corresponds to a 4,000 N tangential force. That force acts through the key's effective shear and bearing areas. Keep millimeters and meters consistent when converting torque into force.
The shear area uses key width and engaged length. The simplified bearing area uses half the key height and engaged length, reflecting the represented contact geometry. A short hub can limit engagement even when a longer key is available. Check whether chamfers, rounded ends, or an incomplete keyway reduce useful contact. Compare both required lengths and use the governing result within the model, then select a practical arrangement with sufficient space. The allowance should be appropriate to the actual key and mating materials. The calculation does not check the weakened shaft section, hub splitting, fretting, or fatigue under reversing torque, so those remain separate parts of the connection design.
Formula
Tangential load = 2T/d; shear area = bL; projected bearing area = hL/2.