Key Shear and Bearing Stress Calculator — Shaft Key Force & Required Length Validator
Calculate key shear stress, bearing stress, and tangential force using torque, shaft diameter, key geometry, and material limits.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Load input
Power input
Key & shaft geometry
Factors (optional)
Material
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
τ, σc and F formula:
For torque mode and design mode:
Teff = T · Kd
For power mode:
ω = (2π · n) / 60
T = P / ω
Teff = T · Kd
F = (2 · Teff) / d
For analysis mode:
leff = kl · l
heff = h / 2
Aτ = b · leff
Ac = heff · leff
τ = F / Aτ
σc = F / Ac
where:
- τ — shear stress in key (Pa)
- σc — bearing crushing stress (Pa)
- F — tangential force (N)
- T — input torque (N·m)
- Teff — effective torque after dynamic factor (N·m)
- P — power (W)
- n — rotational speed (rpm)
- ω — angular speed (rad/s)
- d — shaft diameter (m)
- b — key width (m)
- h — key height (m)
- l — key length (m)
- leff — effective key length (m)
- heff — effective bearing height (m)
- kl — length factor (-)
- Kd — dynamic factor (-)
When to use this calculator
When to use this calculator:
- Check key shear stress from a known transmitted torque.
- Check key bearing stress from shaft diameter, key width, key height, and key length.
- Calculate tangential force from torque and shaft diameter.
- Calculate torque from power and rotational speed before evaluating key stress.
- Estimate required key length in design mode using allowable shear and bearing stress limits.
How to interpret the result
Tangential force is defined as the force transferred at the shaft diameter by the effective torque. Key shear stress is defined as tangential force divided by key shear area. Bearing stress is defined as tangential force divided by the effective bearing area.
The result depends on transmitted torque, shaft diameter, key width, key height, key length, length factor, and dynamic factor. Increasing torque or dynamic factor increases tangential force and therefore increases both stress results. Increasing shaft diameter decreases tangential force. Increasing key width decreases shear stress. Increasing key height decreases bearing stress. Increasing effective key length decreases both stress results.
- Safe — in analysis mode, the highest utilization is greater than 0 and not greater than 0.85. In design mode, the result is marked safe after a valid required key length calculation.
- Warning — in analysis mode, the highest utilization is greater than 0.85 and not greater than 1.0.
- Unsafe — in analysis mode, the highest utilization is greater than 1.0.
- Info — in analysis mode, no positive utilization is available because the relevant material limit is not available for the calculated stress check.
- Invalid — input is invalid when calculation mode is not supported, material limits are missing, geometry values are not greater than zero, torque is not greater than zero, or power and speed inputs cannot produce a valid torque.
The result is used to compare shear and bearing demand in the key and identify whether shear or bearing is the limiting failure mode.
Calculation example
Example:
A user wants to check whether a shaft key can transmit torque without exceeding shear or bearing stress limits.
- Mode: From torque
- T — Torque: 120 N·m
- d — Shaft diameter: 0.04 m
- b — Key width: 0.012 m
- h — Key height: 0.008 m
- l — Key length: 0.05 m
- kl — Length factor: 1
- Kd — Dynamic factor: 1
F = 6000 N, τ = 10000000 Pa, σc = 30000000 Pa.
Assumptions and limitations
- Effective torque is calculated by multiplying input torque or power-derived torque by the dynamic factor.
- Tangential force is calculated from effective torque and shaft diameter using F = 2 · Teff / d.
- Effective key length is calculated by multiplying entered key length by the length factor.
- Effective bearing height is equal to one half of the key height.
- Shear stress uses key width multiplied by effective key length as the shear area.
- Bearing stress uses effective bearing height multiplied by effective key length as the bearing area.
- Allowable shear and bearing limits are divided by the safety factor before utilization is calculated.