Shaft Diameter Calculator for Torsion, Power and Combined Bending Load
Calculate required shaft diameter using applied torque, transmitted power, allowable shear stress, or combined bending and torsion.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Material property
Applied torque
Power transmission
Bending load
Shock and fatigue factors
Existing shaft
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
Required shaft diameter formula:
d = ∛(16 · T / (π · τallow))
From power:
ω = 2 · π · n / 60
T = P / ω
d = ∛(16 · T / (π · τallow))
Combined bending + torsion:
Te = √((Kt · T)2 + (Km · M)2)
d = ∛(16 · Te / (π · τallow))
Check existing shaft:
Te = √(T2 + M2)
τmax = 16 · Te / (π · d3)
Safety factor = τallow / τmax
Utilization = τmax / τallow · 100%
where:
- d — required shaft diameter or checked shaft diameter (length)
- T — applied torque (torque)
- Te — equivalent torque (torque)
- τallow — allowable shear stress (stress)
- τmax — actual shear stress (stress)
- P — transmitted power (power)
- n — rotational speed (rotational speed)
- ω — angular speed (rad/s)
- M — bending moment (torque)
- Kt — shock factor for torsion (-)
- Km — shock factor for bending (-)
When to use this calculator
When to use this calculator:
- Size a shaft diameter from a known applied torque and allowable shear stress.
- Calculate shaft diameter from transmitted power and rotational speed.
- Calculate equivalent torque for a shaft loaded by bending moment and torque with shock factors.
- Check an existing shaft diameter against actual shear stress and allowable shear stress.
- Evaluate utilization of allowable shear stress for an existing shaft under combined bending and torsion.
How to interpret the result
Required shaft diameter is defined as the shaft diameter calculated from torque or equivalent torque so that the calculated shear stress is based on the provided allowable shear stress.
Equivalent torque depends on applied torque and bending moment. In combined bending and torsion mode, applied torque is multiplied by the shock factor for torsion, and bending moment is multiplied by the shock factor for bending. Increasing either factored load increases equivalent torque and increases required shaft diameter.
Actual shear stress is defined as the shear stress calculated for an existing shaft diameter under equivalent torque. Increasing equivalent torque increases actual shear stress. Increasing shaft diameter decreases actual shear stress because the diameter is raised to the third power.
- Safe — in check mode, utilization of allowable shear stress is less than or equal to 85%.
- Warning — in check mode, utilization of allowable shear stress is greater than 85% and less than or equal to 100%.
- Unsafe — in check mode, utilization of allowable shear stress is greater than 100%.
- Info — used outside check mode when the calculator returns calculated diameter or equivalent torque without utilization-based assessment.
- Invalid — used when required inputs are missing, non-finite, zero, negative, or inconsistent with the selected calculation mode.
The result is used to size a shaft diameter or verify whether an existing shaft stays within the allowable shear stress limit.
Calculation example
Example:
A user wants to check whether an existing shaft can carry combined torque and bending moment without exceeding allowable shear stress.
- Calculation mode: Check existing shaft
- τallow — Allowable shear stress = 80 MPa
- T — Applied torque = 500 N·m
- M — Bending moment = 300 N·m
- d — Shaft diameter = 0.05 m
Te = 583.10 N·m, τmax = 23.76 MPa, utilization = 29.7%, safety factor = 3.37.
Assumptions and limitations
- Required shaft diameter is calculated from torsional shear relation d = ∛(16 · T / (π · τallow)).
- In power mode, applied torque is derived from transmitted power and angular speed using T = P / ω.
- In combined bending and torsion mode, equivalent torque includes shock factor for torsion and shock factor for bending.
- In check mode, equivalent torque is calculated directly from applied torque and bending moment without shock factors.
- Utilization-based interpretation is applied only in check mode.