Shaft Diameter Calculator — Torque, Power & Combined Bending
Size solid or hollow shafts from torque or transmitted power, include combined bending with shock/fatigue factors, or check an existing shaft against an allowable shear stress.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Shaft section
Material property
Applied torque
Power transmission
Combined shaft loading
Shock and fatigue factors
Existing shaft
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
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
Shaft diameter formulas
The calculator determines the minimum required outside diameter from an applied torque or a design equivalent torque and the entered allowable shear stress. It supports solid and hollow circular shafts.
1. Torque from transmitted power
When power and rotational speed are entered, angular speed is:
ω = 2πn / 60
and transmitted torque is:
T = P / ω
where P is transmitted power, n is rotational speed in revolutions per minute, and ω is angular speed in rad/s.
2. Equivalent torque for combined bending and torsion
In combined-loading and existing-shaft check modes, the calculator uses:
Te = √[(KtT)2 + (KmM)2]
where T is applied torque, M is bending moment, Kt is the shock/fatigue factor applied to torsion, and Km is the shock/fatigue factor applied to bending.
For the torque-only and power modes, Te = T.
3. Solid and hollow shaft section factor
For a hollow shaft, define the diameter ratio:
k = di / do
and the section factor:
F = 1 − k4
For a solid shaft, k = 0 and therefore F = 1. For a hollow shaft, the calculator requires 0 ≤ k < 1.
4. Minimum required shaft diameter
The minimum required outside diameter is:
do,min = ∛[16Te / (πτallowF)]
For a solid shaft this reduces to:
dmin = ∛[16Te / (πτallow)]
When torque is expressed in N·mm and allowable shear stress in MPa (N/mm²), the resulting diameter is in mm.
5. Existing shaft shear-stress check
For an entered outside diameter, the calculated maximum shear stress is:
τmax = 16Te / (πdo3F)
The calculator then reports:
Safety factor = τallow / τmax
Utilization = (τmax / τallow) × 100%
Symbols
| Symbol | Meaning |
|---|---|
| do,min | Minimum required outside shaft diameter |
| do | Existing outside shaft diameter |
| di | Inside diameter of a hollow shaft |
| T | Applied or transmitted torque |
| Te | Design equivalent torque |
| M | Bending moment |
| τallow | Entered allowable shear stress |
| τmax | Calculated maximum shear stress for an existing shaft |
| Kt | Shock/fatigue factor for torsion |
| Km | Shock/fatigue factor for bending |
| k | Inner-to-outer diameter ratio, di/do |
| P | Transmitted power |
| n | Rotational speed |
When to use this calculator
When to use this shaft diameter calculator
Use this calculator for preliminary sizing or verification of circular power-transmission shafts when the governing design input can be represented by torque, transmitted power, or combined bending and torsion.
- Size a shaft from torque: enter the applied torque and allowable shear stress to calculate the minimum required diameter.
- Size a shaft from power and RPM: enter transmitted power and rotational speed and the calculator first converts them to torque.
- Evaluate combined bending and torsion: enter torque, bending moment, and the applicable torsional and bending shock/fatigue factors.
- Size a hollow shaft: specify the inner-to-outer diameter ratio to calculate the required outside diameter.
- Check an existing shaft: compare the calculated maximum shear stress with the entered allowable shear stress and review the resulting utilization and allowable-to-actual stress ratio.
The calculator is appropriate for first-pass shaft sizing when the allowable shear stress has already been established for the material and design case.
It is not a complete shaft-design verification. It does not calculate fatigue life, stress concentrations at shoulders or keyways, angle of twist, shaft deflection, critical speed, bearing reactions, standard stock diameter selection, or detailed stresses around splines and other geometric discontinuities. These checks may govern the final shaft size and should be evaluated separately where applicable.
How to interpret the result
How to interpret the shaft calculation
do,min — Minimum required outside diameter
This is the outside diameter calculated so that the implemented shear-stress relation reaches the entered allowable shear stress under the design equivalent torque. For a solid shaft, it is the shaft diameter. For a hollow shaft, it is the required outside diameter for the specified di/do ratio.
Te — Design equivalent torque
In torque-only or power mode, the equivalent torque is the transmitted torque. In combined-loading and check modes, it combines the factored torque and bending moment. Increasing torque, bending moment, Kt, or Km increases Te and therefore increases the required diameter.
τmax — Actual maximum shear stress
This result is calculated in existing-shaft check mode. For the same equivalent torque, increasing shaft diameter reduces the calculated shear stress strongly because stress varies inversely with the cube of diameter.
Allowable / actual stress ratio
The reported safety-factor value is τallow/τmax. A value of 1.0 means the calculated stress equals the entered allowable value. Values above 1.0 indicate reserve relative to this criterion; values below 1.0 indicate that the allowable shear stress has been exceeded.
Utilization
Utilization is τmax/τallow × 100%. A result at or below 100% satisfies the evaluated allowable-shear-stress criterion. A result above 100% does not satisfy it.
At constant power, lower rotational speed produces greater transmitted torque and therefore a larger required shaft diameter. Increasing the allowable shear stress reduces the calculated minimum diameter. For a hollow shaft, increasing the inner-to-outer diameter ratio reduces the section factor and increases the required outside diameter for the same loading.
A result within the allowable shear-stress limit confirms only the criterion evaluated by this calculator. It does not confirm fatigue life, stiffness, dynamic behavior, keyway strength, bearing suitability, critical speed, or compliance with a complete shaft-design standard.
Calculation example
Shaft diameter calculation example
A solid shaft carries both torque and bending. Determine the minimum required diameter using the combined bending and torsion mode.
Input data
- Applied torque, T = 500 N·m
- Bending moment, M = 300 N·m
- Allowable shear stress, τallow = 80 MPa
- Torsional shock/fatigue factor, Kt = 1.5
- Bending shock/fatigue factor, Km = 1.5
- Shaft section: solid, so k = 0 and F = 1
Step 1 — Calculate the equivalent torque
Te = √[(KtT)2 + (KmM)2]
Te = √[(1.5 × 500)2 + (1.5 × 300)2]
Te = 874.64 N·m
For calculation in N·mm:
Te = 874,642.8 N·mm
Step 2 — Calculate the minimum shaft diameter
Because 80 MPa = 80 N/mm²:
dmin = ∛[16 × 874,642.8 / (π × 80)]
dmin = 38.19 mm
Interpretation
The calculated minimum diameter for this simplified allowable-shear-stress criterion is approximately 38.2 mm. A practical design diameter should not be selected below the calculated requirement.
This result verifies only the implemented equivalent-torque and allowable-shear-stress model. Final shaft selection may require additional checks for fatigue, geometric stress concentrations, stiffness, twist, critical speed, bearings, keys, manufacturing tolerances, and the governing design standard.
Assumptions and limitations
Assumptions and limitations
- The shaft is modeled as a circular solid or concentric hollow section at the location being evaluated.
- Hollow-shaft geometry is represented only by the constant ratio di/do, which must satisfy 0 ≤ di/do < 1.
- Shaft sizing is based on the entered allowable shear stress. The calculator does not determine the allowable value from material yield strength, ultimate strength, or a design code.
- Combined bending and torsion are represented by Te = √[(KtT)² + (KmM)²]. The calculator does not separately calculate bending normal stress or compare multiple failure theories.
- Kt and Km are the implemented shock/fatigue load factors. They are not a substitute for calculating geometric stress-concentration factors at shoulders, keyways, grooves, holes, splines, threads, or other discontinuities.
- The model does not calculate fatigue life or alternating and mean stress histories for a rotating shaft.
- Shaft deflection, angle of twist, torsional stiffness, lateral vibration, natural frequency, critical speed, and resonance are outside the calculation.
- Bearing reactions, gear or pulley forces, shaft-span load distribution, and the resulting bending moment are not generated by the calculator. The bending moment must already be known when combined loading is evaluated.
- Key, keyway, spline, coupling, bearing-seat, and local contact-stress verification must be performed separately.
- Temperature effects, corrosion, wear, residual stress, manufacturing tolerances, surface condition, and material variability are not explicitly modeled.
- The calculator returns a calculated minimum diameter and does not automatically round the result to a preferred, standardized, or commercially available shaft size.
- Final design should be checked against the applicable engineering standard and all relevant static, fatigue, stiffness, dynamic, manufacturing, and service requirements.