calculatorbrowser-only

Shaft Design Calculator

Estimate required solid or hollow circular-shaft diameter using torque, bending moment, service factors, and equivalent-stress criteria.

Shaft Design inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation mode

Display precision

Material properties

Material property mode

Material preset

Young's modulus

Young's modulus unit

Shear modulus

Shear modulus unit

Yield strength

Yield strength unit

Ultimate strength

Ultimate strength unit

Generic steel values. Use grade-, standard-, temperature-, and process-specific data for real design.

Shaft loads and sizing

Shaft type

Failure criterion

Bending moment

Bending moment unit

Torque

Torque unit

Allowable equivalent stress

Allowable equivalent stress unit

Allowable shear stress

Allowable shear stress unit

Bending service factor

Torsional service factor

Hollow diameter ratio

Existing diameter

Existing diameter unit

Power

Power unit

Rotational speed

Rotational speed unit

Length output unit

Stress output unit

Result section

warningcombined-von-mises

Required solid shaft diameter

48.2443 mm

Secondary results

Required solid diameter: 48.2443 mm
Required hollow outer diameter: 50.5289 mm
Required hollow inner diameter: 30.3173 mm
Bending stress: 90.7115 MPa
Torsional shear stress: 45.3557 MPa
Von Mises equivalent stress: 120 MPa
Tresca equivalent stress: 128.285 MPa
Factor relative to entered allowable: 1
Polar second moment of area: 5.31843e-7 m^4
Area moment of inertia: 2.65922e-7 m^4

Unit conversion summary

Unit-normalization summary: 1,000 N*m; 1,000 N*m; 1.20000e+8 Pa

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.
These calculations are preliminary scalar mechanics checks and do not certify design adequacy.
No keyways, shoulders, fatigue, bearing reactions, deflection, critical speed, or code compliance are evaluated.

Assumptions

Static elastic circular shaft behavior.
Entered service factors are user multipliers and are not code-approved values.

Calculation steps

Apply service factors1,000 N*m, 1,000 N*m
Resolve shaft sectionSolid circular shaft
Calculate stresses9.07115e+7 Pa, 4.53557e+7 Pa
Calculate equivalent stress1.20000e+8 Pa

Circular shaft bending and torsion

sigma_v=sqrt(sigma_b^2+3 tau_t^2); sigma_T=sqrt(sigma_b^2+4 tau_t^2)

sigma_b = 32M/(pi d^3), tau_t = 16T/(pi d^3), with hollow-shaft ratio correction where selected.

Mdesign = 1,000 N*m x 1

Tdesign = 1,000 N*m x 1

Technical visual

Engineering interpretation

Use this as a preliminary circular-shaft sizing check. Fatigue, stress concentrations, and bearing support details often govern real shafts.

What is the shaft design calculator?

This calculator performs preliminary elastic circular-shaft sizing and checking for torque, bending moment, or combined bending and torsion. It reports bending stress, torsional shear stress, Von Mises stress, Tresca stress, and controlling geometry.

How to use the shaft design calculator

Choose the shaft design mode that matches the hand calculation you want to perform.
Enter geometry, loads, material values, and units from a consistent source.
Review the primary result, secondary values, formula substitution, assumptions, and warnings.
Use the related-tool links only as a workflow aid; verify every transferred value before design use.

Input explanations

Choose solid or hollow shaft geometry and enter either required sizing data or existing dimensions.
Use service factors only as user-entered load multipliers; they are not code-approved values.
Combined modes calculate equivalent stress from service-adjusted bending moment and torque.
Power-speed mode derives torque exactly from SI power and angular speed.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.

Notation

Formula notation
Symbol	Meaning	Unit
M	Bending moment	N*m
T	Torque	N*m
sigma_b	Extreme-fiber bending stress	Pa
tau_t	Torsional shear stress	Pa
sigma_v	Von Mises equivalent stress	Pa

Worked examples

Torque-only sizing for 1000 N*m and 50 MPa allowable shear gives the same solid diameter as the torsion calculator.

Bending-only sizing with M = 1000 N*m and 100 MPa normal stress gives a solid diameter of about 0.0467 m.

Combined bending and torsion reports both Von Mises and Tresca equivalent stresses for the same entered loads.

Cross-tool workflow

The shaft design workflow connects torsion, bending stress, factor of safety, and fatigue review for early machine-element sizing.

Review torsion only Use equivalent stress in Fatigue Life Estimator

Common mistakes

Treating static diameter sizing as a complete shaft design.
Forgetting that a larger hollow ratio increases required outer diameter for the same stress limit.
Using shear allowable stress in a Von Mises equivalent-stress check without converting the design basis.
Ignoring shoulders, keyways, fatigue, bearings, deflection, and critical speed.

Limitations

Preliminary static elastic sizing only.
Circular shafts only.
No keyway, spline, shoulder fillet, fatigue, critical-speed, bearing-reaction, deflection, or code-compliance model.

References

Shigley's Mechanical Engineering Design: Budynas and Nisbett, Shigley's Mechanical Engineering Design.
Roark's Formulas for Stress and Strain: Young, Budynas, and Sadegh, Roark's Formulas for Stress and Strain.
Mechanics of Materials: Common mechanics-of-materials texts covering torsion, beam deflection, column buckling, and elastic stress relationships.
Machinery's Handbook: Machinery's Handbook reference material for machine-element formulas and terminology.

How is shaft diameter calculated?

The calculator solves the closed-form circular-shaft stress equations for the selected load case and criterion.

What is the difference between Von Mises and Tresca?

Von Mises uses distortion-energy equivalent stress, while Tresca uses maximum-shear-stress theory and is often more conservative.

Why use service factors?

Service factors let you apply user-selected load multipliers for preliminary sensitivity checks. They are not standards-approved factors.

Can this compare solid and hollow shafts?

Yes. Hollow sizing uses the entered inner-to-outer diameter ratio and reports outer and inner diameters.

Does this include fatigue?

No. Use the fatigue life estimator for S-N and mean-stress checks.

Does this include shaft deflection?

No. Use beam deflection workflows when deflection or alignment is important.

Can power and speed define torque?

Yes. Power-speed mode converts power and angular speed to torque using exact SI units.

Professional support from ScholarEase Consultancy Services LLP

Professional FEA, simulation setup, solid-mechanics calculations, mechanical-design review, technical documentation, and research support are available through the connected services website. These calculators remain free to use without purchasing services.

Visit ScholarEase

Engineering disclaimer

This tool is intended for educational, estimation, and preliminary engineering use. It does not certify designs or replace applicable codes, standards, validated software, physical testing, or qualified professional engineering judgment.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

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Last reviewed: 2026-06-30

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calculatorbrowser-only

Shaft Design Calculator

Estimate required solid or hollow circular-shaft diameter using torque, bending moment, service factors, and equivalent-stress criteria.

Shaft Design inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation mode

Display precision

Material properties

Material property mode

Material preset

Young's modulus

Young's modulus unit

Shear modulus

Shear modulus unit

Yield strength

Yield strength unit

Ultimate strength

Ultimate strength unit

Generic steel values. Use grade-, standard-, temperature-, and process-specific data for real design.

Shaft loads and sizing

Shaft type

Failure criterion

Bending moment

Bending moment unit

Torque

Torque unit

Allowable equivalent stress

Allowable equivalent stress unit

Allowable shear stress

Allowable shear stress unit

Bending service factor

Torsional service factor

Hollow diameter ratio

Existing diameter

Existing diameter unit

Power

Power unit

Rotational speed

Rotational speed unit

Length output unit

Stress output unit

Result section

warningcombined-von-mises

Required solid shaft diameter

48.2443 mm

Secondary results

Required solid diameter: 48.2443 mm
Required hollow outer diameter: 50.5289 mm
Required hollow inner diameter: 30.3173 mm
Bending stress: 90.7115 MPa
Torsional shear stress: 45.3557 MPa
Von Mises equivalent stress: 120 MPa
Tresca equivalent stress: 128.285 MPa
Factor relative to entered allowable: 1
Polar second moment of area: 5.31843e-7 m^4
Area moment of inertia: 2.65922e-7 m^4

Unit conversion summary

Unit-normalization summary: 1,000 N*m; 1,000 N*m; 1.20000e+8 Pa

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.
These calculations are preliminary scalar mechanics checks and do not certify design adequacy.
No keyways, shoulders, fatigue, bearing reactions, deflection, critical speed, or code compliance are evaluated.

Assumptions

Static elastic circular shaft behavior.
Entered service factors are user multipliers and are not code-approved values.

Calculation steps

Apply service factors1,000 N*m, 1,000 N*m
Resolve shaft sectionSolid circular shaft
Calculate stresses9.07115e+7 Pa, 4.53557e+7 Pa
Calculate equivalent stress1.20000e+8 Pa

Circular shaft bending and torsion

sigma_v=sqrt(sigma_b^2+3 tau_t^2); sigma_T=sqrt(sigma_b^2+4 tau_t^2)

sigma_b = 32M/(pi d^3), tau_t = 16T/(pi d^3), with hollow-shaft ratio correction where selected.

Mdesign = 1,000 N*m x 1

Tdesign = 1,000 N*m x 1

Technical visual

Engineering interpretation

Use this as a preliminary circular-shaft sizing check. Fatigue, stress concentrations, and bearing support details often govern real shafts.

What is the shaft design calculator?

How to use the shaft design calculator

Choose the shaft design mode that matches the hand calculation you want to perform.
Enter geometry, loads, material values, and units from a consistent source.
Review the primary result, secondary values, formula substitution, assumptions, and warnings.
Use the related-tool links only as a workflow aid; verify every transferred value before design use.

Input explanations

Choose solid or hollow shaft geometry and enter either required sizing data or existing dimensions.
Use service factors only as user-entered load multipliers; they are not code-approved values.
Combined modes calculate equivalent stress from service-adjusted bending moment and torque.
Power-speed mode derives torque exactly from SI power and angular speed.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.

Notation

Formula notation
Symbol	Meaning	Unit
M	Bending moment	N*m
T	Torque	N*m
sigma_b	Extreme-fiber bending stress	Pa
tau_t	Torsional shear stress	Pa
sigma_v	Von Mises equivalent stress	Pa

Worked examples

Torque-only sizing for 1000 N*m and 50 MPa allowable shear gives the same solid diameter as the torsion calculator.

Bending-only sizing with M = 1000 N*m and 100 MPa normal stress gives a solid diameter of about 0.0467 m.

Combined bending and torsion reports both Von Mises and Tresca equivalent stresses for the same entered loads.

Cross-tool workflow

The shaft design workflow connects torsion, bending stress, factor of safety, and fatigue review for early machine-element sizing.

Review torsion only Use equivalent stress in Fatigue Life Estimator

Common mistakes

Treating static diameter sizing as a complete shaft design.
Forgetting that a larger hollow ratio increases required outer diameter for the same stress limit.
Using shear allowable stress in a Von Mises equivalent-stress check without converting the design basis.
Ignoring shoulders, keyways, fatigue, bearings, deflection, and critical speed.

Limitations

Preliminary static elastic sizing only.
Circular shafts only.
No keyway, spline, shoulder fillet, fatigue, critical-speed, bearing-reaction, deflection, or code-compliance model.

References

Shigley's Mechanical Engineering Design: Budynas and Nisbett, Shigley's Mechanical Engineering Design.
Roark's Formulas for Stress and Strain: Young, Budynas, and Sadegh, Roark's Formulas for Stress and Strain.
Mechanics of Materials: Common mechanics-of-materials texts covering torsion, beam deflection, column buckling, and elastic stress relationships.
Machinery's Handbook: Machinery's Handbook reference material for machine-element formulas and terminology.

How is shaft diameter calculated?

The calculator solves the closed-form circular-shaft stress equations for the selected load case and criterion.

What is the difference between Von Mises and Tresca?

Von Mises uses distortion-energy equivalent stress, while Tresca uses maximum-shear-stress theory and is often more conservative.

Why use service factors?

Service factors let you apply user-selected load multipliers for preliminary sensitivity checks. They are not standards-approved factors.

Can this compare solid and hollow shafts?

Yes. Hollow sizing uses the entered inner-to-outer diameter ratio and reports outer and inner diameters.

Does this include fatigue?

No. Use the fatigue life estimator for S-N and mean-stress checks.

Does this include shaft deflection?

No. Use beam deflection workflows when deflection or alignment is important.

Can power and speed define torque?

Yes. Power-speed mode converts power and angular speed to torque using exact SI units.

Professional support from ScholarEase Consultancy Services LLP

Visit ScholarEase

Engineering disclaimer

Need Professional Support?

Visit ScholarEase

Last reviewed: 2026-06-30

Shaft Design inputs

Calculation mode

Material properties

Shaft loads and sizing

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Circular shaft bending and torsion

Technical visual

Engineering interpretation

What is the shaft design calculator?

How to use the shaft design calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?

Shaft Design inputs

Calculation mode

Material properties

Shaft loads and sizing

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Circular shaft bending and torsion

Technical visual

Engineering interpretation

What is the shaft design calculator?

How to use the shaft design calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?