Shaft Diameter Calculator for Engineering

Inputs

Enter your values and calculate diameter

Calculation scenario

Select what you know: torque, power, or combined loading.

Shaft type

Hollow shafts use k = di/do in sizing.

Inner/outer ratio (k = di/do)

Typical: 0.4 to 0.7 (must be < 1).

Torque

Used directly for torque and combined modes.

Power

Used with speed to derive torque.

Speed

rpm

Required in power-based sizing.

Bending moment

Used only for combined loading.

Shock factor (Kt)

Applies to torque in combined sizing.

Shock factor (Km)

Applies to bending moment in combined sizing.

Material input mode

Choose direct allowable stress or derive from yield.

Allowable shear stress

Used directly in sizing equations.

Yield strength (Sy)

Used to derive allowable shear stress.

Design safety factor (n)

Higher n yields a larger diameter.

Allowable shear criterion

Choose a conservative or yield-based criterion.

Allowance (added to diameter)

Optional extra margin for machining or fit.

Round up step

Example: 0.5 mm or 1 mm increments.

Reset

Example Data Table

Case	Inputs	Allowable	Result (OD)
Torque only	Torque 500 N·m, solid	τ_allow 55 MPa	≈ 36.1 mm
Power & speed	15 kW, 1200 rpm, solid	τ_allow 60 MPa	≈ 30.6 mm
Combined loading	T 450 N·m, M 300 N·m, Kt 1.5, Km 1.8	Sy 370 MPa, n 2.0 (ASME)	≈ 44.7 mm

Example values are illustrative; your results depend on inputs.

Formula Used

Sizing (torsion-based): τ = 16T / (π d³) for a solid shaft.

Hollow shaft: τ = 16T / (π d_o³ (1 − k⁴)), with k = d_i/d_o.

Combined bending + torsion (ASME): T_e = √((K_tT)² + (K_mM)²). The calculator uses T_e in the torsion sizing equation.

Power mode torque: T = P·60 / (2πN), with P in watts and N in rpm.

How to Use

Select a scenario: torque, power, or combined loading.
Choose solid or hollow, then set k if hollow.
Enter torque, or enter power and rpm for derived torque.
For combined loading, add bending moment and factors Kt, Km.
Pick material mode: allowable shear, or yield plus safety factor.
Optional: add allowance and rounding step, then calculate.

Notes

All computations convert to internal units: N·mm and MPa.
For hollow shafts, a k close to 1 increases required diameter.
Use realistic Kt and Km values for your duty cycle.
Use downloads to attach results to your design records.

Engineering purpose of shaft sizing

This calculator estimates the minimum shaft diameter that keeps shear stress within a chosen allowable limit. It supports three design situations: known torque, torque derived from power and speed, or combined torsion and bending using an equivalent torque method. Results are shown in millimetres and inches, so the output can be matched to stock sizes and bearing fits. The approach is intended for preliminary sizing.

Inputs, units, and typical ranges

Torque and bending moment accept N·m, N·mm, or lbf·in. Power can be entered in kW, W, or horsepower, with speed in rpm. For hollow shafts, the inner to outer ratio k equals di/do; values from 0.40 to 0.70 are common when stiffness is adequate. Shock factors Kt and Km account for starts, stops, and impact; steady duty often uses 1.0 to 1.5, while heavier shock may reach 2.0 or more.

Strength criteria used in the calculations

For a solid round shaft, maximum torsional shear is τ = 16T/(πd³). For hollow geometry, τ = 16T/(πdo³(1−k⁴)). In combined loading, the calculator forms an equivalent torque Te = √((KtT)² + (KmM)²) and sizes the diameter from Te. If yield strength is supplied, allowable shear is derived using either 0.30Sy/n (conservative) or 0.577Sy/n (von Mises), where n is the design safety factor.

Understanding the output and margins

The reported diameter is rounded up after adding an optional allowance for machining, corrosion, or fit. The summary also shows calculated shear, bending stress when applicable, and a von Mises value that helps judge overall yield proximity. When yield mode is used, an estimated factor of safety versus yield is presented for quick screening. If the calculated diameter seems small, revisit load assumptions, duty cycle factors, and material data quality.

Practical checks beyond diameter

After selecting a diameter, confirm deflection and torsional twist against alignment and vibration limits. Verify keyway effects, stress concentrations, and fatigue if the load is fluctuating. Check critical speed for long slender shafts, and validate bearing reactions for the chosen span and loading. For hollow shafts, ensure wall thickness supports manufacturing and buckling considerations. Finally, document the chosen inputs and export a CSV or PDF for design reviews.

FAQs

What allowable shear stress should I use?

If you know a verified allowable shear for your material and heat treatment, enter it directly. Otherwise, use yield mode and select a conservative safety factor that reflects duty, uncertainty, and consequences of failure.

How does hollow ratio k affect the diameter?

As k increases, the term (1−k⁴) shrinks, so the required outer diameter rises for the same torque capacity. Lower k gives thicker walls and higher strength, but more weight and material.

When should I apply Kt and Km factors?

Use Kt and Km when torque or bending varies due to starts, braking, shock loads, or reciprocating effects. For smooth, steady rotation, values near 1.0 are typical; increase them as the service becomes harsher.

Why add allowance and rounding?

Allowance covers practical margins such as machining stock, corrosion, minor overloads, or fit requirements. Rounding helps you choose a manufacturable diameter that matches standard tooling, bar sizes, or preferred design increments.

Does this calculator check fatigue life?

No. It sizes for a stress limit under the selected method. For fluctuating loads, you should perform a fatigue analysis using endurance limits, stress concentration factors, surface finish, and reliability targets.

How should I treat keyways and stress raisers?

Keyways, shoulders, and grooves raise local stresses and reduce fatigue strength. Apply appropriate stress concentration factors, consider fillet radii, and increase diameter if needed. Confirm with detailed geometry-based checks.