Shaft Diameter Formula and Method
A power-transmission shaft — the rotating rod inside a motor, gearbox, pump, or conveyor drive — is sized so it can carry its twisting load without exceeding a safe shear stress. This calculator finds the minimum diameter for a solid, circular steel shaft subjected to pure torsion: it converts your transmitted power and rotational speed into a design torque, then solves the torsion formula for the diameter that keeps the shaft's shear stress at or below your chosen allowable value.
Deriving the diameter formula
Power transmitted by a rotating shaft is P = T·ω, where ω is the angular speed in radians per second. Since ω = 2πN/60 for a speed N in revolutions per minute, the torque is T = 60P / (2πN) — commonly written T = 9549·P(kW)/N(rpm) in newton-meters. For a solid circular shaft, mechanics of materials gives the maximum shear stress at the outer surface as τ = T·c/J, where c = d/2 is the outer radius and J = πd⁴/32 is the polar moment of inertia. Substituting gives the classic torsion formula τ = 16T / (πd³). Setting τ equal to the allowable shear stress τallow and solving for d yields d = (16T / (π·τallow))^(1/3), the minimum diameter that keeps the shaft below that stress.
Choosing an allowable shear stress
The allowable stress you enter should already include a safety margin, not just the raw material strength. General-purpose carbon steel shafting is commonly designed to 40-60 MPa (about 5,800-8,700 psi); higher-strength alloy steels or lower safety factors can justify larger values, while shock loads, fatigue, or keyways call for lower ones. Formal codes such as ASME B106.1M set the allowable stress as the smaller of a fraction of the yield strength and a fraction of the ultimate tensile strength, then reduce it further (commonly by 25%) where a keyway is present.
Limits of a torsion-only calculation
This calculator sizes a shaft for torque alone. Most real shafts also carry bending moments from gears, pulleys, belts, or their own weight, and combined bending-torsion loading requires a different equation (for example, the ASME code method or the distortion-energy/maximum-shear-stress approaches in references like Shigley's Mechanical Engineering Design). Treat the diameter here as a torsion-only lower bound: verify bending stresses separately, add the keyway allowance shown in the practical diameter result, and round up to a stocked shaft size before finalizing a design.
Frequently Asked Questions
What formula does this shaft size calculator use?
What allowable shear stress should I use for a steel shaft?
Does this calculator account for bending loads or keyways?
Why does the calculator show a rounded-up "practical diameter"?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
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| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |