Shaft Torque, Power and Shear Stress Calculator
Given power and speed, this calculator returns shaft torque, the torsional shear stress in a solid round shaft of a given diameter, the angle of twist, and the smallest diameter that stays under an allowable stress. It is a quick first pass for motor, gearbox and conveyor shafts.
Your numbers
Conservative values of 40 to 55 MPa are common for keyed commercial steel shafts. Use your design code for the actual limit.
Steel is about 79 GPa, aluminum about 26 GPa.
Your results
Pure torsion of a solid round shaft. Bending, axial load, keyways, stress concentration, fatigue and critical speed are not included and often govern the real design.
Shear stress vs shaft diameter
Sweeps Shaft diameter (solid) from 20 to 80, holding your other inputs fixed.
Automate engineering checks
Optional: a short review of how design calculations could be tied to your ERP engineering change and quoting process.
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How to use the calculator
Enter transmitted power and shaft speed. Choose a service factor that reflects how rough the load is, such as 1.5 for a conveyor with moderate shock. Enter the shaft diameter and length you are considering, plus the allowable shear stress from your design code and the shear modulus of the material. The result shows design torque, actual stress, margin, the minimum diameter and the twist, so you can quickly choose the next standard shaft size.
Formulas and units
Torque in N.m equals 9549.3 times power in kW divided by speed in rpm (in US units, hp x 5252 / rpm gives lb-ft). Torsional shear stress in a solid round shaft is tau = 16 T / (pi d^3), with T in N.mm and d in mm giving MPa. The angle of twist is theta = T L / (J G), where J = pi d^4 / 32. Minimum diameter follows by rearranging the stress formula for d with the allowable stress.
- Design torque equals nominal torque times service factor
- 1 hp = 0.7457 kW
- Hollow shafts need the polar moment J = pi (D^4 - d^4) / 32
Reading the result
At 15 kW and 1450 rpm the nominal torque is about 98.8 N.m, or 148 N.m with a 1.5 service factor. A 40 mm shaft sees roughly 11.8 MPa, which is well below a 40 MPa allowable, so the minimum solid diameter is only about 27 mm. In practice keyways, bending from belt or gear loads and fatigue push shafts well above this minimum, so use the number as a lower bound, not a final size.
Common mistakes
Mixing N.m and N.mm is the most frequent unit error and gives results off by a factor of 1000. Another is applying a torsion-only formula to a shaft that also carries belt pull or gear separating forces, which need a combined bending and torsion check. Starting torque of a motor can be 2 to 3 times rated torque, so check peak torque too, not just rated power.
Frequently Asked Questions
How do I convert kW and rpm to torque?
Torque in N.m equals 9549.3 multiplied by power in kW and divided by speed in rpm. For example 15 kW at 1450 rpm is about 98.8 N.m. In US units, torque in lb-ft equals horsepower times 5252 divided by rpm.
What is the formula for shear stress in a solid shaft?
Maximum torsional shear stress is 16 T divided by pi d cubed for a solid round shaft, where T is torque and d is the diameter. Using T in N.mm and d in mm gives stress directly in MPa.
What service factor should I use?
Use 1.0 for smooth uniform loads such as a lightly loaded fan, around 1.5 for moderate shock such as conveyors or mixers, and 2.0 or more for heavy shock such as crushers or presses. Your driven equipment maker or standard will give recommended values.
Does this replace a full shaft design check?
No. It covers torsion of a plain round shaft only. A full design includes bending, keyways, shoulders, fatigue per a standard such as ASME B106.1M or machine design texts, deflection at bearings and critical speed.
If shaft sizing data and drive specifications need to flow into your ERP item and routing records, Netray can help automate that integration.
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