Calculator
Formula Used
Angle of twist: θ = (T × L) / (J × G)
Solid shaft polar moment: J = πd4 / 32
Hollow shaft polar moment: J = π(Do4 - Di4) / 32
Maximum shear stress: τmax = T r / J
Torsional stiffness: k = T / θ
This calculator assumes a straight circular shaft and elastic behavior.
How to Use This Calculator
- Select solid or hollow shaft.
- Enter the applied torque and choose its unit.
- Enter shaft length and pick the correct unit.
- Enter shear modulus for the shaft material.
- Enter the shaft diameter. Add inner diameter for hollow shafts.
- Click Calculate Angle to see twist, stiffness, stress, and section properties.
- Use the CSV or PDF buttons to save the current result.
Example Data Table
| Case | Shaft Type | Torque | Length | Size | G | Angle (deg) |
|---|---|---|---|---|---|---|
| 1 | Solid | 120 N·m | 1.2 m | 35 mm | 79 GPa | 0.708902 |
| 2 | Solid | 350 N·m | 2.0 m | 50 mm | 80 GPa | 0.817054 |
| 3 | Hollow | 500 N·m | 1.8 m | 60 mm / 30 mm | 77 GPa | 0.561433 |
Article
About This Calculator
This calculator estimates the angle of twist in a shaft under torque. It works for solid and hollow circular shafts. You enter torque, length, shaft size, and shear modulus. The tool then returns angular rotation, polar moment, torsional stiffness, and maximum shear stress. These values help in design checks and quick comparisons. The layout stays simple and practical.
Why Angle of Twist Matters
A shaft can carry torque and still fail a service limit. Too much twist can misalign gears, couplings, and driven parts. It can also reduce control accuracy in rotating systems. Designers often check twist before finalizing diameter and material. This is important in machine shafts, drive lines, mixers, tools, and test rigs. A small change in diameter can greatly reduce rotation because polar inertia depends on the fourth power of diameter.
What The Tool Gives You
The main output is angle of twist in radians and degrees. The calculator also reports polar moment of inertia. That value shows how the section resists torsion. Maximum shear stress is included for a quick strength review. Torsional stiffness is also shown. A higher stiffness means less angular movement for the same torque. Twist per unit length is useful when comparing shafts with different spans.
Useful Design Insight
Keep units consistent. This page converts common engineering units before calculation. Solid shafts use one diameter. Hollow shafts use outer and inner diameters. A larger outer diameter usually improves stiffness quickly. A higher shear modulus also reduces twist. Longer shafts rotate more under the same load. Higher torque increases twist in direct proportion. These simple trends help when screening options early.
When To Use It
Use this calculator during concept design, homework checks, maintenance review, or shop floor planning. It is suitable for straight circular shafts with elastic behavior. It is not intended for noncircular sections, plastic deformation, or dynamic vibration studies. For detailed design, also verify fatigue, stress concentrations, keyways, supports, and allowable deflection limits.
Practical Reading
Read results together. Low stress does not always mean low twist. Serviceability and strength are different checks. If twist is too high, increase diameter, shorten length, reduce torque, or select a material with higher shear modulus. Compare several options before choosing one.
FAQs
1. What does this calculator find?
It finds the shaft angle of twist from applied torque, shaft length, geometry, and shear modulus. It also reports polar moment, stiffness, and maximum shear stress.
2. Which shafts are supported?
It supports straight circular solid shafts and straight circular hollow shafts. Noncircular sections are not included in this version.
3. Why does diameter change the result so much?
Diameter strongly affects polar moment of inertia. Because the diameter term is raised to the fourth power, even a small increase can sharply reduce twist.
4. What unit system can I use?
You can mix the provided torque, length, diameter, and modulus units. The page converts them internally before calculation.
5. What is shear modulus?
Shear modulus measures how resistant a material is to shear deformation. A larger value means less twist under the same loading and geometry.
6. Does this calculator include plastic deformation?
No. It assumes elastic behavior. If the shaft yields, this simple torsion relation is no longer enough for accurate design.
7. Can I download the result?
Yes. After calculation, you can download the shown result as a CSV file or as a simple PDF report.
8. Is low stress enough for a safe shaft?
Not always. A shaft can have acceptable stress but still twist too much for service requirements. Check both strength and allowable rotation.