ONE FORMULA, ONE ANSWER
Circular Shaft Twist Angle Calculator
Check twist between the ends of a uniform circular shaft. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
End-to-end twist angle φ
Enter values and select Calculate.
φ = T L / (G J)
Assumptions
Use L,G,J>0. Assume a uniform circular shaft, constant torque and linear elasticity. J is a polar area moment, not a mass moment in kg·m². Degrees and radians display the same angle.
Displayed values are floating-point approximations. Measurement uncertainty and design safety factors are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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