ONE FORMULA, ONE ANSWER
Critical Sliding Incline Angle Calculator
Calculate the onset-of-sliding incline angle in a Coulomb friction model. 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
Critical sliding incline angle θ
Enter values and select Calculate.
θ = atan(μ_s)
Assumptions
Required: μ_s≥0 and quasistatic onset of sliding on an incline. Excluded: cohesion, rolling, tipping and vibration. This is not an automatic prediction of a granular pile angle of repose.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions 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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