Enter the shear stress and normal stress into the calculator to determine the angle of internal friction.

Angle Of Internal Friction Calculator

Basic (τ = σ·tanφ)
Cohesive (τ = c + σ·tanφ)
Friction Coefficient (μ = tanφ)

Enter any 2 values to calculate the missing variable

Related Calculators

Angle of Internal Friction Formula

The following formula is used to calculate the angle of internal friction for a given shear stress and normal stress. 

τ = σ * tan(φ)

Variables:

  • Ï„ is the shear stress
  • σ is the normal stress
  • φ is the angle of internal friction in degrees

To calculate the angle of internal friction, divide the shear stress by the normal stress and then take the arctangent of the result. Convert the result from radians to degrees.

What is the Angle of Internal Friction?

The angle of internal friction, also known as the friction angle, is a measure of the shear strength of soils and other granular materials. It represents the angle at which the material begins to fail due to shear stress. This angle is crucial in geotechnical engineering for designing foundations, slopes, and retaining structures. The angle of internal friction is determined through laboratory tests such as the direct shear test or triaxial test and is influenced by factors such as soil type, density, and moisture content.

How to Calculate the Angle of Internal Friction?

The following steps outline how to calculate the Angle of Internal Friction.

  1. First, determine the shear stress (Ï„).
  2. Next, determine the normal stress (σ).
  3. Next, calculate the tangent of the angle of internal friction using the formula tan(φ) = τ / σ.
  4. Finally, calculate the angle of internal friction (φ) by taking the arctangent of the result and converting it to degrees.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Shear Stress (Ï„) = 50 kPa

Normal Stress (σ) = 100 kPa