CE Calculators > Stress Transformation > Maximum and Minimum Principal Stress

Maximum and Minimum Principal Stress Calculator

Maximum and Minimum Principal Stresses
principal stresses

This calculator is for finding maximum and minimum in-plane principal stressess(σp1 and σp2) and the angle of orientation (θp1 and θp2) of the principal planes.
Sign Convention: If the outward normal to a plane is acting in the positive direction it is termed as positive face otherwise it is negative face. Normal stresses acting in the positive direction on the positive face or in the negative direction on a negative face are taken as positive whereas the normal stresses acting in the negative direction on a positive face or in the positive direction on a negative face are taken as negative. Shear stress is taken as positive if it acts in the positive coordinate direction on a positive face, or it acts in negative coordinate direction on negative face. Otherwise it is negative. Angle of orientation (θ) is -ve for clock-wise and +ve for anti-clockwise rotation with reference to the positive x-axis.
The angles of principal planes are at right angles to each other.

By default this calculator is using the units of stress as MPa, but other units N/mm2, kN/m2, ksi, psi etc. can also be used without affecting the results.

This calculator can also be used for principal strains because the equations are same in that case also, just by ignoring the units as strains are dimensionless.

Please refer to the figure and enter the required values in the form given below and then click "Calculate".

INPUT VALUES
Normal Stress σx (MPa):
Normal Stress σy (MPa):
Shear Stress τxy (MPa):

Please make sure that
all the values are entered

OUTPUT RESULTS
Principal Stress σp1 (MPa):
Angle θp1 (degree):
Principal Stress σp2 (MPa):
Angle θp2 (degree):

The following Principal Stress Equations are used in this calculator

stress transformation equations

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