Warping Angle is the measure of angular deviation of a quad element from the plane. The quad is divided into two triangles along the diagonal and the angle between the normals of the triangles are measured. The allowed range of value for Warping Angle is from 0 to 90 degrees.

You can calculate Warping Angle from the faces of volume elements. Warping angle is applicable to quad faces only. Hence, you cannot compute warping angle for tet elements. You can compute warping angle for quad elements in sheet and any elements containing quad faces for solid bodies. A pyramid element has only one quad face for computing the warping angle. The worst warping angle of all the quad faces determines the warping angle for hex elements.

Here,

n1 is the normal for Plane-1(1,2,4)

n2 is the normal for Plane-2 (2,3,4)

n3 is the normal for Plane-3 (1,4,3)

n4 is the normal for Plane-4 (1,2,3)

θ₁ is the angle between n1 and n2 for Plane-1 and Plane-2.

θ₂ is the angle between n3 and n4 for Plane-3 and Plane-4.

Warping Angle is calculated as the max(θ₁,θ₂). Warping Angle is measure of how far the two triangles deviate from being coplanar. A warpage angle of 0 denotes the quad is perfectly planar whereas larger angles denote more warping.