How to Calculate the Torsion Angle

A torsion angle (also known as a dihedral angle) is an angle between two planes. Calculating a torsion angle is relatively straightforward, if you know the normal unit vector of the two planes. A normal unit vector is the measure of a line perpendicular to a plane; in general, the normal unit vector will be a given in these equations. If the normal unit vector is not given, but you know the x, y, and z coordinates of each surface, then you can plug this information into an online calculator (see reference and section two) to get the angle. One of the most common uses for torsion angles is to determine the angles between bonds in a polypeptide.

Things You'll Need

  • Normal unit vector of a plane
  • Normal unit vector of a second plane
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Instructions

    • 1

      Find the normal unit vector of the first plane (denote this is as "A"). Note that the measurement for a normal unit vector varies depending on the shape of the plane and that the calculations for a normal unit vector can be quite complex. In most instance, the normal unit vector is a given. Additionally, there are no units attached to the normal unit vector, thus there will be no units in the torsion angle.

    • 2

      Find the normal unit vector for the second plane (denote this as "B").

    • 3

      Multiply A by B to determine the torsion angle.

    On the Calculator

    • 4

      Plug in the x, y and z coordinates for three different points on surface 1. The x coordinate is where a straight line passes through the surface's vertical axis, the y coordinate is where the line passes through the surface's horizontal axis and the z coordinate is a bit more difficult to visualize, but it's the value when x and y = 0 on the line.

    • 5

      Plug in the x, y and z coordinates for the different points on surface 2.

    • 6

      Press Enter on the calculator. All the calculator needs are these three intercepts from three different lines on the two different planes. This greatly simplifies the overall equation because finding the normal unit vectors, even knowing the three points, is much more complex (it involves multiplying each coordinate by its corresponding angle on the opposite plane, and then dividing through by various square roots of the angles at different dimensions).

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