Calculate Angle Pairs
Calculator for angle pairs in degrees and radiant. Angle pairs are two angles that are in relation to each other. Here those angles can be calculated in degrees and in radiant as rad or as multiples of π. Please enter one angle into the according field, all the other angles will be calculated. Normalize brings the angles to values between 0° and 360°, respectively between 0 and 2π.
Angle pairs example with α=32°
α: angle
β: complementary angle, expands α to a right angle, if α<90°. β = 90° − α
γL: left perpendicular angle, γL = α + 90°
γR: right perpendicular angll, γR = α − 90°
δ: supplementary angle, expands α to a straight line, if α<180°. δ = 180° − α
ε: opposite angle, points in the opposite direction. ε = α + 180°
ζ: explementary angle, brings α back to 360°, which is 0, if α<360°. ζ = 360° − α
The complement angle derives from the Latin complementum. Two angles are complementary if they add up to a right angle. This relationship plays a particularly important role in trigonometry.
Perpendicular angles are formed by a 90-degree rotation. They are orthogonal to the original direction and are distinguished here as left and right perpendicular angles to clearly define the direction of rotation.
The supplementary angle comes from the Latin supplementum (addition). Two angles are supplementary if they together form a straight angle, i.e., 180 degrees. Such pairs of angles frequently occur on straight lines or as supplementary angles.
The opposite angle corresponds to a half rotation around the vertex. It points in the opposite direction.
The explementary angle completes the full rotation. It adds the original angle to a full angle of 360 degrees, thus returning to the original direction.