Tangent Calculator
Calculate the tangent of any angle in degrees or radians. Get the tan value, its inverse (arctan), the cotangent, and related angle information. The calculator handles undefined values at 90° and 270°.
The tangent function is defined as the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ). For a right triangle, tan(θ) equals the ratio of the opposite side to the adjacent side. Unlike sine and cosine, tangent has no upper or lower bound; its range is all real numbers.
Tangent has a period of 180° (π radians) and is undefined at 90° and 270° (where cosine is zero). It has vertical asymptotes at these angles. Tangent is positive in Quadrants I and III (where sine and cosine have the same sign) and negative in Quadrants II and IV.
The inverse tangent function, arctan(x) or tan⁻¹(x), returns the angle whose tangent is x. Unlike arcsin and arccos, arctan is defined for all real numbers and returns values in (-90°, 90°). The cotangent, cot(θ) = 1/tan(θ) = cos(θ)/sin(θ), is the reciprocal of tangent and is undefined when sin(θ) = 0.