Tangent Calculator (tan)

You can use either degrees or radians — just select the appropriate unit before entering your angle. Degrees are more common in everyday geometry, while radians are standard in higher mathematics and calculus. This calculator supports both.

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side: tan(α) = opposite / adjacent. It can also be expressed as the ratio of sine to cosine: tan(α) = sin(α) / cos(α).

In the unit circle context, tangent is defined as y/x, where y is the vertical coordinate and x is the horizontal coordinate of the point on the circle. In a right triangle, it is the opposite side divided by the adjacent side.

The tangent of π/4 radians (45°) is exactly 1. This is because at 45°, the opposite and adjacent sides of the right triangle are equal, so their ratio is 1.

Use the inverse tangent function, written as arctan or tan⁻¹. For example, if tan(α) = 1, then arctan(1) = 45° or π/4 radians. This calculator's inverse tangent section does this conversion automatically.

Yes. The tangent is undefined at 90° (π/2 radians) and 270° (3π/2 radians), and at any odd multiple of 90°. At these angles, the cosine equals zero and division by zero is not defined. The function has vertical asymptotes at these points.

Yes, tangent is a periodic function with a period of 180° (π radians). This means tan(x) = tan(x + 180°) = tan(x + π). Unlike sine and cosine, whose period is 360°, tangent completes a full cycle every 180°.

For common angles like 0°, 30°, 45°, 60°, and 90° you can use known exact values (e.g., tan(30°) = √3/3 ≈ 0.5774, tan(45°) = 1, tan(60°) = √3 ≈ 1.7321). For other angles, a calculator or trigonometric tables are needed.