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Provide the angle, and the calculator will readily calculate the tangent values for it, with step-by-step calculations shown.
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The Online Tangent Calculator is a fast and reliable tool used to determine tangent values for any given angle. You can calculate results in degrees, radians, milliradians, or π radians. This trigonometry calculator instantly evaluates tan(α) and provides accurate outputs for academic and professional use.
Along with calculations, you can also explore the tangent formula, calculation steps, properties, graphs, tables, and related trigonometric concepts.
Tangent is one of the primary trigonometric ratios, commonly written as tan. In a right-angled triangle, tangent represents the ratio between the opposite side and the adjacent side of a specific angle. The tangent calculator applies this relationship to compute values quickly.
Tangent can also be defined using sine and cosine:
\[ \tan x = \frac{\sin x}{\cos x} \]
Here, sin(x) denotes the sine function and cos(x) denotes the cosine function.
Using similar tools, cosine values can also be calculated for multiple angle units.
The Law of Tangents establishes a relationship between two sides of a triangle and the tangents of half the sum and difference of their opposite angles. For triangle ABC:
\[ \frac{a - b}{a + b} = \frac{\tan\frac{1}{2}(A - B)}{\tan\frac{1}{2}(A + B)} \]
This rule is helpful in solving oblique triangles and advanced trigonometric problems.
To calculate tangent manually, divide the opposite side length by the adjacent side length:
\[ \tan(\alpha) = \frac{opposite}{adjacent} \]
If opposite = 9 and adjacent = 3:
\[ \tan(\alpha) = \frac{9}{3} = 3 \]
Instead of manual calculation, the Tangent Calculator provides the result instantly.
The table below lists commonly used tangent values between 0° and 180°:
| x (°) | x (rad) | tan(x) |
| 0° | 0 | 0 |
| 30° | π/6 | 0.577350 |
| 45° | π/4 | 1 |
| 60° | π/3 | 1.732051 |
| 90° | π/2 | undefined |
| 120° | 2π/3 | -1.732051 |
| 135° | 3π/4 | -1 |
| 150° | 5π/6 | -0.577350 |
| 180° | π | 0 |
For angles outside this table, the Tangent Calculator computes precise values automatically.
It represents the angle whose tangent value equals 1. On the unit circle, this occurs at 45° (π/4).
Since tan(90°) approaches infinity:
\[ \tan^{-1}(\infty) = 90° = π/2 \]
Yes. On the coordinate plane, tan(θ) equals y/x and also sin(θ)/cos(θ). It represents the slope of a line from the origin.
In calculus, a tangent line touches a curve at one point and has the same slope as the curve at that point.
The Tangent Calculator is a practical tool for evaluating tangent values without manual formulas or memorization. It supports multiple angle units and assists in solving trigonometric and calculus-based problems efficiently.
Wikipedia – Trigonometric Functions
LibreTexts – Law of Tangents
Cliff Notes – Tangent Identities
Other Languages: Turkish, Polish, Indonesian, German, Japanese, Czech, French, Spanish, Italian, Russian.
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