Tangent Angle Calculator

In trigonometry or geometry, the tangent of an angle (simply denoted as tan) is the length of the side opposite the angle divided by the adjacent side. Note that this only applies to a right-angle triangle. Sounds complicated? Don't worry. Let's look at the image to help explain:

If αα is the angle between bb and cc sides of the triangle, then the tangent of an angle tan(θ)tan(θ) is the ratio between opposite side aa and adjacent side bb.

Another definition states that tangent is the ratio of the sine function and cosine function, so tangent is the sin/cos ratio.

The tangent function is one of the main trigonometric functions. The graph of the tangent function has the peculiarity that it has no definite value at x = -π/2, π/2, -3π/2, 3π/2, 5π/2, etc. (or -90°, 90°, -270°, 270°, 450°, etc.).

Unlike the sine or cosine, the tangent function has a period of ππ, so its values repeat after every π radian.

💡 Test it yourself! Try entering the angle π/2 (or 90° in degrees) into this tangent angle calculator and see what value it gives you.

If you want to find the tangent of a given angle, enter the degree into our tangent angle calculator or follow these steps:

1. Identify the hypotenuse in your triangle. Usually, it is the longest side of the triangle.

2. Measure the two sides between which there is an angle and denote them as aa (opposite) and bb (adjacent), for example, a=21a=21 and b=8b=8.

3. Divide aa by bb – a/b=21/8a/b=21/8 =2.63=2.63. You will get a tangent of an angle.

Once you know how to use the tangent of angle calculator, check out our other trigonometric tools:

• Trigonometry calculator;
• Cosine triangle calculator;
• Trig triangle calculator;
• Sine cosine tangent calculator; and
• Tangent ratio calculator.