The tangent of an angle is the ratio of the opposite side to the adjacent side – the slope of a line making angle α with the x-axis. It is used for heights and distances, road grades, ramp angles and in navigation.
How to use the Tangent Calculator
- Angle unit
- Angle α
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the angle and pick its unit. The angle is converted to radians and tan is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.
Formula
tan α = opposite / adjacent = sin α / cos α
Range: all real numbers · Domain: α ≠ 90° + k·180° · Period: π (180°)
Worked example
Inputs — Angle unit: Degrees (°); Angle α: 30.
Results — tan(α) = √3/3 ≈ 0.5773502692; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; csc(α) = 2; sec(α) = 1.154700538; cot(α) = 1.732050808.
Key terms
- Tangent
- tan α = opposite / adjacent = sin α / cos α.
- Exact value
- A value written with integers and square roots instead of decimals.
Frequently asked questions
Why is tan 90° undefined?
cos 90° = 0, and tangent divides by cosine.
What is tan 45°?
Exactly 1 – the opposite and adjacent sides are equal.
What is the period of tangent?
180° (π radians), half that of sine and cosine.
How is tangent related to slope?
The slope of a line equals the tangent of its angle with the x-axis.