What the Tangent Function Does
The tangent function (tan) is one of the three core trigonometric functions. In a right triangle it relates an angle to the ratio of the side opposite the angle to the side adjacent to it, which is the same as sin(θ) divided by cos(θ). Enter any angle and this calculator returns tan(θ) the moment you type.
tan(θ) = opposite / adjacent = sin(θ) / cos(θ). Wherever cos(θ) = 0, the tangent is undefined.Key Properties
Unbounded Range
Undefined Points
Periodic
How to Calculate a Tangent
Enter the Angle
Type your angle in the input field. You can enter whole numbers, decimals, π notation such as π/4 or π/3, or a short expression like 2π/3.
Choose DEG or RAD
Select DEG for degrees (the default) or RAD for radians. The input unit updates to match your choice.
Read the Result Instantly
The result updates automatically as you type. Angles like 90° and 270°, where cosine is zero, are reported as undefined (∞).
View Exact & Related Values
For special angles an exact value such as √3 is shown. The reciprocal cot (= 1/tan) appears as a related value, and a collapsible special-angles table is available for reference.
Tangent Calculator Features
Degrees & Radians
Switch between DEG and RAD with one click, including π notation like π/4 and simple expressions.
Exact Special Angles
Shows exact values such as √3/3, 1 and √3 for common angles instead of long decimals.
Handles Undefined Values
Correctly reports undefined results at 90°, 270° and other points where cosine is zero.
Related Cotangent
Displays the reciprocal cot (= 1/tan) alongside the tangent result for quick reference.
Common Tangent Values
| Angle | tan value | Decimal |
|---|---|---|
| tan(0°) | 0 | 0.000 |
| tan(30°) | √3/3 | 0.577 |
| tan(45°) | 1 | 1.000 |
| tan(60°) | √3 | 1.732 |
| tan(90°) | undefined | — |
Tangent Calculator FAQ
Why is tan(90°) undefined?
Because tan(x) = sin(x) / cos(x), and cos(90°) = 0. Division by zero has no value, so tan(90°) is undefined — the calculator shows this as ∞. The same happens at 270° and every odd multiple of 90°.
What is the range of the tangent function?
Unlike sine and cosine, tan(x) is unbounded: it can be any real number from negative infinity to positive infinity.
What is tan(45°)?
tan(45°) = 1. This is because sin(45°) = cos(45°) = √2/2, and dividing them gives exactly 1.
Can I enter a negative angle?
Yes. Tangent is an odd function, so tan(−θ) = −tan(θ). Entering −60°, for example, returns −√3.
How do I enter radians?
Click the RAD button, then enter the value. You can use π notation such as π/4, an expression like 2π/3, or a plain decimal like 0.7854.
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