Tangent (tan) calculator
Calculate the tangent of an angle in degrees or radians, with an explained result and worked examples.
Enter your values, then calculate.
Your calculation stays in your browser.
The formula, explained
tan(x)Tangent gives a dimensionless ratio. It is undefined at 90° + 180° × k, or π/2 + π × k radians, for any integer k.
Source and reference : NIST DLMF ↗
An example to check
Using the starting values below, the calculation gives:
What your result means — tan(30°) ≈ 0.57735027. The answer is a dimensionless ratio, not an angle.
For an acute angle in a right triangle, tan(θ) = opposite ÷ adjacent. Check whether your input is in degrees or radians. Tangent is undefined at odd multiples of 90° (π/2 radians).
How to use this tool
- Enter the angle as a decimal number.
- Select the matching input unit. 30 degrees and 30 radians are different angles.
- Read the tangent ratio. The answer has no angle unit; use the inverse calculator when you need an angle.
A worked example
tan(45°) = 1. The same angle is π/4 ≈ 0.785398 radians.
How do I enter an angle written with π?
These fields accept decimal numbers. For π/6 radians, enter approximately 0.523599 and select Radians, or enter 30 and select Degrees.
What does this ratio mean in a right triangle?
For an acute angle θ, tan(θ) = opposite ÷ adjacent. Label the sides relative to the angle you are using.
Why is tangent undefined at 90°?
tan(θ) = sin(θ) ÷ cos(θ). At 90° and odd multiples of 90°, cosine is zero. Close to these angles, tiny input changes can cause very large outputs.
Can I use a decimal comma?
Yes. Numeric fields accept 12.5 or 12,5 and spaces for thousands, such as 1 234.50. Do not mix a point and comma in one number.
Where are my inputs processed?
Calculations run in your browser. Form values are not sent to Analytics. Copying, printing, sharing or opening an external service is your choice.
Method and interface checked on 2026-10-15 · Report an error