Tangent Calculator
Compute the tangent of an angle. Undefined at 90° (π/2) shows a clear message.
Calculator
Use the Tangent Calculator
Result
—
Formula
tan(θ) = sin(θ) ÷ cos(θ)
Step-by-step
- 1
Enter the angle
Any numeric value.
- 2
Pick the unit
Degrees or radians.
Worked example
Example input: angle: 45, mode: deg
Result: 1
Related tools
- Sine Calculator
sin(θ).
- Cosine Calculator
cos(θ).
Frequently asked questions
What is tan of 45 degrees?
Exactly 1. In a 45-45-90 triangle the two legs are equal, so opposite ÷ adjacent = 1. It also works as a mental checkpoint: angles under 45° give tangents below 1, angles over 45° give tangents above 1.
Why is tangent undefined at 90 degrees?
Tangent is sine over cosine, and cos(90°) = 0 — dividing by zero has no value. The calculator returns an empty result for those angles instead of a number; values just before them, like tan(89.9°) ≈ 573, are enormous.
How does tangent connect to slope?
The tangent of the angle a ramp makes with the horizontal is its slope: tan(30°) ≈ 0.577 means a 30° incline rises 0.577 units for every 1 unit across. Converting a slope like 0.577 back gives 30° through the inverse tangent.