Tan Calculator
Calculate the tangent of any angle in degrees or radians, with pole detection.
About Tan Calculator
The tangent function returns the ratio of the opposite side to the adjacent side (equivalently sin/cos). It is undefined at 90° + k·180° where cos = 0. This calculator detects those poles and returns a descriptive message rather than an error value.
Formula
Tangent definition
tan θ = sin θ / cos θ = opposite / adjacent
- θ
- The angle
- opposite
- Side opposite to θ
- adjacent
- Side adjacent to θ
Worked example
With the default values below, Tan Calculator returns tan(θ) of 1.0000000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Angle (θ)
- 45
- Angle unitone of Degrees, Radians
- Degrees
Results
- tan(θ)
- 1.0000000000
- Angle (degrees)
- 45.000000 °
- Angle (radians)
- 0.78539816
Step by step
- 1Convert to radians
- 2Check for poles= No singularity detected
- 3Apply tan function= 1
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At 90°, cos = 0, so we divide by zero. The function has vertical asymptotes at all odd multiples of 90°.
What is tan(45°)?
tan(45°) = 1, because sin(45°) = cos(45°) ≈ 0.7071, and their ratio is exactly 1.