Tangent Calculator

What is Tangent?

Tangent (tan) is one of the three primary trigonometric functions, along with Sine and Cosine. In a right-angled triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Unlike sine and cosine, which are bounded between -1 and 1, the tangent function can take any real value from negative infinity to positive infinity. It represents the slope of the line created by the angle on the unit circle.

Usage Areas

Frequently Used Values

Real-World Examples

How to Use This Tangent Calculator

Enter the angle in degrees or radians. The Tangent Calculator returns tan(θ) and may show solution steps. Tangent is the ratio opposite/adjacent in a right triangle and corresponds to slope. Use it for trigonometry, engineering, and geometry. For angles where cos(θ)=0 (e.g. 90°), tangent is undefined. For the inverse (angle from a ratio), use an arctangent calculator. This tool is for informational and educational use only.

When Tangent Calculations Are Used

Tangent is used for slopes, heights and distances (e.g. building height from an angle), and road grades. In calculus, the derivative of tan is sec². This calculator is for general reference only; for high-stakes applications verify with authoritative sources.

In a right triangle, tan(θ) = opposite / adjacent. The tangent function is periodic with period 180° (π radians) and is undefined at 90° and 270° (where cosine is zero). For the inverse (angle from a ratio), use an arctangent calculator. tan(θ) = sin(θ)/cos(θ). This tool is for informational and educational use only.

Limitations

The calculator assumes angles are in degrees or radians as selected. At 90° and 270° (and equivalent in radians), tangent is undefined; the tool may show an error or infinity. For very large angles, reduce modulo 180° (or π) for the equivalent angle. Floating-point precision may cause small errors. This tool is for informational use only; for critical use verify with your curriculum or authority.

For slope m, the angle of inclination is θ = arctan(m). For height at distance d and angle θ, height = d × tan(θ). Tangent is odd: tan(-θ) = -tan(θ). For hyperbolic tangent (tanh), use a dedicated hyperbolic calculator. This tool computes only the circular tangent of an angle. This tool is for informational and educational use only.

Common values: tan(0°)=0, tan(30°)=1/√3, tan(45°)=1, tan(60°)=√3. The tangent function has vertical asymptotes at 90° and 270° (π/2 and 3π/2 radians). In the unit circle, tan(θ) is the y-coordinate divided by the x-coordinate. For sine and cosine use the dedicated calculators; for the inverse (angle from ratio) use an arctangent tool. This calculator is for informational and educational use only.

In surveying and construction, tangent is used to find heights and distances from angles. In physics, slopes and inclines are often expressed as rise over run, which equals tan(θ) when θ is the angle of inclination. This tool gives the numeric value of tan(θ); for symbolic work or step-by-step solutions use your curriculum or a math package. This tool is for informational and educational use only.

Ensure your angle unit (degrees or radians) matches the calculator setting. For angles near 90° or 270°, tangent becomes very large in magnitude; the result may be displayed as undefined or infinity. This calculator is for informational use only; for professional engineering or academic work verify values with authoritative sources. For sine and cosine use the dedicated calculators. Confirm critical values with your curriculum or authority. This tool is for general reference only.

Disclaimer

This tool is for informational use only. It does not replace professional engineering or academic standards. Confirm critical values with your curriculum or authority.

Other Trigonometry Tools