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Tangent Calculator

Calculate the tangent of any angle in degrees. The tangent is the ratio sin(θ)/cos(θ).

Reviewed by Chase FloiedUpdated

This free online tangent calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Results

tan(θ)

1

Angle (radians)

0.785398 rad

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Tangent Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Tangent Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Tangent Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Tangent Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Tangent Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the tangent of any angle in degrees. The tangent is the ratio sin(θ)/cos(θ). The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Tangent Calculator

The tangent function is the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ). In a right triangle, it equals the ratio of the opposite side to the adjacent side. Unlike sine and cosine, tangent is unbounded — its values range from negative infinity to positive infinity. Tangent has a period of 180° (π radians), half the period of sine and cosine. It is undefined at 90° and 270° where the cosine equals zero. The tangent function is widely used for calculating slopes, angles of elevation and depression, and gradients. In navigation, the tangent of the bearing angle gives the ratio of east-west to north-south displacement. In calculus, tan is important for trigonometric substitution and appears in many integration problems. Key values: tan(0°) = 0, tan(45°) = 1, tan(60°) = √3.

The Math Behind It

The tangent function can be interpreted geometrically as the length of the line segment tangent to the unit circle from the point (1, 0) to the terminal ray of angle θ — which is how it got its name. The Taylor series is tan(x) = x + x³/3 + 2x⁵/15 + 17x⁷/315 + ..., which converges for |x| < π/2. The derivative is d/dx tan(x) = sec²(x) = 1 + tan²(x), leading to the integral ∫ sec²(x) dx = tan(x) + C. The tangent function has vertical asymptotes at x = π/2 + nπ for any integer n. In surveying, the tangent of an angle of elevation multiplied by the horizontal distance gives the height difference. The tangent addition formula is tan(A + B) = (tan A + tan B)/(1 − tan A tan B). The inverse tangent function (arctan) is used to compute angles from slope ratios. The tangent half-angle substitution t = tan(x/2) is a powerful technique for evaluating integrals of rational trigonometric functions.

Formula Reference

Tangent Function

tan(θ) = opposite / adjacent = sin(θ) / cos(θ)

Variables: θ = angle

Worked Examples

Example 1: Building height

From 50 m away, the angle of elevation to a building's top is 32°.

Step 1:tan(32°) = height / 50
Step 2:height = 50 × tan(32°)
Step 3:height = 50 × 0.6249

height ≈ 31.24 meters

Common Mistakes & Tips

  • !Trying to compute tan(90°) — it is undefined (division by zero).
  • !Confusing tangent with cotangent (which is the reciprocal).
  • !Forgetting that tangent has period 180°, not 360°.

Related Concepts

Arctan Calculator

Find the angle from a tangent value.

Cotangent Calculator

The reciprocal of tangent: cot(θ) = 1/tan(θ).

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Arctan Calculator (Inverse Tangent)

Cotangent Calculator

Frequently Asked Questions

Why is tan(90°) undefined?

Because tan(90°) = sin(90°)/cos(90°) = 1/0, which is undefined. Geometrically, the tangent line at 90° is vertical and has infinite slope.

What does a negative tangent value mean?

A negative tangent means the angle is in Q2 (90°–180°) or Q4 (270°–360°), where sine and cosine have opposite signs.