Skip to main content
math

Tangent Calculator

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

By Christopher FloiedPublished Updated

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. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.

2

Review your inputs

Double-check that all values are correct and match the units or format shown 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 computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — 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.

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.

Related Calculators

Arc Length Calculator

Calculate the length of a circular arc given the radius and central angle in degrees.

Arctan Calculator (Inverse Tangent)

Calculate the inverse tangent (arctan) of a value. Returns the angle whose tangent equals the input.

Complementary Angles Calculator

Find the complement of an angle (90 minus the given angle). Complementary angles sum to 90 degrees and appear in right triangles, architecture, optics, and navigation. Enter any angle between 0 and 90 degrees to find its complement instantly.

Cosine Calculator

Calculate the cosine of any angle in degrees or radians. Returns values between -1 and 1.

Cotangent Calculator

Calculate the cotangent of any angle. Cotangent is the reciprocal of tangent: cot(θ) = cos(θ)/sin(θ).

Coterminal Angle Calculator

Find the positive and negative coterminal angles of a given angle by adding or subtracting 360 degrees. Coterminal angles share the same terminal side in standard position, essential for trigonometry, unit circle problems, and rotational mechanics.

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.

Add the live Tangent Calculator to your site. Free to embed, with a link back to MegaCalc.