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Cotangent Calculator

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

Reviewed by Christopher FloiedPublished Updated

This free online cotangent 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

cot(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 Cotangent 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 Cotangent 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.

When to Use This Calculator

  • •Use the Cotangent 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

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

Secant Calculator

Calculate the secant of any angle. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).

Tangent Calculator

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

Unit Circle Calculator

Find the sine, cosine, and tangent values for any angle on the unit circle.

Arc Length Calculator

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

Arccos Calculator (Inverse Cosine)

Calculate the inverse cosine (arccos) of a value. Returns the angle whose cosine equals the input.

About Cotangent Calculator

The cotangent function is the reciprocal of the tangent function: cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). In a right triangle, it equals the ratio of the adjacent side to the opposite side. Like tangent, cotangent is unbounded and has a period of 180° (π radians). It is undefined at 0° and 180° where sin(θ) = 0. The cotangent function appears less frequently in elementary applications than sine, cosine, or tangent, but it is important in advanced mathematics, physics, and engineering. It appears in the formulas for the area of a regular polygon: A = ¼ns² cot(π/n), where n is the number of sides and s is the side length. In complex analysis, the cotangent function has simple poles at every multiple of π and appears in the partial fraction expansion of π cot(πz). This calculator computes cotangent for any angle.

The Math Behind It

The cotangent function cot(θ) = cos(θ)/sin(θ) has vertical asymptotes at θ = nπ for any integer n, where sin(θ) = 0. Its derivative is d/dx cot(x) = −csc²(x), and the integral is ∫ cot(x) dx = ln|sin(x)| + C. The Pythagorean identity for cotangent is 1 + cot²(θ) = csc²(θ). The cotangent addition formula is cot(A + B) = (cot A cot B − 1)/(cot A + cot B). In the context of regular polygons, the area A = ¼ns² cot(π/n) and the apothem a = (s/2) cot(π/n). As n → ∞, this approaches the circle area πr². The Laurent series of cot(x) near x = 0 is cot(x) = 1/x − x/3 − x³/45 − 2x⁵/945 − .... The partial fraction expansion π cot(πz) = 1/z + Σ(1/(z−n) + 1/n) for n ≠ 0 is fundamental in complex analysis and leads to many important series identities, including ζ(2) = π²/6.

Formula Reference

Cotangent Function

cot(θ) = cos(θ) / sin(θ) = 1 / tan(θ)

Variables: θ = angle

Worked Examples

Example 1: Regular polygon area

Find the area of a regular hexagon with side 4 using cot formula.

Step 1:A = ¼ × 6 × 4² × cot(π/6)
Step 2:cot(π/6) = cot(30°) = cos(30°)/sin(30°) = (√3/2)/(1/2) = √3
Step 3:A = ¼ × 6 × 16 × √3 = 24√3

A ≈ 41.57 square units

Common Mistakes & Tips

  • !Trying to compute cot(0°) or cot(180°) — they are undefined.
  • !Confusing cotangent with arctan (inverse tangent).
  • !Forgetting that cot has period 180°, just like tangent.

Related Concepts

Tangent Calculator

cot(θ) = 1/tan(θ).

Secant Calculator

Another reciprocal trig function: sec(θ) = 1/cos(θ).

Used in These Calculators

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

Secant Calculator

Tangent Calculator

Frequently Asked Questions

Is cotangent the same as inverse tangent?

No. Cotangent is the reciprocal of tangent (1/tan), while inverse tangent (arctan) finds the angle given a tangent value. They are completely different functions.

When is cotangent equal to zero?

cot(θ) = 0 when cos(θ) = 0, which occurs at 90° and 270° (and their multiples with ±360°).

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