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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 Chase FloiedUpdated

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.

Formula Reference

Cotangent 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 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.

About This Calculator

The Cotangent Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the cotangent of any angle. Cotangent is the reciprocal of tangent: cot(θ) = cos(θ)/sin(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 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°).