How to Calculate the Area of a Circle

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Circle Area Calculator

Enter the radius or diameter to calculate the area instantly.

Radius (r) Diameter (d)
Centimeters (cm) Meters (m) Inches (in) Feet (ft)
Calculated Area:
Circumference:

How to Calculate the Area of a Circle

The area of a circle is the amount of space occupied inside the boundary of the circle. Understanding how to calculate this is a fundamental skill in geometry, architecture, and various engineering fields.

The Area Formula

The standard formula to find the area (A) of a circle when you know the radius (r) is:

A = π × r²

Where:

  • A is the total area.
  • π (Pi) is a mathematical constant approximately equal to 3.14159.
  • r is the radius (the distance from the center to the edge).

Calculating with Diameter

If you have the diameter (d) instead of the radius, remember that the diameter is exactly twice the length of the radius (d = 2r). You can use this formula:

A = (π × d²) / 4

Step-by-Step Calculation Example

Suppose you have a circle with a radius of 10 cm. Here is how you solve it:

  1. Identify the radius: r = 10.
  2. Square the radius: 10 × 10 = 100.
  3. Multiply by Pi (3.14159): 100 × 3.14159 = 314.159.
  4. The result is 314.16 cm² (rounded).

Quick Reference Table

Radius (units) Diameter (units) Area (sq units)
1 2 ~3.14
5 10 ~78.54
10 20 ~314.16
12 24 ~452.39

Why Is This Useful?

Calculating the area of a circle is vital in daily life. From determining the size of a pizza to calculating the amount of paint needed for a circular wall, or even designing mechanical gears and irrigation systems, the circle area formula is used everywhere.

function updateLabels() { var type = document.getElementById('inputType').value; var label = document.getElementById('valueLabel'); if (type === 'radius') { label.innerText = 'Radius Value'; } else { label.innerText = 'Diameter Value'; } } function calculateCircleArea() { var type = document.getElementById('inputType').value; var val = parseFloat(document.getElementById('circleValue').value); var unit = document.getElementById('unitType').value; var areaResult = document.getElementById('areaOutput'); var circResult = document.getElementById('circumferenceOutput'); var display = document.getElementById('resultDisplay'); if (isNaN(val) || val <= 0) { alert('Please enter a valid positive number.'); return; } var radius; if (type === 'radius') { radius = val; } else { radius = val / 2; } var area = Math.PI * Math.pow(radius, 2); var circumference = 2 * Math.PI * radius; areaResult.innerHTML = area.toLocaleString(undefined, {maximumFractionDigits: 4}) + " " + unit + "²"; circResult.innerHTML = circumference.toLocaleString(undefined, {maximumFractionDigits: 4}) + " " + unit; display.style.display = 'block'; }

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