Area of a Circle Calculator: Formula & Examples

This calculator works out the area of a circle from its radius, diameter, or circumference. You enter one of those three values, and you get the area in square units (like square meters, square feet, or square inches) instantly. The tool uses the standard formula A = πr², and the steps below explain how it works so you can also do the math by hand.

Formula

The area of a circle is the total space enclosed inside its circumference. The most common formula uses the radius:

A = π × r²

• A = area of the circle (square units, e.g., m², ft², cm²)
• π (pi) ≈ 3.14159 (a constant, the ratio of circumference to diameter)
• r = radius, the distance from the center to the edge (same unit as the area’s base unit)

If you know the diameter instead, the formula becomes:

A = π × (d/2)²

where d is the diameter (twice the radius).

If you know the circumference, use:

A = C² / (4π)

where C is the circumference.

Worked Example

Using the default values from the calculator above (radius = 5 m):

1. Start with the formula: A = π × r²
2. Plug in the radius: A = π × (5)²
3. Square the radius: 5² = 25
4. Multiply by π: A = 3.14159 × 25 = 78.53975
5. Round to two decimal places: A ≈ 78.54 m²

The calculator’s first output shows 78.54 m², matching this result. The second output (from diameter 10 m) gives the same: π × (10/2)² = π × 25 = 78.54 m². The third output (from circumference 31.4159 m) gives 31.4159² / (4π) ≈ 986.96 / 12.566 = 78.54 m².

When to Use This Calculator

Use this tool whenever you need the area of a circular surface: a round garden bed, a circular tabletop, a pipe cross-section, a pizza, or a circular pond. It is also useful in construction, crafting, landscaping, and geometry homework. The calculator accepts any of the three common inputs (radius, diameter, or circumference), so you can work with whatever measurement you already have.

Common Mistakes

• Mixing up radius and diameter: The radius is half the diameter. Using the diameter directly in A = πr² gives an area four times too large. Always halve the diameter first (or use the dedicated diameter input).
• Forgetting to square the radius: A common error is multiplying π by the radius without squaring it. For r = 5, π × 5 = 15.7, but the correct area is π × 25 = 78.5.
• Unit confusion: If the radius is in centimeters, the area is in square centimeters, not square meters. Convert all measurements to the same unit before calculating.
• Using circumference as if it were the diameter: The circumference is the distance around the circle, not across it. If you have the circumference, use the third formula (C²/4π), not the radius formula.
• Rounding too early: If you round π to 3.14 instead of 3.14159, the result will be slightly off. For most purposes, rounding to two decimal places at the end is fine, but keep more digits during intermediate steps.

Tips

• When measuring a physical circle, measure the diameter (across the center) because it is easier to measure accurately than the radius (which requires finding the exact center).
• If you only have a ruler or tape measure, wrap it around the circle to get the circumference, then use the circumference formula.
• For quick mental estimates, use π ≈ 3.14. For precise work (engineering, large areas), use more digits of π (3.14159 or the π button on a calculator).
• Remember that area units are always squared: if the radius is in feet, the area is in square feet (ft²); if in meters, square meters (m²).
• If you need the area of a half-circle or quarter-circle, calculate the full area first, then multiply by 0.5 or 0.25.

Troubleshooting

The result looks too large or too small. Check which input you filled in. If you entered a diameter where the radius is expected, the area will be four times too big. If you entered a circumference where the diameter is expected, the area will be far too small. Re-read the labels on the inputs.

You get an error or a blank result. Make sure you entered a positive number. The calculator expects numbers greater than zero for radius, diameter, or circumference. If you left a field empty, it uses the default value shown.

You need a different unit (e.g., inches instead of meters). The calculator does not convert units automatically. Convert your measurement to the unit you want the area in before entering it. For example, to get square inches, enter the radius in inches.

The area seems too large for a small circle. Remember that squaring amplifies numbers. A circle with radius 10 m has an area of about 314 m², which is correct because the area grows with the square of the radius.

Frequently Asked Questions

Can I use this calculator if I only know the diameter?
Yes. Enter the diameter in the second input field. The calculator automatically halves it and uses the radius formula, giving the same result as if you had entered the radius.

What is the difference between area and circumference?
Area is the space inside the circle (measured in square units, like m² or ft²). Circumference is the distance around the circle (measured in linear units, like m or ft). They are related: C = 2πr, and A = πr².

Why is the area always in square units?
Area measures two-dimensional space. When you multiply two lengths (radius × radius), you get square units. That is why the result is labeled m², ft², cm², etc.

What if my circle is not perfect?
The formula assumes a perfect circle. Real-world objects like a slightly squashed bowl or a hand-drawn circle will give an approximate area. Measure at several points and average the radius for better accuracy.

Can I calculate the area of an oval or ellipse with this?
No. An ellipse uses a different formula: A = π × a × b, where a and b are the semi-major and semi-minor axes. This calculator is only for circles.

How precise is the result?
The calculator rounds to two decimal places, which is accurate enough for most practical purposes. If you need more precision, you can do the calculation manually with more digits of π, but the difference is negligible for typical measurements.

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in r | Radius | m | 5 | 0
in d | Diameter | m | 10 | 0
in c | Circumference | m | 31.4159 | 0
out area | Area | m² | pi * r^2 | 2
out area_d | Area from diameter | m² | pi * (d/2)^2 | 2
out area_c | Area from circumference | m² | c^2 / (4 * pi) | 2