Calculate the area of a circle from radius, diameter, or find the radius from area. Instant results with the formula: A = πr²
Area Formula: A = πr²
From Diameter: A = π(d/2)² = πd²/4
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The area of a circle is the amount of space enclosed within the circle's boundary (circumference). It represents the total surface covered by a perfectly round shape. Area is measured in square units, such as square centimeters (cm²), square meters (m²), or square inches (in²).
Unlike the circumference, which measures the distance around a circle, the area measures the space inside. Understanding circle area is essential in countless real-world applications, from calculating the size of a pizza to determining the coverage area of a sprinkler system.
The fundamental formula for calculating the area of a circle uses the radius. If you know the diameter or circumference instead, you can derive the radius first or use alternative formulas.
A = πr²
Where A is area, π ≈ 3.14159, and r is the radius
A = πd²/4
Where d is the diameter (since r = d/2)
The area of a circle is proportional to the square of its radius. This means if you double the radius, the area increases by a factor of 4 (2² = 4). If you triple the radius, the area increases by a factor of 9 (3² = 9). This squared relationship is why circles grow much larger in area than their radius might suggest.
Sometimes you know the area and need to find the radius. By rearranging the area formula, you can solve for radius:
r = √(A/π)
Divide the area by π (3.14159...)
This gives you r²
Take the square root of the result
This gives you the radius
Example: Area = 78.54 cm²
r = √(78.54 ÷ 3.14159) = √25 = 5 cm
| To Find | Formula | Given |
|---|---|---|
| Area | A = πr² | Radius |
| Area | A = πd²/4 | Diameter |
| Area | A = C²/(4π) | Circumference |
| Radius | r = √(A/π) | Area |
| Diameter | d = 2√(A/π) | Area |
| Circumference | C = 2√(πA) | Area |
A circular garden has a radius of 7 meters. Find its area.
Given: r = 7 m
Formula: A = πr²
Step 1: Square the radius: 7² = 49
Step 2: Multiply by π: π × 49 = 3.14159 × 49
Answer: A = 153.94 m²
A circular table has a diameter of 1.2 meters. What is its surface area?
Given: d = 1.2 m
Step 1: Find radius: r = d/2 = 1.2/2 = 0.6 m
Step 2: Apply formula: A = πr² = π × (0.6)²
Step 3: Calculate: A = π × 0.36 = 1.131
Answer: A = 1.13 m²
A circular pool has an area of 314.16 square feet. What is its radius?
Given: A = 314.16 ft²
Formula: r = √(A/π)
Step 1: Divide by π: 314.16 ÷ 3.14159 = 100
Step 2: Take square root: √100 = 10
Answer: r = 10 feet
Calculate material needed for circular patios, ponds, fountains, and garden beds. Determine concrete volume for circular foundations and the coverage area of round structures.
Calculate the surface area of circular components like wheels, gears, and discs. Essential for material cost estimation and quality control in production.
Determine irrigation coverage for circular pivot systems. Calculate the area of grain silos, storage tanks, and circular crop fields for yield estimation.
Calculate pizza sizes, cake portions, and circular serving areas. Compare value between different sized circular products like pies and tortillas.
Calculate the area of circular fields, targets in archery and darts, and swimming pools. Used for maintaining playing surfaces and equipment specifications.
Calculate cross-sectional areas of blood vessels, cells, and biological structures. Essential in physics for calculating pressure on circular surfaces.
The formula A = πr² uses the radius, not diameter. If you use diameter by mistake, your answer will be 4 times too large. Always divide diameter by 2 first.
The formula is πr², not πr. Forgetting to square the radius gives an answer that's too small (it would actually give you half the circumference, not the area).
Area is measured in square units (cm², m², in²). If radius is in centimeters, area is in square centimeters. Don't forget the "squared" part of the unit.
Area (A = πr²) measures enclosed space. Circumference (C = 2πr) measures distance around. They have different formulas and different unit types.
Find the area of a circle with radius 5 cm.
A = πr² = π × 5² = π × 25 = 78.54 cm²
A pizza has a diameter of 14 inches. What is its area?
r = d/2 = 14/2 = 7 inches
A = πr² = π × 7² = π × 49 = 153.94 in²
A circular rug has an area of 50.27 square feet. What is its radius?
r = √(A/π) = √(50.27/3.14159) = √16 = 4 feet
Which has more area: a circle with radius 6 cm or a circle with diameter 10 cm?
Circle 1: A = π × 6² = 113.10 cm²
Circle 2: r = 10/2 = 5 cm, A = π × 5² = 78.54 cm²
Circle 1 (radius 6 cm) has more area.
The area of a circle is A = πr², where A is the area, π (pi) is approximately 3.14159, and r is the radius. If you have the diameter, use A = πd²/4 or first convert diameter to radius (r = d/2).
First divide the diameter by 2 to get the radius, then use A = πr². For example, if diameter is 10 cm: radius = 5 cm, area = π × 5² = 78.54 cm². Alternatively, use A = πd²/4 directly.
Use the formula r = √(A/π). Divide the area by π (3.14159...), then take the square root of the result. For example, if area = 100 cm², radius = √(100/3.14159) = √31.83 = 5.64 cm.
A = πr² = π × 10² = π × 100 = 314.159 square units. The units depend on the radius measurement (cm² if radius is in cm, in² if in inches, etc.).
Yes, when the radius equals 2 units. At r = 2: Area = π × 2² = 4π and Circumference = 2π × 2 = 4π. Both equal approximately 12.566. However, they have different unit types (area in units², circumference in units).
First find the radius: r = C/(2π), then calculate area: A = πr². Or use the direct formula: A = C²/(4π). For example, if C = 31.42, then A = (31.42)²/(4 × 3.14159) = 78.54.
2πr is the circumference formula (distance around). Area requires squaring the radius because you're measuring two-dimensional space. The πr² formula comes from calculus, representing the sum of infinitely many thin concentric rings.
The area quadruples (becomes 4 times larger). Since A = πr², if you replace r with 2r: A = π(2r)² = π × 4r² = 4πr². This is why the area grows much faster than the radius.
The area of a circle formula A = πr² is one of the most fundamental concepts in geometry with countless practical applications. Whether you're calculating the size of a pizza, designing a circular garden, or solving homework problems, understanding this formula is essential.
Our free Area of a Circle Calculator makes these calculations instant and accurate. Simply enter any measurement—radius, diameter, or area—and get all other circle properties with step-by-step explanations. No more manual calculations or worrying about π approximations!