How to Calculate the Area of a Circle in Square Inches
The area of a circle is found using the formula A = πr², where r is the radius. When you measure the radius in inches, the result is automatically in square inches (in² or sq in).
Circle Formulas
Area from Radius
Square the radius and multiply by pi.
A = πr²
Area from Diameter
Divide the diameter by 2, then use the radius formula.
A = π(d/2)² = πd²/4
Circumference
The perimeter of the circle.
C = 2πr = πd
Common Circle Sizes in Square Inches
- 3-inch radius circle: A = π x 9 = 28.27 sq in
- 6-inch radius circle: A = π x 36 = 113.10 sq in
- 12-inch radius (1 ft) circle: A = π x 144 = 452.39 sq in
- 10-inch diameter circle: A = π x 25 = 78.54 sq in
Unit Conversions
1 square foot = 144 square inches. To convert square inches to square feet, divide by 144. To convert square inches to square centimeters, multiply by 6.4516.
Practical Applications
Calculating the area of a circle in square inches is useful for determining the cross-sectional area of pipes, determining pizza sizes, calculating the area of circular labels or stickers, and many crafting and engineering applications where precision in inches is needed.