Enter any one value to calculate all the rest
A circle is the set of all points in a plane at a fixed distance (radius) from a center point. Key elements include: Radius (center to circumference), Diameter (through center, endpoints on circumference, twice the radius), Circumference (distance around the circle), and Area (region inside the circle).
Diameter d = 2r (r = radius)
Circumference C = 2πr = πd
Area S = πr² = πd²/4
π ≈ 3.1415926535...
Engineering & Construction: Calculate dimensions and materials for pipes, cylindrical tanks, and circular foundations.
Education: Essential for geometry curriculum, helping students understand π and circle properties.
Everyday Life: Determine tablecloth size for round tables, garden bed area, pool volume, pizza size comparisons, and more.
The area of a circle is S = πr², where r is the radius and π ≈ 3.14159. If you know the diameter d, area S = π(d/2)² = πd²/4. For example, a circle with radius 5cm has an area of 3.14159 × 5² ≈ 78.54 square centimeters.
The circumference formula is C = 2πr or C = πd, where r is the radius and d is the diameter. For example, radius 5cm gives circumference = 2 × 3.14159 × 5 ≈ 31.42 cm. Using diameter 10cm: 3.14159 × 10 ≈ 31.42 cm.
Diameter d = 2r (twice the radius), radius r = d/2 (half the diameter). The diameter is the longest chord passing through the center. The radius is any line from the center to the circumference—the most fundamental parameters of a circle.
Pi (π) is the ratio of a circle's circumference to its diameter, approximately 3.1415926535... It's an irrational number that never terminates or repeats. Pi is one of the most important constants in mathematics and physics, appearing in circle formulas, trigonometry, and wave equations.
Given area S, radius r = √(S/π). For example, area = 78.54 cm², then r = √(78.54/3.14159) = √25 = 5 cm. From there you can calculate diameter d = 2r = 10 cm, and circumference C = 2πr ≈ 31.42 cm.
A circle calculator has many practical applications: calculating garden bed area for soil estimation; determining tablecloth circumference for trim length; computing pool volume (with depth); engineering pipe cross-sections; comparing pizza sizes; calculating round duct airflow; and solving geometry homework problems.