Radius, diameter, circumference and area — in any unit.
Area (A) = π × r² Circumference (C) = 2 × π × r Diameter (d) = 2 × r Derived conversions: r = d / 2 r = C / (2π) A = π × (d/2)² C = π × d
All circle measurements derive from the radius (r) — the distance from the center to the edge. The three core formulas are:
All formulas use π (pi) ≈ 3.14159265358979.
Diameter d = 2 × 7 = 14 cm Circumference C = 2 × π × 7 = 2 × 3.14159265 × 7 ≈ 43.98 cm Area A = π × 7² = 3.14159265 × 49 ≈ 153.94 cm²
Result: Diameter = 14 cm | Circumference ≈ 43.98 cm | Area ≈ 153.94 cm²
For a circle with a 7 cm radius:
All values scale with the square (for area) or linearly (for circumference and diameter) as the radius changes.
A circle is defined as the set of all points in a plane that are exactly the same distance — the radius — from a fixed central point. This single constraint produces a shape with unique mathematical properties not shared by any polygon.
Pi is the constant ratio of a circle's circumference to its diameter for every circle, regardless of size. Its approximate decimal value is 3.14159265…, though it is irrational (non-terminating, non-repeating). For most practical calculations, using π ≈ 3.14159 or your calculator's built-in π key gives sufficient accuracy.
The radius and diameter are directly related (d = 2r), so knowing either one is sufficient to compute all other measurements. The radius is typically the more fundamental value in formulas.
This is why a pizza that is 16 inches in diameter has significantly more than twice the area of an 8-inch pizza — it has four times the area.
Area is always expressed in square units (cm², m², in², ft²), while circumference and diameter use linear units (cm, m, in, ft). Make sure your input and output units match to avoid calculation errors.
Solve for r first: r = √(A/π) = √(200/3.14159) ≈ √63.66 ≈ 7.979 cm. Then d = 2r ≈ 15.96 cm.
A square with side length equal to the circle's diameter d has perimeter = 4d. The circle's circumference = πd ≈ 3.14159d. So the circle's circumference is about 21.5% shorter than the square's perimeter.
A semicircle's area = (π × r²) / 2. Its perimeter = π × r + 2r = r(π + 2). For r = 6 cm: area ≈ 56.55 cm², perimeter ≈ 30.85 cm.
π is defined as the ratio C/d for any circle. Mathematically it is computed via infinite series (e.g., the Leibniz or Nilakantha series) or the Gauss–Legendre algorithm. Its decimal expansion is 3.14159265358979… and never repeats or terminates.
The circle's diameter equals the square's side, so r = 5 cm. Area = π × 5² = 25π ≈ 78.54 cm². This covers about 78.54% of the square's 100 cm² area.
The area of a circle is A = π × r², where r is the radius. For example, a circle with radius 5 cm has area = π × 25 ≈ 78.54 cm².
Use C = π × d. Multiply the diameter by pi (≈ 3.14159). For a diameter of 10 m, circumference = π × 10 ≈ 31.42 m.
Yes. First find the radius: r = C ÷ (2π). Then compute A = π × r². Alternatively, A = C² ÷ (4π) in one step.
You can enter any linear unit (mm, cm, m, inches, feet, etc.). Area results will be in the corresponding square unit. The calculator does not convert between unit systems, so keep your inputs consistent.
Results are displayed to two decimal places by default, which is appropriate for most practical uses. Scientific or engineering applications may require more precision — use the full π value in your own calculations for maximum accuracy.
Area increases with the square of the radius (A = πr²). If you triple the radius, the area increases by a factor of 9. This quadratic relationship is why small increases in radius produce large gains in area.
Only sources that have been reviewed are shown. Unverified citations are never published.