Circle Calculator (Area, Circumference)
Enter a radius, diameter, circumference or area and get every other circle measurement.
Step-by-step working
- Convert the given radius to radius r
- C = 2πr, A = πr², d = 2r
Mathematical Formula
Overview & Explanation
All circle measurements follow from the radius; the calculator inverts whichever one you know.
How It Works
- Convert the known quantity to the radius.
- Compute diameter, circumference and area.
Practical Applications
- Pipe and tank cross-sections.
- Garden and pizza sizes.
Circle formulas, term by term
Every circle measurement follows from the radius r, the distance from the centre to the edge. The diameter is d = 2r, the circumference (perimeter) is C = 2πr = πd, and the area is A = πr². The constant π ≈ 3.14159 is the ratio of any circle's circumference to its diameter.
For a circle of radius 7 cm: d = 14 cm, C = 2 × π × 7 ≈ 43.98 cm and A = π × 7² = 49π ≈ 153.94 cm². Using the school approximation 22/7 gives exactly 44 cm and 154 cm², which is why 7 is a popular radius in textbook problems.
Working backwards
From a known circumference, r = C ÷ (2π); a running track lane with a 400 m circumference would have r ≈ 63.66 m if it were a perfect circle. From a known area, r = √(A ÷ π): a 100 m² circular lawn has r ≈ 5.64 m.
Area scales with the square of the radius, so doubling the radius makes the area four times larger. A 12-inch pizza has (12 ÷ 8)² = 2.25 times the area of an 8-inch pizza, which is worth knowing when comparing prices.
Example 1: radius 5
Area 78.54.
Inputs
I know the: Radius · Value: 5
Step 1
Convert the given radius to radius r
Step 2
C = 2πr, A = πr², d = 2r
Area
Result
Example 2: area 100
Find radius.
Inputs
I know the: Area · Value: 100
Step 1
Convert the given area to radius r
Step 2
C = 2πr, A = πr², d = 2r
Area
Result
How it's calculated & sources
d = 2r; C = 2πr; A = πr². From area: r = √(A/π). From circumference: r = C / 2π.
Frequently Asked Questions
What value of π is used?
Area units?
Diameter vs radius?
What units does the area come out in?
Is 3.14 accurate enough?
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