Circle calculator
This circle calculator takes any one measure – radius, diameter, circumference or area – and gives you all the others, plus arc length, chord, sector and segment for the angle you choose.
Example: Known value: Radius r · Value 5 · Length unit: cm · Central angle θ 60 ° → Result: Area: 78.5398 cm² · Circumference: 31.4159 cm. Source: Wikipedia – Kreis (Geometrie): Umfang, Fläche, Sehne, Bogen, Sektor, Segment. Updated: .
How it is calculated
With radius r, circumference C = 2πr and area A = πr². A circle with a 5 cm radius has a circumference of 31.42 cm and an area of 78.54 cm².
How it is calculated
Each of the four measures can be turned back into the radius: r = d/2, r = C/(2π) or r = √(A/π). Everything else follows from r. For a part of the circle with central angle θ (in radians): arc length = r·θ, chord = 2r·sin(θ/2), sector area = r²·θ/2 and segment area = r²/2·(θ − sin θ).
Good to know
- Double the radius and the circumference doubles, but the area grows fourfold.
- At 180° the segment is a half circle and the chord is the diameter.
- Areas appear in the chosen unit squared (cm², m²); the calculation itself is unit-free.
Frequently asked questions
How do you calculate the area of a circle?
A = π · r². Square the radius and multiply by π (3.14159…). If you only know the diameter d, use A = π · d² / 4.
How do you calculate the circumference?
C = 2 · π · r or C = π · d. A 10 cm diameter gives 31.42 cm.
How do you find the radius from the circumference?
Divide the circumference by 2π: r = C / (2π). A circumference of 62.83 cm gives a radius of 10 cm.
What is the difference between a sector and a segment?
A sector is a pie slice (between two radii and the arc); a segment is the piece between a chord and its arc.
Sources and legal basis
- Wikipedia – Kreis (Geometrie): Umfang, Fläche, Sehne, Bogen, Sektor, Segment
- Wikipedia – Kreissegment: segment area r²/2·(θ − sin θ) and segment height
As of: · Editorial policy
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