Circle Calculator: Radius, Diameter, Circumference, Area

Real-world use cases

• Check a geometry homework answer in seconds

  A worksheet gives a circle with radius 7 cm and asks for area and circumference. Pick Radius, type 7, and read area ≈ 153.94 cm² and circumference ≈ 43.98 cm, with A = πr² and C = 2πr printed so you can match the steps your teacher expects. Because the URL carries your input, you can paste the link into a study-group chat and everyone lands on the same solved circle.

• Size a round table, rug or planter from the space you have

  You have room for a circle about 47 inches across. That width is a diameter, so pick Diameter, type 47, and the tool gives radius 23.5, circumference ≈ 147.7 inches for trim or edging, and area ≈ 1735 square inches to estimate a tablecloth or fabric. No need to remember which formula halves and which squares — the labels keep diameter and radius from getting mixed up.

• Work backwards from a known circumference

  A tree trunk measures 94 cm around and you need its cross-section area for a growth estimate. Pick Circumference, type 94, and the tool recovers radius ≈ 14.96 cm and reports area ≈ 703 cm², showing the r = C / (2π) step it used. Tape-measure-around is often the only dimension you can get, and this turns it into everything else.

• Lay out an arc or pie slice for a design or build

  Cutting a 120° sector from a 30 cm radius disc for a lampshade or a fan pattern? Pick Radius, type 30, switch on the sector panel and enter 120. The tool returns arc length ≈ 62.83 cm to mark the curved edge and sector area ≈ 942.5 cm² for material, with the wedge shaded in the diagram so the geometry is obvious before you cut.

Common pitfalls

• Mixing up radius and diameter. The radius goes from the center to the edge; the diameter goes all the way across and is twice as long. Feeding a diameter into the Radius tab doubles every answer. If your measurement is the full width of the circle, pick the Diameter tab instead.

• Forgetting to square the radius in the area. Area is πr², not πr, so a radius of 4 gives π·16 ≈ 50.27, not π·4 ≈ 12.57. The extra factor of r is what makes area grow much faster than circumference as the circle gets bigger.

• Putting the central angle in radians when the tool expects degrees. The arc and sector boxes read the angle in degrees and convert internally. Typing 1.57 thinking in radians gives a tiny 1.57° wedge instead of the quarter circle you meant; enter 90 for a quarter, 180 for a half, 360 for the whole circle.

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