Circle Calculator - Radius, Diameter, Circumference, and Area

A circle calculator recovers every standard measure of a circle from any one of them. The four quantities are locked together: diameter d = 2r, circumference C = 2πr, and disk area A = πr². If you know radius you know the rest; if you know only the area of a round table, you can still get back to r = √(A/π) and then to the rim length.

This page asks for exactly one known value - r, d, C, or A - and fills the other three. The default is r = 7, so d = 14, C = 14π ≈ 43.9822971502571, and A = 49π ≈ 153.93804002589985. An optional central angle θ in degrees adds arc length (θ/360)×2πr and sector area (θ/360)×πr². π is always JavaScript Math.PI, not 3.14.

A circle is a plane curve (or, casually, the disk it bounds). It is not a sphere. If you needed the wrapping of a ball, use the surface area calculator. If you needed other plane shapes (rectangle, triangle, ellipse), use the area calculator. A right triangle inscribed in a circle is a different object; the right triangle calculator is the place for legs and hypotenuse, not for r and C.

Using this radius diameter circumference area solver takes four steps:

1. Choose what you know: radius, diameter, circumference, or area. Do not mix two knowns in one box - pick the quantity you actually measured.
2. Enter a positive number. Zero radius is not a circle here. Negative circumference is rejected.
3. Optionally type a central angle θ in degrees if you need an arc or a pizza-slice sector. Leave it blank to skip those two extra lines.
4. Copy r, d, C, A, or the arc. Inputs are stored locally for up to 30 days.

Note: θ is interpreted in degrees, not radians. A full turn is 360°, which reproduces C and A. Angles larger than 360° are allowed and mean more than one full wrap of the arc. Chord length, inscribed angle, and tangent segments are not implemented.

Circumference is the one-dimensional length of the rim. For the default r = 7, C = 14π. Equivalently C = πd with d = 14. If a running track is a perfect circle of radius 50 m, one lap on the line is 100π ≈ 314.16 m; that is a length you could walk, not an area you could pave.

Worked example - known radius 7:

• d = 2 × 7 = 14
• C = 2 × π × 7 = 14π ≈ 43.982297150257104
• A = π × 49 ≈ 153.93804002589985

Worked example - known circumference 10π:

Type the numeric circumference your problem used. If the textbook wrote C = 10π and you type 31.41592653589793 (which is 10×Math.PI), then r = C/(2π) = 5. If you type 31.4 instead, r will be slightly off because you rounded π before dividing. This calculator does not accept a symbolic “10π” string - it wants a number.

Worked example - known area 25π:

A = 25π means r² = 25, r = 5 (positive root only). Then d = 10 and C = 10π. Starting from area never produces a negative radius here.

Area scales with r²; circumference scales with r. Double the radius and the rim doubles but the disk becomes four times as large. That is why a 16-inch pizza is not twice a 8-inch pizza in cheese: diameters 16 and 8 give radii 8 and 4, areas 64π and 16π, a factor of four. People who compare pizzas by diameter without squaring are buying a worse deal than they think.

Units follow the formula: C is metres if r is metres; A is square metres. Mixing “the circumference is 20 square metres” is dimensionally false. This tool does not convert cm to m; enter every quantity already in one consistent length unit (or its square, if you start from area).

The most expensive mix-up is putting a measured diameter into a radius formula. C would come out twice too large; A would come out four times too large. This UI labels the field from your “I know” choice so you are less likely to do that, but it cannot know whether your tape measure was a full width or a centre-to-edge reading.

A central angle is measured at the centre, with sides that are radii. If θ is in degrees, the arc is the fraction θ/360 of the full circumference: arc = (θ/360) × 2πr. The matching pizza slice (sector) has area = (θ/360) × πr². A 90° angle on the default r = 7 circle is one-quarter of 14π for the arc and one-quarter of 49π for the sector.

If your textbook used radians, convert first: θ_degrees = θ_radians × 180/π. This field does not accept radian mode. An inscribed angle that sits on the rim is half the central angle that subtends the same arc; this calculator does not convert inscribed to central for you.

Arc length is not chord length. The chord is the straight shortcut 2r sin(θ/2) with θ in radians. A 180° arc is a semicircle of length πr; the chord is the diameter 2r, which is shorter. Do not paste an arc result into a truss as if it were a straight beam.

JavaScript Math.PI is a double-precision approximation of π, printed as 3.141592653589793. It is not the fraction 22/7 (≈ 3.14286) and not the three-digit 3.14 many homework keys use. If a worksheet insists on 3.14, your numeric C and A will differ in the third decimal or so. That is expected; the geometry is the same.

The tool never switches π mid-problem. Recovering r from C uses the same Math.PI that expanding C from r uses, so round-trips are consistent within floating point. Very large inputs can overflow to Infinity; that is an IEEE-754 limit, not a second definition of π.

• Diameter in a radius formula. Area becomes 4× too big; circumference 2× too big.
• Using 3.14 in one step and Math.PI in another and then wondering why r from C does not match the original r.
• Calling circumference “area” or attaching m² to 2πr.
• Degrees vs radians in the θ box. 2 is a tiny central angle in degrees and more than a full turn in radians (2 rad ≈ 114.6°).
• Confusing arc with chord or sector with segment (the segment is sector minus a triangular piece, not implemented here).

Invert the definitions. From circumference, r = C / (2π). From area, r = √(A/π). This page does both when you choose “I know” circumference or area. Using the same Math.PI in both directions means that if you start from r = 7, copy C, then paste C back as the known, you recover r = 7 within floating-point noise. Using 3.14 to go one way and Math.PI the other way will not close.

Diameter is the lazy sibling of radius: d = C/π and d = 2√(A/π). A circular pond whose area is listed as 50 m² has r = √(50/π) ≈ 3.989422804014327 m, not 50/π and not √50. People who take the square root of area without dividing by π first are computing the side of a square with that area, which is a different shape.

If a problem gives both C and A and they are inconsistent (a misprint), this calculator will not average them. Pick the quantity you trust. Manufacturing drawings that tolerance both diameter and circumference are over- constrained; geometry has only one independent size.

In careful language a circle is the curve (circumference 2πr) and a disk is the filled region (area πr²). School worksheets usually say “area of a circle” and mean the disk; this tool follows that habit. A sphere is a 3-D surface with area 4πr²; the solid ball has volume (4/3)πr³. None of those spherical formulas live here. If a word problem says “round tank” and asks how much water it holds, you are not on the right page.

An annulus (washer) is π(R² − r²), the difference of two disks. Compute two areas on this calculator and subtract by hand. A circular segment (the cap between a chord and its arc) is sector area minus a triangular piece; that extra subtraction is not automated. A stadium (running-track) shape is a rectangle plus two semicircles - again, compose by hand from this tool plus the area calculator’s rectangle.

• One known at a time. It does not least- squares fit inconsistent r and A.
• No unit conversion. r in cm and A in m² will be garbage unless you convert first.
• No ellipse, annulus, or spherical geometry.
• θ in degrees only for arc and sector.
• Positive knowns only. Empty, zero, and negatives error.