Free circle calculator. Enter the radius, diameter, circumference, or area to get all four measurements plus arc length and sector area, with formulas shown.
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Enter your values and press Calculate.
Every circle measurement is a function of the radius, so the calculator first solves for the radius from whichever value you provide: r = d/2 from the diameter, r = C/(2*pi) from the circumference, or r = sqrt(A/pi) from the area. From the radius it derives the rest: diameter d = 2r, circumference C = 2*pi*r, and area A = pi*r². If you also enter a sector angle, it adds the arc length (r times the angle in radians) and the sector area (half r² times the angle in radians), which is the pie-slice portion of the full circle.
Three linked formulas describe every circle. The diameter is twice the radius: d = 2r. The circumference, the distance around the circle, is C = 2*pi*r, equivalently pi*d. The area, the space inside, is A = pi*r².
Pi is the fixed ratio of any circle's circumference to its diameter, about 3.14159, the same for every circle. Because pi is irrational, exact answers are often written with pi in them (for example 14*pi cm) and only converted to decimals at the end.
Each formula rearranges to solve for the radius: r = d/2, r = C/(2*pi), r = sqrt(A/pi). Knowing any single measurement unlocks all the others.
Choose which measurement you know: radius, diameter, circumference, or area. Enter its value in any unit you like; the calculator is unit-agnostic, so lengths come back in your unit and the area in that unit squared.
You get all four measurements at once. Optionally enter a sector angle (in degrees) to also get the arc length and sector area for that wedge of the circle; leave it at zero to skip the sector math.
A worked check: radius 5 gives diameter 10, circumference 31.42, and area 78.54. Enter the area 78.54 instead and the calculator works backward to the same radius.
From the radius, everything is direct: d = 2r, C = 2*pi*r, A = pi*r².
From the diameter, halve it to get the radius, then proceed as above. A diameter of 10 gives r = 5, C = 31.42, A = 78.54.
From the circumference, divide by 2*pi: r = C/(2*pi). A circumference of 100 gives r = 15.92, d = 31.83, and A = C²/(4*pi) = 795.77.
From the area, take r = sqrt(A/pi). An area of 50 gives r = 3.99, d = 7.98, C = 25.07.
The calculator does the inversion automatically; the table above is what runs under the hood. Keep this four-way inversion as a quick reference: from the radius everything is direct, from the diameter halve first, from the circumference divide by 2*pi, from the area take the square root over pi.
Circumference is a length: the distance around the circle. Area is the two-dimensional space inside it, measured in square units. Diameter is the straight-line distance across the circle through its center.
Circumference is the circle's word for perimeter; the idea (total distance around the boundary) is the same one used for polygons. A common mix-up is treating circumference and area as interchangeable: they are not even the same kind of quantity, one is a length and the other an area.
A curiosity worth knowing: at radius 2, the numbers coincide (circumference 12.57, area 12.57), but the units still differ, so the equality is numerical only.
A sector is a pie-slice wedge of a circle cut by a central angle theta. Its area is the fraction theta/360 of the full area: (theta/360)*pi*r². The arc length, the curved edge of the slice, is the same fraction of the circumference: (theta/360)*2*pi*r.
A semicircle is the theta = 180 degree case: area pi*r²/2 and a curved edge of pi*r (plus the diameter if you count the full perimeter).
Enter any sector angle in the calculator to get both values instantly, which is handy for anything from pizza slices to irrigation arcs.
Pizza math is the classic: area grows with the square of the radius, so a 16-inch pizza has about 78 percent more area than a 12-inch one, not 33 percent. This pizza area comparison is the fastest intuition pump for squared growth. Doubling the radius quadruples the area.
Paint coverage: a circular ceiling of radius 1.5 m has area 7.07 m², so at 12 m² per liter one liter covers a single coat.
Pipe sizing: wrap a tape around a pipe to get its circumference, divide by pi for the diameter, and square from there to the cross-sectional area.
Gardens and sprinklers: a sprinkler with a 6 m radius waters about 113 m². Add 5 to 10 percent extra material on real projects, since nothing is perfectly round.
Start with radius 5 units. Diameter = 2*5 = 10. Circumference = 2*pi*5 = 31.42. Area = pi*25 = 78.54.
Now reverse it: enter area 78.54. Radius = sqrt(78.54/pi) = sqrt(25) = 5, and the diameter and circumference follow. The round trip confirms the inversion.
With a 90-degree sector angle: arc length = (90/360)*31.42 = 7.85, and sector area = (90/360)*78.54 = 19.63, exactly one quarter of the circle.
Multiply pi by the radius squared: A = pi*r². A circle with radius 5 has area 25*pi, about 78.54 square units. If you only know the diameter, halve it first to get the radius.
Multiply 2*pi by the radius (C = 2*pi*r), or multiply pi by the diameter (C = pi*d). A radius of 5 gives 31.42; a diameter of 10 gives the same.
Rearrange A = pi*r² to r = sqrt(A/pi). An area of 50 square units gives r = sqrt(50/pi) = 3.99.
Divide by pi: d = C/pi. A circumference of 100 gives a diameter of 31.83.
Pi (about 3.14159) is the fixed ratio of any circle's circumference to its diameter, identical for every circle. It appears in both the circumference and area formulas because it captures that universal relationship.
Circumference is the distance around the circle, a length. Area is the space inside the circle, measured in square units. They describe different things and cannot be compared directly.
Effectively yes: circumference is the term used for the perimeter of a circle, while perimeter is used for polygons. The underlying idea, the total distance around the boundary, is the same.
Any unit you like. The calculator is unit-agnostic: enter the radius in cm and the area comes back in cm². Lengths (radius, diameter, circumference) stay in your unit; area is always in that unit squared.
Pi is used at full double precision (about 15 significant digits) internally, and results are shown rounded for display. For exact work, keep answers in terms of pi (for example 14*pi) until the final step.
Not from the circle alone, since a circle is two-dimensional. For a cylinder, multiply the circle area by the height. For a sphere, use V = (4/3)*pi*r³ in a volume calculator.
Use the ellipse area formula A = pi*a*b, where a and b are the two semi-axes. The circle formula is the special case where a and b are equal.
Because the radius is squared in A = pi*r². Doubling r multiplies r² by four. A pizza with radius 8 has (8/7)² = 1.31 times the area of a radius-7 pizza: 31 percent more pizza.
Measure straight across the widest part for the diameter and halve it for the radius, or wrap a tape around the edge for the circumference and divide by pi. Take each measurement twice.
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