Circle Calculator (Area, Circumference, Radius & Diameter)
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A circle calculator turns one known measurement into all the others with three formulas: d = 2r, C = 2πr and A = πr². For a radius of 5 cm, the diameter is 10 cm, the circumference is 10π ≈ 31.42 cm and the area is 25π ≈ 78.54 cm². You can start from the radius, diameter, circumference or area.
A circle with radius 5 cm has diameter 10 cm, circumference 10π ≈ 31.42 cm and area 25π ≈ 78.54 cm².
Parts of this circle and the sphere with the same radius
Show steps
- You know the radius: r = 5 cm. Every other measurement follows from it.
- Diameter: d = 2r = 2 × 5 = 10 cm.
- Circumference: C = 2πr = 2 × π × 5 = 10π ≈ 31.42 cm.
- Area: A = πr² = π × 5² = π × 25 = 25π ≈ 78.54 cm². Area is in square units.
- The exact answers keep π as a symbol. Round only at the end: π ≈ 3.14159265.
How to use the circle calculator
- Choose the measurement you know: Radius, Diameter, Circumference or Area.
- Type the value. Whole numbers, decimals, fractions such as 3/4 and multiples of π such as 18π all work.
- Pick a unit. To convert, choose a different unit under Show results in (for example inches to centimeters).
- Read the four measurements as exact values in terms of π and as decimals, then the semicircle, quarter circle and sphere values. Open Show steps to see each formula with your numbers in it.
Circle formulas
Every circle is fixed by one length. The radius r runs from the center to the edge, the diameter d runs edge to edge through the center, the circumference C is the distance around, and the area A is the space inside. The number π ≈ 3.14159 is the ratio C ÷ d, the same for every circle.
| You know | Radius | Circumference | Area |
|---|---|---|---|
| Radius r | r | C = 2πr | A = πr² |
| Diameter d | r = d ÷ 2 | C = πd | A = πd² ÷ 4 |
| Circumference C | r = C ÷ (2π) | C | A = C² ÷ (4π) |
| Area A | r = √(A ÷ π) | C = 2√(πA) | A |
Lengths (r, d, C) share one unit, such as cm. Area is in square units, such as cm². If you double the radius, the circumference doubles but the area becomes four times as large.
Worked examples
Example 1: area and circumference from the radius
A circle has a radius of 5 cm. The diameter is 2 × 5 = 10 cm. The circumference is 2 × π × 5 = 10π ≈ 31.42 cm. The area is π × 5² = 25π ≈ 78.54 cm². A diameter of 10 cm gives the same area, because the radius is still 5 cm.
Example 2: radius and area from the circumference
A tree trunk measures 44 cm around. The diameter is 44 ÷ π ≈ 14.01 cm and the radius is 22 ÷ π ≈ 7.00 cm. The area of the cross-section is C² ÷ (4π) = 1,936 ÷ (4π) = 484/π ≈ 154.06 cm².
Example 3: radius from the area
A round patio covers 154 ft². Divide by π and take the square root: r = √(154 ÷ π) ≈ 7.00 ft. The diameter is about 14.00 ft and the circumference is 2√(154π) ≈ 43.99 ft, which is the length of edging you would need.
Example 4: circumference from the diameter
A bike wheel is 26 inches across. Its circumference is π × 26 = 26π ≈ 81.68 in, so the bike moves about 81.68 inches for each turn of the wheel. A mile is 63,360 inches, which takes about 775.7 turns.
Exact answers in terms of π
Teachers often ask for answers “in terms of π”. That means you leave π as a symbol: the area of a circle with radius 5 is 25π, not 78.5. The exact form has no rounding error, and it shows the structure of the answer. If the circumference is given as 18π, the diameter is exactly 18 and the radius exactly 9. The calculator shows the exact form first and the decimal after the ≈ sign, rounded to the number of places you choose. When the exact form gets long, as after a unit conversion, it shows the decimal only.
Common radius values
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 2π ≈ 6.28 | π ≈ 3.14 |
| 2 | 4 | 4π ≈ 12.57 | 4π ≈ 12.57 |
| 3 | 6 | 6π ≈ 18.85 | 9π ≈ 28.27 |
| 4 | 8 | 8π ≈ 25.13 | 16π ≈ 50.27 |
| 5 | 10 | 10π ≈ 31.42 | 25π ≈ 78.54 |
| 6 | 12 | 12π ≈ 37.70 | 36π ≈ 113.10 |
| 7 | 14 | 14π ≈ 43.98 | 49π ≈ 153.94 |
| 10 | 20 | 20π ≈ 62.83 | 100π ≈ 314.16 |
Notice that a radius of 2 gives the same number for the circumference and the area (4π). The units are different, though: one is a length and the other is an area.
Common mistakes
- Using the diameter in A = πr². Halve the diameter first. A 10 cm circle has area 25π, not 100π.
- Squaring π instead of r. πr² means π × r × r. Only the radius is squared.
- Forgetting the square root. From the area, r = √(A ÷ π). Dividing by π alone gives r², not r.
- Mixing up units. Area is in square units. Converting 1 m² to cm² multiplies by 10,000, not by 100.
- Rounding π too early. Using 3.14 in the middle of a problem can shift the last digit. Keep π exact, then round once.
Where circle measurements are used
Pizza is a good test: one 12-inch pizza has area 36π ≈ 113.10 in², more than two 8-inch pizzas at 2 × 16π = 32π ≈ 100.53 in². The circumference tells you how far a wheel rolls per turn, how much fencing goes around a round garden and how long a belt around a pulley must be. The area tells you how much paint covers a round tabletop, how much soil a circular bed needs (area × depth) and how much material is in a pipe’s cross-section.
Circle practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
A = πr² = π × 6² = 36π cm². 12π is the circumference, and 144π comes from squaring the diameter.
r = √(A ÷ π) = √(100 ÷ π) ≈ √31.83 ≈ 5.64 cm. Stopping at 100 ÷ π gives r², not r.
Area depends on r². (3r)² = 9r², so the area becomes 9 times as large. The circumference only triples.
d = C ÷ π = 44 ÷ π ≈ 14.01 cm. Dividing by 2π gives the radius, about 7.00 cm.
A full circle has area π × 4² = 16π, so half of it is 8π ≈ 25.13. 8π + 8 is the semicircle's perimeter.
12-inch: π × 6² = 36π ≈ 113.10 in². Two 8-inch: 2 × π × 4² = 32π ≈ 100.53 in². Using the diameter instead of the radius gives the wrong comparison.
Quiz complete
Frequently asked questions
How do you find the area of a circle?
Square the radius and multiply by π: A = πr². For a radius of 5 cm, A = 25π ≈ 78.54 cm². If you have the diameter, halve it first, so a 10 cm diameter gives the same 78.54 cm².
How do you find the circumference of a circle?
Multiply the diameter by π, or twice the radius by π: C = πd = 2πr. A 26-inch diameter gives 26π ≈ 81.68 in, and a 4 m radius gives 8π ≈ 25.13 m.
How do you find the diameter of a circle?
Double the radius, or divide the circumference by π: d = 2r = C ÷ π. A circumference of 18π gives a diameter of exactly 18, and a circumference of 44 cm gives 44 ÷ π ≈ 14.01 cm.
How do you find the radius of a circle?
Halve the diameter, divide the circumference by 2π, or use r = √(A ÷ π) from the area. An area of 154 ft² gives r ≈ 7.00 ft, and a circumference of 30 m gives r = 15/π ≈ 4.77 m.
What is the surface area of a circle?
A circle is flat, so its "surface area" is just its area, πr². People often mean a sphere, whose surface area is 4πr². A sphere with radius 3 in has surface area 4π × 9 = 36π ≈ 113.10 in². The calculator lists the sphere values for your radius too.
How do you find the chord length of a circle?
If a chord is a distance h from the center, its length is 2√(r² − h²). With r = 10 and h = 6, the chord is 2√(100 − 36) = 2 × 8 = 16. For a chord from a central angle, use the arc length and sector area calculator below.
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