Circle Calculator (Area, Circumference, Radius)
- Free
- No sign-up
- Works on phones
- Shows the working
By Yasir Hafeez · Updated
This circle calculator works from any one measurement. Enter the radius, the diameter, the circumference or the area, and it returns all four. When you start from the radius or diameter, the circumference and area are shown exactly (such as \( 10\pi \)) and as decimals.
It works as an area of a circle calculator and a circumference calculator in one. It’s free and needs no sign-up.
How to use the circle calculator
- In I know the, choose radius, diameter, circumference or area.
- Enter the value.
- Press Calculate to see r, d, C and A.
Circle formulas
| Quantity | Formula |
|---|---|
| Diameter | \( d = 2r \) |
| Circumference | \( C = 2\pi r = \pi d \) |
| Area | \( A = \pi r^2 = \frac{\pi d^2}{4} \) |
| Radius from circumference | \( r = \frac{C}{2\pi} \) |
| Radius from area | \( r = \sqrt{\frac{A}{\pi}} \) |
\( \pi \approx 3.14159 \) is the ratio of every circle’s circumference to its diameter.
Worked example: from the radius
\( r = 5 \) (as loaded above): \( d = 10 \), \( C = 10\pi \approx 31.42 \), \( A = 25\pi \approx 78.54 \).
Worked example: from the diameter
A pizza 12 inches across has \( r = 6 \), so its area is \( 36\pi \approx 113.1 \) in² and its crust is \( 12\pi \approx 37.7 \) inches long. A 16-inch pizza has area \( 64\pi \approx 201 \) in², almost twice as much, because area grows with the square of the radius.
Worked example: from the area
A circular garden has area 50 m². Then \( r = \sqrt{50/\pi} \approx 3.99 \) m, and the fence around it is \( C = 2\pi r \approx 25.07 \) m.
Arcs and sectors
A sector with angle \( \theta \) (in radians) has arc length \( s = r\theta \) and area \( \frac12r^2\theta \). Convert degrees first with degrees to radians. For a \( 60^\circ \) slice of the \( r = 5 \) circle, \( \theta = \frac{\pi}{3} \), so the arc is \( \frac{5\pi}{3} \approx 5.24 \) and the slice’s area is \( \frac{25\pi}{6} \approx 13.09 \).
Tips and common mistakes
- Radius vs diameter. The most common error is using the diameter in \( \pi r^2 \).
- Circumference vs area. Circumference is a length (cm); area is in square units (cm²).
- Rounding \( \pi \). Use the \( \pi \) key or the exact answer; 3.14 is fine only for rough work.
Related guides
Further reading
- Circle (Wikipedia) — terminology, formulas and properties.
- Pi (Wikipedia) — what \( \pi \) is and how it’s calculated.
FAQ
How do you find the area of a circle?
\( A = \pi r^2 \). For a radius of 4, \( A = 16\pi \approx 50.27 \).
How do you find the circumference of a circle?
\( C = 2\pi r \) or \( C = \pi d \).
How do you find the radius from the circumference?
Divide by \( 2\pi \): \( r = \frac{C}{2\pi} \).
How do you find the radius from the area?
\( r = \sqrt{A/\pi} \).