How to use it
- Pick circle, sector and arc, or ring.
- Choose which value you know and enter it.
- Pick the unit and the number of decimal places.
- Read the radius, diameter, circumference and area.
Circle formulas
| Quantity | Formula |
|---|---|
| Diameter | d = 2r |
| Circumference | C = 2πr = πd |
| Area | A = πr² |
| Radius from circumference | r = C / 2π |
| Radius from area | r = √(A / π) |
π (pi) is about 3.14159265. The calculator uses its full floating-point value and rounds only the display, to as many decimal places as you choose. Units include inches, feet, yards, miles and metric units. Everything happens in your browser.
Worked examples
From the radius: a circle with r = 5 in has
- diameter 10 in,
- circumference 2π × 5 ≈ 31.42 in,
- area π × 5² ≈ 78.54 sq in.
From the circumference: a tree trunk measures 50 in around. Its radius is 50 / 2π ≈ 7.96 in, its diameter about 15.9 in, and its cross-section area about 198.9 sq in.
Pizza math
Area grows with the square of the diameter, so a slightly bigger pizza is a lot more pizza.
| Pizza | Area |
|---|---|
| 12-inch | 113.1 sq in |
| 14-inch | 153.9 sq in |
| 16-inch | 201.1 sq in |
A 16-inch pizza has about 1.78 times the area of a 12-inch one. Two 12-inch pizzas (226.2 sq in) give only a little more than one 16-inch pizza, so compare the price per square inch before you order. If a 12-inch pizza costs $12 and a 16-inch one $18, you pay about 10.6 cents per square inch for the small one and only 9 cents for the large.
Sectors, arcs and chords
A sector is a slice of a circle between two radii with central angle θ.
- Arc length: s = 2πr × θ / 360°
- Sector area: A = πr² × θ / 360°
- Chord length: c = 2r × sin(θ / 2)
Example: r = 10 ft, θ = 90°: arc ≈ 15.71 ft, sector area ≈ 78.54 sq ft, chord ≈ 14.14 ft. That is useful for curved garden beds, quarter-round patios or pie charts. For more segment details such as arc height, see the arc length calculator.
Rings (annulus)
A ring or annulus is the area between two circles with the same center:
A = π(R² − r²)
Example: a circular path around a 4 ft radius pond, out to a 6 ft radius: π(36 − 16) ≈ 62.83 sq ft of paving. The calculator also shows the ring width and both circumferences, handy for edging.
Common mistakes
- Mixing radius and diameter. If you measure across the circle, that is the diameter; halve it for the radius.
- Forgetting to square. Area uses r², so doubling the radius quadruples the area.
- Unit confusion. Area is in square units: a radius in feet gives square feet.
- Measuring the circumference loosely. Wrap a flexible tape snugly and level; a tape that sags adds length and makes the radius too big.
- Using 3.14 for precise work. It is fine for rough estimates, but over large circles the difference from the full value of π adds up.
Measuring a round object without finding its center: wrap a string or tape around it to get the circumference, enter that value, and the calculator returns the diameter. A 47-inch trunk circumference, for example, means a diameter of about 15 inches. For other shapes, use the area calculator.
Frequently asked questions
How do I find the circumference of a circle?
Multiply the diameter by π, or the radius by 2π. A 10-inch circle is about 31.42 inches around.
How do I find the area of a circle?
A = πr². For a 5-inch radius: 3.14159 × 25 ≈ 78.54 square inches.
How do I get the radius from the circumference?
Divide the circumference by 2π: r = C / 2π.
What is the difference between radius and diameter?
The radius runs from the center to the edge; the diameter goes all the way across and is twice the radius.
How precise is the calculator?
It uses the full value of π and lets you choose up to 8 decimal places in the display.
Last updated: November 12, 2026