What is a circle calculator?
A circle calculator computes the area, circumference, and diameter of a circle from a single input: the radius. The radius is the distance from the center of the circle to any point on its edge. Once you enter the radius, the calculator applies the standard formulas—area = πr², circumference = 2πr, and diameter = 2r—to give you all three measurements in one go. No sign-up or download is required; the tool runs in your browser and is useful for homework, design, construction, and any task that involves circular shapes.
Circles appear everywhere: wheels, plates, pools, gardens, and in many geometry and engineering problems. Knowing the area helps with material coverage (e.g. paint or turf); circumference helps with fencing or piping; diameter is often used in specifications. This free circle calculator gives you area in square units, circumference and diameter in the same linear units as your radius, so you can work in meters, feet, inches, or any unit as long as you stay consistent.
How to use this circle calculator
Enter the radius of your circle in the input box. The radius must be a positive number. You can use decimals (e.g. 2.5) or whole numbers (e.g. 5). As soon as the radius is valid, the results appear: area in square units, circumference in units, and diameter in units. The formulas are shown under the input: area = π × r², circumference = 2πr, diameter = 2r. If you enter zero or a negative value, the calculator will ask you to enter a positive radius. Use the same unit for radius as you want for circumference and diameter (e.g. if radius is in meters, circumference and diameter are in meters; area is in square meters).
Circle area formula
The area of a circle is given by A = πr², where r is the radius and π (pi) is approximately 3.14159. So if the radius is 5 units, the area is π × 25 ≈ 78.54 square units. The formula comes from the fact that the circle can be thought of as many thin rings or as a limit of regular polygons with more and more sides. Area is always in square units: square meters, square feet, square inches, etc. Use it when you need to know how much space is inside the circle—for example, how much grass seed for a circular lawn or how much paint for a circular sign.
Circumference formula
The circumference of a circle is the distance around it, like the length of a string wrapped once around the circle. The formula is C = 2πr (or C = πd, where d is the diameter). So for radius 5, circumference = 2 × π × 5 ≈ 31.42 units. Circumference is a length, so it uses the same unit as the radius. It is useful when you need to know the perimeter of a circle—for fencing a circular garden, ordering a trim strip, or finding how far a wheel travels in one rotation (one circumference per full turn).
Diameter and radius
The diameter of a circle is twice the radius: d = 2r. It is the longest distance across the circle, passing through the center. Many real-world specs use diameter (e.g. pipe size, pizza size, lens diameter). This calculator gives you the diameter whenever you enter the radius. If you only know the diameter, divide it by 2 to get the radius and enter that. Similarly, if you know the circumference, you can find the radius with r = C / (2π) and then enter it to get area and diameter. The tool is radius-based for simplicity; one input gives you all three outputs.
Why use π (pi)?
Pi (π) is the ratio of a circle's circumference to its diameter. For any circle, C ÷ d = π, so π is approximately 3.14159 and is the same for all circles. It appears in both the area and circumference formulas. Calculators and this tool use a precise value of π so results are accurate to many decimal places. When you need a quick mental estimate, π ≈ 3.14 is often enough; for exact work, use the value from the calculator. The circle calculator uses the full precision of π so your area, circumference, and diameter are computed accurately from the radius you enter.
Applications of circle calculations
Circle area, circumference, and diameter are used in many fields. In construction and landscaping, area determines material quantities; circumference helps with edging and borders. In engineering, pipe and cable cross-sections are often circular; diameter is a standard spec. In education, circle formulas are a core part of geometry. In design and graphics, circles are used for logos, buttons, and layouts. This circle calculator helps you get quick, accurate results without manual formula work—whether you are a student, designer, or professional. Always use consistent units: if the radius is in feet, area is in square feet and circumference and diameter are in feet.
Summary
This circle calculator finds the area, circumference, and diameter of a circle from the radius. Enter the radius (a positive number) and get area = πr², circumference = 2πr, and diameter = 2r instantly. The tool is free, runs in the browser, and requires no account. Use it for homework, design, construction, or any task involving circles. Remember to keep units consistent: the same unit for radius, circumference, and diameter, and square units for area.