Circle Calculator
Calculate all circle properties from any single measurement. Enter the radius, diameter, circumference, or area to instantly find all other values. Essential for geometry, engineering, construction, and design projects.
How to Use This Circle Calculator
- Select what measurement you know: radius, diameter, circumference, or area
- Enter the known value in the input field
- Click "Calculate Circle" or simply type to see instant results
- View all calculated properties: radius, diameter, circumference, and area
The calculator automatically converts between all circle measurements. For example, if you only know the circumference of a circular pool, enter that value to find the radius you need for calculating the area of a pool cover.
What is a Circle?
A circle is a perfectly round shape where every point on its edge is exactly the same distance from the center. This distance is called the radius. The circle is one of the most fundamental shapes in mathematics and appears everywhere in nature, from planets and stars to ripples in water and the pupils of eyes.
Circles have fascinated mathematicians for thousands of years. The ancient Greeks studied circles extensively, and Archimedes calculated one of the first accurate values of pi. Today, circles are essential in engineering, architecture, physics, and design. Understanding circle properties is crucial for calculating everything from gear ratios to satellite orbits.
Circle Formulas
All circle calculations rely on the mathematical constant pi, which is approximately 3.14159265359. Here are the fundamental formulas:
- Diameter from radius:
d = 2r - Radius from diameter:
r = d / 2 - Circumference:
C = 2 x pi x rorC = pi x d - Area:
A = pi x r² - Radius from circumference:
r = C / (2 x pi) - Radius from area:
r = sqrt(A / pi)
Arc length formula: For a portion of the circumference subtended by angle theta (in radians): Arc = r x theta. For degrees: Arc = (theta / 360) x 2 x pi x r