Radius of a Circle Calculator

How Radius of a Circle Calculator Works?

The calculator determines a circle's radius from one of three measurements: diameter, circumference, or area. The radius is the distance from the center of a circle to any point on its boundary. A valid positive value is required for each selected input, and the calculator supports linear units such as nm, µm, mm, cm, m, km, in, ft, yd, and mi. Area inputs support mm², cm², m², km², in², ft², yd², mi², hectares, and acres.

Radius from diameter

The diameter is the full distance across the circle through its center, so it contains two radii. Dividing the diameter by two gives the radius.

For example, a diameter of 10 cm produces a radius of 5 cm.

Radius from circumference

The circumference is the complete distance around the circle. The standard circumference relationship is $C=2\pi r$. Rearranging this equation gives the radius formula:

Using a circumference of 31.416 cm gives a radius of approximately 5 cm, with the exact result depending on the value of π and the precision of the entered measurement.

Radius from area

The area of a circle is calculated with $A=\pi r^2$. Solving for the positive radius requires dividing the area by π and taking the square root:

For an area of 78.54 cm², the calculated radius is approximately 5 cm. The positive square-root result is used because a physical radius cannot be negative.

Practical Use Cases

Students: Students can use the calculator to check geometry homework involving circles when a problem provides the diameter, circumference, or enclosed area instead of the radius. It is also useful for comparing the results of rearranging the three standard circle formulas.

Engineers: Engineers can estimate circular dimensions for shafts, pipes, bearings, tanks, and other round components when a drawing or measurement specifies a diameter, boundary length, or cross-sectional area.

Designers: Product, graphic, and industrial designers can determine the radius needed to create circular layouts, rounded components, wheels, buttons, openings, or other radial features from a known overall size or surface area.

Architects and construction professionals: Professionals working with circular rooms, arcs, columns, landscaping features, or site plans can find a radius from a measured circumference or area to support accurate layout and planning.

DIY users and makers: Home users, fabricators, and makers can calculate the radius for circular cutouts, tabletops, garden features, signs, and craft projects when only the full width, perimeter, or surface area is known.

Accuracy and Limitations

The calculator applies the exact geometric relationships $r=d/2$, $r=C/2\pi$, and $r=\sqrt{A/\pi }$, using π to the calculator's numerical precision. Results are only as accurate as the supplied measurements and may be rounded for display. Inputs must be positive and within the calculator's supported ranges: diameter from 0.000001 to 1,000,000,000, circumference from 0.000001 to 10,000,000,000, and area from 0.000001 to 1,000,000,000,000,000. The formulas assume a perfect circle; they do not correct measurements for oval, irregular, distorted, or physically imperfect shapes.

Quick Examples