Diameter to Radius Calculator
Enter a diameter or a radius and the calculator fills in the other value along with the circumference and area of the circle. You can work in either direction: type the diameter and get the radius, or type the radius and get the diameter. Switch freely between millimetres, centimetres, metres, inches, and feet - every result updates as you type.
Formula
Worked example
A circle with diameter 10 cm: radius = 10 / 2 = 5 cm. Circumference = 2 x pi x 5 = 31.416 cm. Area = pi x 5^2 = 78.540 cm^2.
Diameter and radius: what they are
The radius of a circle is the distance from the exact centre of the circle to any point on its edge. The diameter is a straight line that passes through the centre and connects two opposite points on the edge. Because it crosses the centre, the diameter is always exactly twice as long as the radius. These two measurements are fundamental to every circle calculation: circumference, area, arc length, and sector area all start with radius or diameter.
The formulas behind the calculator
Converting between the two values is a single arithmetic step in either direction. To find the radius from the diameter, divide by 2: r = d/2. To find the diameter from the radius, multiply by 2: d = 2r. Once you have the radius, the circumference follows from C = 2 x pi x r (equivalently C = pi x d), and the enclosed area from A = pi x r squared. This calculator carries out all four values at once so you never need to do multiple separate lookups.
Bidirectional conversion and unit flexibility
The calculator works in both directions. If you know the diameter (perhaps a pipe fitting, wheel rim, or round table), select "Radius (from diameter)" and type the diameter. If you know the radius instead (perhaps from a geometry problem or a radius stamp on a lens), select "Diameter (from radius)" and type the radius. The unit selector covers millimetres, centimetres, metres, inches, and feet, so you can match the unit on the object or drawing without any manual conversion. All four outputs - radius, diameter, circumference, and area - are reported in that same unit (area in the squared version of it).
Practical uses
Plumbers and engineers use this conversion when working with pipe diameters listed on fittings but need the radius for bending calculations. Woodworkers and fabricators cut circular pieces from diameter specs but draw arcs using a compass set to the radius. Cyclists convert wheel diameters to radii for speed and gear-ratio computations. Architects and interior designers convert column diameters to radii when laying out curved walls or round seating areas. Teachers and students use the calculator to check homework and explore how circumference and area scale with size: doubling the diameter doubles the circumference but quadruples the area, because area grows with the square of the radius.
Common diameter and radius pairs
| Diameter | Radius | Circumference | Area |
|---|---|---|---|
| 1 | 0.5 | 3.14159 | 0.7854 |
| 2 | 1 | 6.28319 | 3.14159 |
| 5 | 2.5 | 15.70796 | 19.63495 |
| 10 | 5 | 31.41593 | 78.53982 |
| 20 | 10 | 62.83185 | 314.15927 |
| 50 | 25 | 157.07963 | 1963.49541 |
| 100 | 50 | 314.15927 | 7853.98163 |
Quick reference for frequently used circle sizes (values in same unit as input).
Frequently asked questions
What is the relationship between diameter and radius?
The diameter of a circle is always exactly twice the radius. Stated as formulas: d = 2r, and r = d/2. There are no exceptions: this relationship holds for every circle regardless of size or unit.
How do I convert diameter to radius?
Divide the diameter by 2. For example, a diameter of 14 inches gives a radius of 7 inches. If the diameter is 3.5 metres the radius is 1.75 metres. The operation is always the same single step.
How do I convert radius to diameter?
Multiply the radius by 2. A radius of 6 cm gives a diameter of 12 cm. A radius of 0.5 miles gives a diameter of 1 mile. Again, one step in either direction.
How does diameter relate to circumference?
Circumference equals pi times the diameter, C = pi x d (approximately 3.14159 x d). This is the same as 2 x pi x r. For a circle with a 10 cm diameter the circumference is about 31.42 cm.
How do I find the area from the diameter?
First find the radius (r = d/2), then use A = pi x r squared. Equivalently you can use A = pi x d squared / 4 directly. For a diameter of 10 cm: r = 5, area = pi x 25 = 78.54 cm squared.
Does it matter which unit I use?
The unit affects the numeric value of the answer but not the method. As long as you enter the diameter in the same unit you select in the dropdown, every output - radius, circumference, and area - is returned in that unit (area in the squared version). Converting between units beforehand, or after, is separate from the diameter-to-radius conversion itself.
Why does area grow so much faster than circumference when the diameter increases?
Circumference grows linearly with radius, so doubling the diameter doubles the circumference. Area grows with the square of the radius, so doubling the diameter multiplies the area by four (2 squared = 4). Tripling the diameter gives nine times the area. This is why large circular shapes - pools, pipes, wheels - need disproportionately more material as they scale up.