Convert between diameter, radius, circumference, and area of a circle. Batch mode for multiple values, circle diagram, and complete conversion table.
The diameter-to-radius calculator instantly converts between the four fundamental measurements of a circle: diameter, radius, circumference, and area. The relationships are elegantly simple — the radius is half the diameter, the circumference is π times the diameter, and the area is π times the radius squared — yet these conversions come up constantly in everyday life and professional work. A plumber needs the radius from a pipe diameter, a landscaper needs the area from a sprinkler circumference, and a machinist needs a diameter from a bore radius. This calculator goes beyond a simple converter: enter any one measurement and get all others instantly, use batch mode to convert a whole list of values at once, and see the relationships visualized in a circle diagram. Presets cover common sizes, and you can choose from millimeters to feet. The proportions bar illustrates the famous C/d = π ratio that has fascinated mathematicians for millennia, from the ancient Babylonians who approximated π as 3.125 to modern computers that have calculated trillions of digits.
Circle measurement conversions are simple formulas but come up frequently in plumbing, machining, landscaping, sewing, and schoolwork. Instead of remembering whether to multiply or divide by 2 or π, enter any one value and get all four instantly. Batch mode handles entire lists at once, and the proportions bar visualizes the C/d = π relationship that connects all the formulas.
d = 2r r = d/2 C = πd = 2πr A = πr² = πd²/4
Result: 10: radius = 5
For diameter = 10: radius = 5, circumference ≈ 31.416, area ≈ 78.540.
The ratio of circumference to diameter, π, has been studied for over 4,000 years. Ancient Babylonians used 3.125, Egyptians used 256/81 ≈ 3.16, and Archimedes bounded it between 3 10/71 and 3 1/7 using inscribed and circumscribed 96-gons. Today π is known to trillions of digits, but for circle conversions, 15 digits of precision (IEEE 754 double) more than suffice. The relationships d = 2r, C = πd, and A = πr² are among the most universally used formulas in all of mathematics.
Plumbing and HVAC work specifies pipes by nominal diameter. A 6-inch pipe has radius 3 inches, circumference ≈ 18.85 inches, and cross-sectional area ≈ 28.27 in². Landscapers calculate sprinkler coverage from the spray radius. Machinists measure bore diameter with calipers and need the radius for CNC programming. This calculator handles all these conversions from any starting measurement.
When working with multiple circle sizes (e.g., a set of pipe fittings: 1/2", 3/4", 1", 1-1/4", 1-1/2", 2"), batch mode converts all diameters to radii, circumferences, and areas in a single step. Notice that area scales with the square of the diameter — doubling the diameter quadruples the area — which is why flow rates through pipes increase dramatically with diameter.
The diameter is exactly twice the radius: d = 2r. Conversely, r = d/2.
Multiply the diameter by π: C = πd. This is the fundamental definition of π.
Yes. Since A = πr², you can solve for r = √(A/π). The calculator handles this automatically.
Enter multiple values separated by commas to convert them all at once — useful for converting a list of pipe sizes or circle dimensions. Use this as a practical reminder before finalizing the result.
π is the ratio of any circle's circumference to its diameter; it appears in every circle formula and is approximately 3.14159265.
Any consistent unit works. The calculator supports mm, cm, m, inches, and feet, but the formulas are unit-agnostic.