Circle Calculator

A circle is fully described by a single measurement. The radius, diameter, area, and circumference are all mathematically linked through pi. Know one and you know all four. This calculator handles any starting point and returns the complete set. The relationship is straightforward: diameter is twice the radius, circumference is 2πr, and area is πr². The only subtlety is working backward from area or circumference, which requires a square root or division by 2π respectively. This calculator is useful for anything circular: sizing a circular garden bed, finding the coverage of a round table, calculating pipe cross-sections, or checking geometry homework.

• Landscaping and garden beds: Enter the diameter of a round garden bed to find the area for mulch or soil calculations, or enter area to check what diameter fits the space.
• Pipe and duct sizing: Plumbers and HVAC engineers start with a known pipe diameter and need the cross-sectional area to calculate flow rates.
• Wheels and circular components: Given a tire's diameter, find the circumference to calculate distance per revolution. Or start with a circumference to find the corresponding wheel size.
• Geometry and math education: Students can enter any known measurement and verify all related values, checking their manual calculations step by step.

1. 1Select which measurement you already know: radius, diameter, area, or circumference.
2. 2Enter the numerical value in the input box.
3. 3The calculator converts your input to the radius as an intermediate step.
4. 4It then computes the remaining three measurements from the radius.
5. 5All four values are displayed in the results.

• Confusing radius and diameter: Many people give the diameter when asked for the radius. If your measurement is from edge to edge through the center, that is the diameter. The calculator has an explicit "Diameter" input to avoid this error.
• Wrong units for area: If your radius is in centimeters, the area is in cm², not cm. A circle with a 5 cm radius has an area of about 78.5 cm², not 78.5 cm.
• Using diameter in the area formula directly: A = πr², not πd². Using the diameter directly gives a result four times too large. Always use the radius in the area formula.
• Rounding pi too early: Using 3.14 instead of the full value of π introduces errors that grow with the size of the circle. For precise work, carry at least 6 decimal places of π or let the calculator handle it.

• Start from whatever you measured: No need to convert before entering. If you measured the circumference of a pipe with a tape measure, select "Circumference" and enter that value directly.
• Doubling the radius increases area by 4x: Because area scales as r², doubling the radius quadruples the area. This matters for circular gardens, pools, and pipes: a pipe with twice the radius carries four times the flow at the same velocity.
• Use circumference for distance-per-revolution: The circumference equals the distance a wheel covers in one full rotation. Useful for calculating speedometer calibration, conveyor belt length, or gear ratios.
• Area of a half or quarter circle: Calculate the full circle area first, then divide by 2 or 4. A semicircle with radius 5 has area (78.54)/2 = 39.27 square units.