Calculators
Circle Calculator
Solve radius, diameter, circumference, and area from one measurement, with common length units.
Circle Calculator tool
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About This Tool
A circle's main measurements are tightly connected: knowing just one of radius, diameter, circumference, or area is enough to determine the others. This calculator handles the rearrangement automatically, which is useful when a drawing, measurement, homework problem, craft project, or engineering sketch gives a different starting value than the quantity you need. It keeps units generic so you can work in millimeters, centimeters, meters, inches, feet, or another consistent length unit.
How To Use It
- Choose the circle measurement you already know: radius, diameter, circumference, or area.
- Enter a non-negative number or a simple π expression such as 100π. If you enter a length, keep that length unit consistent; if you enter area, use the corresponding square unit.
- Read the calculated radius, diameter, circumference, and area. Length results are in your chosen length unit and area is in square units.
- Use the labeled diagram to distinguish the radius from the full diameter and connect the circumference and area formulas to the circle.
- Use the formulas and precision notes below when you need to show your working or interpret a measured value.
Examples
Radius of 5 cm
For r = 5 cm, the diameter is 10 cm, circumference is 10π ≈ 31.416 cm, and area is 25π ≈ 78.540 cm².
Diameter of 12 inches
A 12 in diameter means a 6 in radius. The circumference is 12π ≈ 37.699 in and the area is 36π ≈ 113.097 in².
Area back to radius
If a circle has area 100π in², r = √(A/π) gives a radius of 10 in, a diameter of 20 in, and a circumference of 20π in.
Useful Notes
Radius and diameter
The radius r runs from the center to the circle. The diameter d crosses the circle through its center and is twice the radius: d = 2r. Rearranging gives r = d/2.
Reading the circle diagram
The center-to-edge segment is the radius, while the full line through the center is the diameter. The outer boundary represents circumference, and the filled interior represents area. The drawing explains the relationships but is not a printable scale drawing.
Circumference formula
Circumference is the distance around a circle. C = 2πr, which is also C = πd. If circumference is known, radius is r = C/(2π) and diameter is d = C/π.
Area formula
Circle area is A = πr². To recover radius from area, use r = √(A/π). Because area is squared, an area input must use square units such as cm² when the desired length outputs are centimeters.
How units carry through
Radius, diameter, and circumference are lengths and share the same length unit. Area uses the square of that unit. For example, entering a radius in meters produces lengths in meters and area in square meters. Do not mix centimeters and inches within the same calculation.
Exact values and rounding
Many circle results contain π and cannot be written exactly as a terminating decimal. You can enter simple forms such as 100π, 100*pi, or pi. The calculator displays exact π forms when the algebra remains simple, alongside a practical decimal result.
Measurement precision
A calculated result cannot make a physical measurement more precise. If a measured diameter is approximate, the derived circumference and area are approximate too. Area is especially sensitive because it depends on the square of radius.
FAQ
How do I find circumference from diameter?
Multiply diameter by π: C = πd. For diameter 10 units, circumference is about 31.416 units.
How do I find radius from circumference?
Divide circumference by 2π: r = C/(2π).
How do I find radius from area?
Divide area by π and take the square root: r = √(A/π).
Can I use inches or centimeters?
Yes. Use any consistent unit. Length results keep that unit, while area is expressed in the corresponding square unit.
Why is zero allowed?
A zero-radius circle is a degenerate mathematical boundary with zero diameter, circumference, and area. Physical circular objects normally have positive dimensions.