Radius 5 — find all properties
Input
r = 5
Expected result
Diameter = 10; Circumference ≈ 31.42; Area ≈ 78.54
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Calculators
Circle Calculator
Calculate all circle properties — area, circumference, diameter, radius, arc length, and sector area from any single input.
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About this tool
The Circle Calculator computes radius, diameter, area, and circumference from any one of those measurements. It also calculates arc length and sector area when you provide a radius and a central angle in degrees. Results use JavaScript's Math.PI and are rounded to six decimal places for display. The calculator is unit-neutral: enter values in a consistent length unit and the linear results use that unit while area uses its squared form. It accepts positive values only; it does not calculate chord length, circle segments, or three-dimensional solids.
Why use it
Enter any one value and all other circle properties are derived automatically.
Includes arc length and sector area calculation.
High-precision results using JavaScript's Math.PI constant.
Supports multiple unit systems with consistent output labeling.
Single source of truth for any circle property — eliminates the need to manually rearrange π formulas.
Privacy-first: all geometry inputs stay in your browser, no values logged or transmitted.
How to use
- Enter any one circle property: radius, diameter, area, or circumference.
- All other properties are calculated instantly.
- For arc/sector calculations, enter radius and central angle in degrees.
- Copy any individual result using the copy button next to it.
- If your input is a circumference and you need fabric/length, switch to the cm/m unit system for direct material planning.
- For multi-circle layouts, copy the radius value and apply to each subsequent circle to maintain consistency.
When it helps
- Geometry homework involving circles, sectors, or arcs.
- Engineering or construction calculations for circular components.
- Converting between circle measurements (area to radius, circumference to diameter).
- Calculating fabric, fencing, or material needed for circular shapes.
- Designing round tables, garden layouts, or other circular components and needing exact dimensions.
- Working geometry homework where quick conversion between radius, diameter, area, and circumference is needed.
Examples
Area 100 — find radius and circumference
Input
Area = 100
Expected result
Radius ≈ 5.642; Diameter ≈ 11.28; Circumference ≈ 35.45
Sector area: r=10, central angle 60°
Input
r = 10, θ = 60°
Expected result
Arc length ≈ 10.47; Sector area ≈ 52.36
Tips
- Always confirm whether the input is the radius or diameter — the most common error is entering diameter when the formula expects radius.
- For arc/sector problems, double-check whether the angle is in degrees or radians before computing — both are valid inputs in different contexts.
- For practical applications (cutting fabric, fence layout), add a 5-10% material buffer to the calculated circumference for waste and overlaps.
- When the problem gives only chord length and arc height, use the formula r = (h² + (chord/2)²) / (2h) to find the radius first.
- Approximate π as 22/7 only for back-of-envelope estimates — the calculator uses Math.PI for full 15-digit precision.
- Sector area scales linearly with central angle — half a sector (angle/2) has half the area, useful for proportional planning.
Frequently Asked Questions
What is the formula for circle area?
Area = π × r², where r is the radius.
What is the formula for circumference?
Circumference = 2 × π × r = π × d, where r is radius and d is diameter.
What is a sector?
A sector is a pie-slice portion of a circle defined by two radii and the arc between them. Its area = (θ/360) × π × r², where θ is the central angle in degrees.
What is arc length?
Arc length is the distance along the curved edge of a sector: arc = (θ/360) × 2πr.
What value of π is used?
The tool uses JavaScript's Math.PI (3.141592653589793), providing 15-digit precision.
How does this compare to a CAD tool's circle properties?
Identical math, but this tool is browser-instant for back-of-envelope work without opening AutoCAD or SolidWorks. For drafting with tolerances and dimensions, CAD remains the right tool — this is for quick lookups.
How precise is the π value used?
The tool uses JavaScript's Math.PI = 3.141592653589793 (15 significant digits). This exceeds the precision needed for any practical application — even space mission calculations use 15-16 digits.
Can I use it for cylinder or sphere calculations?
Indirectly — compute the circle's area or circumference, then multiply by length (cylinder volume = area × height) or use 4πr² for sphere surface area. A dedicated 3D solid solver gives volumes directly.
Explore the category
Glossary
- Radius (r)
- Distance from the center of a circle to any point on its edge. Half the diameter.
- Diameter (d)
- Distance across a circle through the center; d = 2r. The longest chord of a circle.
- Circumference (C)
- The total perimeter (boundary length) of a circle. C = 2πr = πd.
- Area (A)
- The two-dimensional space inside a circle. A = πr².
- Arc length (s)
- Length along the curved edge between two points. s = rθ (θ in radians) or s = (θ/360) × 2πr (degrees).
- Sector
- A pie-slice region bounded by two radii and an arc. Sector area = ½r²θ (radians) or (θ/360) × πr² (degrees).
- Chord
- A straight line segment whose endpoints both lie on the circle. Length = 2r·sin(θ/2) where θ is the central angle.