Radius 5 — find all properties
Input: r = 5
Output: Diameter = 10; Circumference ≈ 31.42; Area ≈ 78.54
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Circle Calculator
Calculate all circle properties — area, circumference, diameter, radius, arc length, and sector area from any single input.
About Circle Calculator
The Circle Calculator computes all properties of a circle from a single input — enter any one of radius, diameter, area, or circumference and every other property is calculated instantly. The tool also includes an arc length and sector area calculator, where you provide the radius and central angle in degrees to find the arc length and sector area. All results use the exact value of π (Math.PI in JavaScript) for maximum precision. Unit flexibility allows inputs in mm, cm, m, inches, feet, or any custom unit, with all outputs in the same unit system. The constant π is irrational and transcendental — its decimal representation never terminates or repeats. JavaScript's Math.PI provides 64-bit double-precision (about 15-16 significant digits), which is more than sufficient for any practical engineering or geometry calculation.
Why use Circle Calculator
- 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 Circle Calculator
- 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 to use Circle Calculator
- 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
Output: Radius ≈ 5.642; Diameter ≈ 11.28; Circumference ≈ 35.45
Sector area: r=10, central angle 60°
Input: r = 10, θ = 60°
Output: Arc length ≈ 10.47; Sector area ≈ 52.36; Chord length ≈ 10.0
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.