Find radius, diameter, area, circumference, sector area, arc length, chord length and annulus — all from a single known value.
Results update live as you type.
Area
Radius
5 m
r
Diameter
10 m
d = 2r
Area
78.5398 m²
A = πr²
Circumference
31.4159 m
C = 2πr
| Quantity | Symbol | Formula | Unit |
|---|---|---|---|
| Radius | r | — | length |
| Diameter | d | 2r | length |
| Area | A | πr² | area |
| Circumference | C | 2πr | length |
| Sector area | As | ½ r²θ | area |
| Arc length | L | rθ | length |
| Chord | c | 2r sin(θ/2) | length |
| Annulus area | Aa | π(R² − r²) | area |
The Method
Every property of a circle is determined by a single number: its radius. The radius defines the diameter (d = 2r), the circumference (C = 2πr), and the area (A = πr²). The constant π ≈ 3.14159 is the ratio of circumference to diameter — a property of every circle, no matter how big or small. Sector area and arc length use the same constant scaled by the central angle θ (in radians): As = ½ r² θ and L = r θ.
Working for r = 5
About This Tool
A circle calculator — also called a circumference and area calculator — finds every measurable property of a circle from a single known input. Give it the radius, diameter, area, or circumference, and it returns the others. It also handles three closely related shapes: sectors (a "pie slice"), arcs (a curved segment of the circumference), and annuli (the ring between two concentric circles).
Circle geometry is everywhere: pizzas and CDs, tyres and wheels, plumbing and ducting, orbits and gears, logos and dashboards. Knowing how to compute circumference, area, sector area, and arc length lets you size circular tanks, lay out garden borders, plan running tracks, design clock faces, and solve any number of practical problems. The same formulas appear in physics (angular displacement, rotational motion), engineering (gear ratios, belt lengths), and computer graphics (drawing curves, computing pie charts).
The mathematical heart of all of this is the constant π ≈ 3.14159 — the ratio of any circle's circumference to its diameter. π is irrational (its decimal expansion never terminates or repeats) and transcendental (it's not the root of any polynomial with rational coefficients), but for practical work the first 5–8 digits are more than enough. This calculator uses JavaScript's Math.PI, which is accurate to about 16 significant figures.
Use this free circle calculator for homework, DIY projects, engineering quick-checks, or anywhere you need a clean answer in seconds. Everything runs locally in your browser — no sign-up, no data sent anywhere.
Any Input Works
Start from radius, diameter, area or circumference — the rest is solved.
Sector & Arc
Compute sector area, arc length, chord and segment area for any angle.
Annulus / Ring
Find the area between two concentric circles — useful for pipes and rings.
Live Diagram
Auto-scaling SVG diagram updates as you change the inputs.
Multiple Units
Pick metric (m, cm, mm, km) or imperial (ft, in) — units carry through.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Three modes, one diagram, every result in seconds.
Choose Full circle for radius / diameter / area / circumference; Sector / arc for a pie slice; Annulus for the area between two rings.
In Full-circle mode, tell the calculator which value you know — radius, diameter, area or circumference. All other values are derived from this one.
Type the known value (or drag the slider). Pick the unit — metric or imperial — and units carry through to the result (e.g. m for length, m² for area).
The summary card shows every derived quantity — radius, diameter, area, and circumference — alongside a scaled diagram that updates live.
Enter a radius and an angle in degrees. The calculator returns sector area, arc length, chord length and segment area — handy for laying out curves and pie charts.
Enter outer (R) and inner (r) radii. The calculator returns the ring's area — useful for washers, pipe cross-sections, and disc-shaped objects.
Everything you need to know about circles, π, sectors, arcs, and how to interpret your result.
A = π r², where r is the radius and π ≈ 3.14159. If you know the diameter d, area becomes A = π d² / 4. If you know the circumference C, area becomes A = C² / (4π). All three are equivalent — they're just rearrangements of the same identity.
Circumference is the perimeter of a circle — the distance once around. C = 2πr = πd. For r = 1 (the unit circle), C = 2π ≈ 6.2832. The ratio C / d is always exactly π, which is the defining property of the constant.
Sector area = ½ r² θ, where θ is the central angle in radians. To convert from degrees, multiply by π/180: for a 90° sector, θ = π/2, so area = ½ × r² × π/2 = πr² / 4 — exactly a quarter of the full circle's area. For θ = 2π (a full revolution), the formula recovers A = πr².
Arc length L = r θ, with θ in radians. A quarter arc (90°) of a unit circle has length π/2 ≈ 1.5708. A semicircular arc (180°) has length πr. Arc length is also the foundation of angular displacement in physics: the linear distance travelled around a curve is r × (angle swept).
A chord is a straight line connecting two points on a circle. For a chord subtending a central angle θ, its length is c = 2r sin(θ/2). The longest chord is the diameter (θ = 180°, c = 2r). Chords appear in trigonometry (the chord function predates sine and was used by ancient Greek astronomers).
An annulus is the region between two concentric circles — picture a washer, a CD, or a doughnut shadow. Its area is A = π(R² − r²), where R is the outer radius and r is the inner radius. Annuli appear constantly in plumbing (pipe wall cross-sections), mechanical engineering (washers and bearings), and astronomy (planetary ring areas).
π (pi) is the ratio of any circle's circumference to its diameter — about 3.14159265358979… It is both irrational (its decimal expansion never terminates or repeats) and transcendental (it isn't the root of any polynomial with rational coefficients). For practical work, the first 5 – 8 digits are far more than enough. This calculator uses JavaScript's Math.PI, accurate to about 16 significant figures.
Multiply degrees by π/180 to get radians; multiply radians by 180/π to get degrees. Common conversions: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π. Radians are the "natural" unit because arc length and area formulas simplify when angle is in radians — you avoid the π/180 conversion factor.
A sector is a "pie slice" bounded by two radii and an arc. A segment is the region bounded by an arc and the chord that joins its endpoints — like the curved part of a pie slice when you cut off the pointy bit. Segment area = sector area − triangle area = ½ r² (θ − sin θ).
Area measures two-dimensional extent, so units come in pairs: a square metre (m²) is the area of a 1 m × 1 m square. When you multiply two lengths (r × r), the units multiply too: m × m = m². Length stays as a single unit (m), and volume — three multiplied lengths — becomes m³.