Enter Radius
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Unit:
Enter the radius of the circle
Examples:
⭕ Circle Visual
Circle Formulas — Area, Circumference, Diameter & Radius
All circle measurements are related through a single value: the radius (r). Once you know the radius, everything else follows from two core formulas.
Area: A = π × r² | Circumference: C = 2 × π × r
Diameter: d = 2r | Radius from diameter: r = d/2
Radius from circumference: r = C / (2π) | Radius from area: r = √(A/π)
Diameter: d = 2r | Radius from diameter: r = d/2
Radius from circumference: r = C / (2π) | Radius from area: r = √(A/π)
Arc Length and Sector Area
Arc Length = (θ / 360) × 2πr
Sector Area = (θ / 360) × πr²
where θ = central angle in degrees
Sector Area = (θ / 360) × πr²
where θ = central angle in degrees
Real-World Uses of Circle Calculations
- Pizza: A 12" pizza has radius=6" → Area=π×36≈113 in². A 16" pizza has 78% more area than 12"!
- Wheels & Tires: Circumference = rolling distance per rotation. r=35cm → C=220cm per rotation
- Swimming Pools: Circular pool with r=3m → Area=28.27 m² → Volume = Area × depth
- Engineering: Pipe cross-sections, flange sizing, circular plates
- Gardening: Circular garden bed area for soil/mulch calculation
Value of π (Pi)
π = 3.14159265358979... It is the ratio of any circle's circumference to its diameter. π is irrational — its decimal representation never ends or repeats. This calculator uses π to 10 significant figures for accurate results.
Quick Reference — Circle Formulas
From radius (r): d=2r | C=2πr | A=πr²
From diameter (d): r=d/2 | C=πd | A=πd²/4
From circumference (C): r=C/2π | d=C/π | A=C²/4π
From area (A): r=√(A/π) | d=2√(A/π) | C=2√(πA)
From diameter (d): r=d/2 | C=πd | A=πd²/4
From circumference (C): r=C/2π | d=C/π | A=C²/4π
From area (A): r=√(A/π) | d=2√(A/π) | C=2√(πA)
Common Circle Values (Exact)
r=1: d=2, C=2π≈6.2832, A=π≈3.1416
r=5: d=10, C=10π≈31.416, A=25π≈78.540
r=10: d=20, C=20π≈62.832, A=100π≈314.159
r=7: d=14, C=14π≈43.982, A=49π≈153.938
r=5: d=10, C=10π≈31.416, A=25π≈78.540
r=10: d=20, C=20π≈62.832, A=100π≈314.159
r=7: d=14, C=14π≈43.982, A=49π≈153.938
Chord Length Formula
Chord = 2 × r × sin(θ/2)
where θ = central angle in degrees
Example: r=5, θ=60° → Chord = 2×5×sin(30°) = 2×5×0.5 = 5 cm
where θ = central angle in degrees
Example: r=5, θ=60° → Chord = 2×5×sin(30°) = 2×5×0.5 = 5 cm
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