PanMaths.comFree Printable Math Formula Reference Sheet
Area of a Circle
Geometry • Grades 5, 6, 7, 8
Geometry
Area of a Circle
The essential formula for calculating the space inside any circle.
The Formula
A = πr²
Used for: Finding the 2D area enclosed by a circle given its radius or diameter
AArea of the circle (square units)
πPi constant ≈ 3.14159265...
rRadius (distance from center to boundary)
dDiameter (distance across center = 2r)
⚡Live Interactive Quick Solver
Instant Calculationunits
Calculated Area (A):78.54 units²
Exact form: 25π• Step: A = π × 5² = π × 25 = 78.54
A = \pi r^2 = \frac{\pi}{4} d^2
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🎯 Key Concepts
Understanding these concepts will help you master circle calculations:
📏
Radius = Diameter ÷ 2Always convert diameter to radius first
🔢
π ≈ 3.14159Use 3.14 for quick estimates, π button for exact
📐
Units are squaredIf radius is in cm, area is in cm²
📝 Worked Examples
Example 1: Given Radius
Problem:
Find the area of a circle with radius 5 cm1
Write the formula
A = πr²2
Substitute radius
A = π × (5)²3
Calculate
A = π × 25 = 25π4
Using π ≈ 3.14159
A ≈ 78.54 cm²Answer: A ≈ 78.54 cm² (or 25π cm²)
Example 2: Given Diameter
Problem:
Find the area of a circle with diameter 10 cm1
Find radius
r = d/2 = 10/2 = 5 cm2
Apply formula
A = πr² = π × (5)²3
Calculate
A = 25π ≈ 78.54 cm²Answer: A ≈ 78.54 cm²
Example 3: Finding Radius
Problem:
A circle has area 100 cm². Find its radius.1
Start with formula
A = πr²2
Solve for r²
r² = A/π = 100/π3
Take square root
r = √(100/π) ≈ √31.83Answer: r ≈ 5.64 cm
💡 Pro Tips
Double radius = 4× area
Since area uses r², doubling the radius makes the area 4× larger!
Quick estimation
Area ≈ 3 × r² is a quick mental estimate (since π ≈ 3)
From diameter
A = π(d/2)² = πd²/4 — alternative when given diameter
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