⭕ Area of a Circle Calculator
Calculate the area of a circle
How to Use This Calculator
Choose What You Know
Select whether you know the radius, diameter, or circumference of the circle.
Enter Your Value
Input the known measurement. Make sure it's a positive number.
Calculate
Click the "Calculate Area" button to get the area and all related measurements.
Formula
Area = π × r²
Where r is the radius of the circle
Alternative Formulas:
- Area = π × (d/2)² where d is diameter
- Area = C² / (4π) where C is circumference
Where:
- π (pi) ≈ 3.14159...
- r = radius (distance from center to edge)
- d = diameter (distance across through center) = 2r
- C = circumference (distance around) = 2πr
Example 1: Find area for r = 5 units
Area = π × 5² = π × 25 = 78.54 square units
Using π ≈ 3.14159
Example 2: Find area for d = 10 units
Step 1: Radius = 10 / 2 = 5 units
Step 2: Area = π × 5² = 78.54 square units
Example 3: Find area for C = 31.42 units
Step 1: Radius = 31.42 / (2π) ≈ 5 units
Step 2: Area = π × 5² = 78.54 square units
About Area of a Circle Calculator
The Area of a Circle Calculator computes the space enclosed within a circle. The area represents the amount of 2D space inside the circle's boundary, measured in square units.
When to Use This Calculator
- Construction: Calculate material needed for circular surfaces (pools, patios, floors)
- Landscaping: Determine area for circular gardens, lawns, or flower beds
- Design: Plan circular furniture, rugs, or decorative elements
- Mathematics: Solve geometry problems and verify calculations
- Real Estate: Calculate usable space in circular rooms or structures
- Education: Learn and practice circle area concepts
Why Use Our Calculator?
- ✅ Multiple Input Options: Works with radius, diameter, or circumference
- ✅ Instant Results: Calculate area immediately
- ✅ Comprehensive Output: Shows all circle measurements
- ✅ Accurate: Precise mathematical calculations
- ✅ Educational: Displays formulas and calculation steps
- ✅ 100% Free: No registration required
Understanding Circle Area
The area of a circle is π (pi) times the square of the radius. This formula comes from calculus and geometry, representing the accumulation of space within the circular boundary.
- Area grows with the square of the radius (doubling radius quadruples area)
- The formula πr² is one of the most famous in mathematics
- Circle area is always less than a square with side equal to diameter
- For a square inscribed in a circle: square area = (diameter)² / 2
Real-World Applications
Pool Construction: Calculate the area of a circular pool to determine the amount of tile, paint, or other materials needed.
Pizza Size Comparison: Compare pizza areas. A 12-inch pizza (r=6) has area 113.1 in², while an 8-inch pizza (r=4) has area 50.3 in².
Garden Planning: Determine how many plants can fit in a circular garden bed based on spacing requirements.
Manufacturing: Calculate material usage for circular components, gaskets, or circular cutouts.
Frequently Asked Questions
Why is the area formula πr² and not 2πr?
2πr gives the circumference (1D perimeter). πr² gives the area (2D space inside). The squared term accounts for two dimensions. Think of it as the circle "sweeping out" area as the radius increases.
What's the difference between area and circumference?
Area is the 2D space inside (measured in square units). Circumference is the 1D distance around (measured in linear units). They're completely different measurements with different units.
How do I find area if I only know the diameter?
Divide diameter by 2 to get radius, then use Area = πr². Or use Area = π × (d/2)² = π × d²/4 directly.
Can area be negative?
No, area is always positive. It represents physical space, which cannot be negative. Even if you enter a negative radius, the calculator uses the absolute value.
What if I need to find the area of part of a circle?
For a sector (pie slice), multiply the full area by (angle/360°) or (angle/2π) if using radians. Sector Area = (θ/360°) × πr².
How accurate is π in the calculation?
Calculators typically use π to many decimal places (15+ digits). For most practical purposes, π ≈ 3.14 or 3.14159 is sufficient. The calculator uses high precision automatically.
What units should I use?
Any consistent unit works! If radius is in inches, area is in square inches. If radius is in meters, area is in square meters. Just keep units consistent.