Circle Geometry Calculator - Radius, Area & Circumference
Calculate all circle properties including radius, diameter, area, circumference, arc length, and sector area. Get instant results with complete formulas and explanations.
Circle Measurements
Formulas Used
Basic Properties:
• Diameter: d = 2r
• Radius: r = d/2
• Area: A = πr²
• Circumference: C = 2πr = πd
Arc & Sector (with angle θ):
• Arc Length: s = rθ (θ in radians)
• Sector Area: A = ½r²θ (θ in radians)
Note: 1° = π/180 radians
Results
What is a Circle Geometry Calculator?
A Circle Geometry Calculator is a comprehensive tool that computes all essential properties of a circle based on a single input. Enter either the radius or diameter to instantly calculate area, circumference, and other geometric properties.
This calculator provides:
- Basic Properties - Radius, diameter, area, and circumference
- Arc Calculations - Arc length based on central angle
- Sector Area - Area of circular sectors with any angle
- Real-time Updates - Instant calculations as you type
For right triangle calculations, try our Pythagorean Theorem Solver with step-by-step solutions.
To find distance and midpoints between points, check our Distance, Midpoint & Slope Calculator for coordinate geometry.
For solving quadratic equations, use our Quadratic Equation Solver with multiple solution methods.
How the Calculator Works
The calculator uses fundamental circle geometry formulas:
Basic Formulas:
• Diameter: d = 2r
• Area: A = πr²
• Circumference: C = 2πr = πd
Arc & Sector Formulas:
• Arc Length: s = rθ (θ in radians)
• Sector Area: A = ½r²θ (θ in radians)
• Conversion: θ(rad) = θ(deg) × π/180
Where:
- r = radius (distance from center to edge)
- d = diameter (distance across through center)
- π ≈ 3.14159 (pi, the circle constant)
- θ = central angle (in radians or degrees)
Key Concepts Explained
Radius
The distance from the center of the circle to any point on its edge. All radii of a circle are equal.
Diameter
The distance across the circle through its center. Always twice the radius (d = 2r).
Circumference
The total distance around the circle's edge. The perimeter of a circle.
Area
The space enclosed within the circle. Measured in square units (e.g., cm², m²).
Arc Length
The distance along the curved line of the circle between two points.
Sector Area
The area of a "slice" of the circle, bounded by two radii and an arc.
How to Use This Calculator
Choose Input Method
Select "By Radius" or "By Diameter"
Enter Value
Input your radius or diameter
Add Angle (Optional)
Enter angle for arc/sector calculations
View Results
Get all circle properties instantly
Benefits of Using This Calculator
- • All-in-One Tool: Calculate all circle properties from a single input.
- • Instant Calculations: Get immediate results with high precision.
- • Comprehensive Results: Includes basic properties plus arc and sector calculations.
- • Clear Formulas: Shows all formulas used for educational purposes.
- • Flexible Input: Enter radius or diameter based on what you know.
Factors That Affect Your Calculations
1. Units of Measurement
Ensure consistent units (cm, m, inches, etc.). Area will be in square units, circumference in linear units.
2. Precision of Pi
This calculator uses π ≈ 3.14159265359 for accurate results. More decimal places increase precision.
3. Angle Units
Arc and sector calculations require angles. Enter in degrees; the calculator converts to radians automatically.
4. Input Validation
Radius and diameter must be positive numbers. Angles should be between 0° and 360°.
Frequently Asked Questions (FAQ)
Q: What is the relationship between radius and diameter?
A: The diameter of a circle is always twice the radius (d = 2r). Conversely, the radius is half the diameter (r = d/2). This is a fundamental relationship in circle geometry.
Q: How do you calculate circle area?
A: The area of a circle is calculated using the formula A = πr², where r is the radius. Pi (π) is approximately 3.14159. For example, a circle with radius 5 has area = π × 5² = 78.54 square units.
Q: What is circumference?
A: Circumference is the distance around the circle's edge (the perimeter). It's calculated as C = 2πr or C = πd, where r is radius and d is diameter. It represents the total length of the circle's boundary.
Q: What is pi (π)?
A: Pi (π) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter (C/d). Pi is an irrational number with infinite non-repeating decimals.
Q: How do you find arc length?
A: Arc length is calculated using the formula s = rθ, where r is the radius and θ is the central angle in radians. If the angle is in degrees, first convert to radians by multiplying by π/180.