Diameter to Radius Calculator
Convert between diameter and radius measurements with step-by-step calculations
Circle Diameter and Radius Converter
The distance across the circle through its center
Calculated radius value
Formula Used
r = d ÷ 2
Radius equals diameter divided by 2
Example Problems
Example 1: Diameter to Radius
Problem: A circular table has a diameter of 150 cm. What is its radius?
Solution:
• Formula: r = d ÷ 2
• r = 150 ÷ 2
• Answer: r = 75 cm
Example 2: Radius to Diameter
Problem: A wheel has a radius of 35 inches. What is its diameter?
Solution:
• Formula: d = r × 2
• d = 35 × 2
• Answer: d = 70 inches
Example 3: Real-world Application
Problem: A circular pool has a radius of 4 meters. What's its diameter and circumference?
Solution:
• Diameter: d = r × 2 = 4 × 2 = 8 m
• Circumference: C = 2πr = 2π(4) = 25.133 m
• Answer: Diameter = 8 m, Circumference = 25.133 m
Quick Reference
Key Relationships
• Diameter = 2 × Radius
• Radius = Diameter ÷ 2
• Circumference = π × Diameter
• Area = π × Radius²
Important Facts
• Radius is half the diameter
• Diameter is the longest chord
• All radii are equal length
• π ≈ 3.14159
Common Applications
Construction
Circular foundations, pipes, tanks
Automotive
Wheels, gears, engine components
Manufacturing
Bolts, screws, circular parts
Home Projects
Tables, pools, garden beds
Understanding Diameter and Radius
What is Diameter?
The diameter is the longest straight line that can be drawn across a circle. It passes through the center of the circle and connects two points on the circumference that are directly opposite each other. The diameter is always exactly twice the length of the radius.
What is Radius?
The radius is the distance from the center of a circle to any point on its circumference. All radii of a circle are equal in length. The radius is exactly half the length of the diameter.
Why is this Important?
- •Essential for calculating area and circumference
- •Critical in engineering and construction
- •Used in manufacturing specifications
- •Important for fitting circular components
Conversion Formulas
Diameter to Radius
r = d ÷ 2
Divide the diameter by 2 to get the radius
Radius to Diameter
d = r × 2
Multiply the radius by 2 to get the diameter
Related Formulas
• Circumference = π × d = 2π × r
• Area = π × r² = π × (d÷2)²
Common Mistakes to Avoid
- • Don't confuse radius with diameter
- • Remember: diameter is always larger
- • Check units are consistent
- • Verify calculations with reverse formula