Circumference to Radius Calculator
A circumference to radius calculator converts the outer perimeter of a circle into its radius using the formula R = C ÷ (2π). Enter the circumference and get the radius, diameter, and area in real-time with interactive visualization.
What is a Circumference to Radius Calculator?
A circumference to radius calculator is an online tool that converts the outer perimeter of a circle into its radius using the formula R = C ÷ (2π). This tool exists because finding the radius from circumference requires dividing by 2π (≈ 6.28318) — a calculation that is not intuitive to do mentally. Engineers, students, and professionals use this tool to quickly determine the radius from any known circumference, along with the diameter and area, for applications in circular track design, pipe sizing, and geometry coursework.
The Radar Sweep
R = C ÷ 2πCircumference to Radius Calculator Formula
The circumference to radius formula is R = C ÷ (2π), where C is the circumference and π (Pi) is the mathematical constant approximately equal to 3.14159265. This formula works because the circumference of every circle equals 2 times Pi (π) times the radius (C = 2πR). Rearranging that equation gives the radius from any known circumference value.
Circumference to Radius Conversion Chart
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.283 | 3.142 |
| 5 | 10 | 31.416 | 78.54 |
| 10 | 20 | 62.832 | 314.159 |
| 25 | 50 | 157.08 | 1963.495 |
| 50 | 100 | 314.159 | 7853.982 |
| 100 | 200 | 628.318 | 31415.927 |
| 250 | 500 | 1570.796 | 196349.541 |
| 500 | 1000 | 3141.593 | 785398.163 |
All values in standard units. Circumference = 2πR • Area = πR²
Circumference to Radius Ratio
The ratio of a circle's circumference to its radius is the constant 2π (approximately 6.28318). For every circle — regardless of size — dividing circumference by radius always yields: 3.14159265...
The 2π Uncoiling Spiral
Every circle's circumference is exactly 2π times its radius. Watch the radius uncoil itself to perfectly map the boundary of the circle.
Circumference and Radius: The Difference
Circumference and radius are 2 distinct measurements of a circle. The circumference is the total curved distance around the outer edge. The radius is the straight-line distance from the center to any point on that edge. One is a perimeter measurement; the other is a linear distance.
Core vs Boundary
Hover over the floating orbs to isolate the perimeter measurement versus the linear core measurement.
CIRCUMFERENCE
The Continuous Boundary
RADIUS
The Core Origin Vector
Circumference vs Radius of a Circle
Circumference and radius of a circle are directly proportional. When the radius doubles, the circumference doubles. This proportionality holds because the circumference over radius ratio is always 2π (≈ 6.28318). Drag the slider to see circumference and radius scale together.
The Expanding Node
Slide to increase the radius vector. Notice how the circumference boundary expands proportionally in perfect sync. The ratio remains locked at 2π.
How to Calculate Radius from Circumference
The circumference radius formula connects these 2 measurements in a single equation. The circumference equals 2 times Pi (π) times the radius. Rearranging gives the radius from any circumference value.
The 2π Division Gate
Watch how the circumference travels through the mathematical gate, being divided by exactly 6.283 (2π) to forge the radius line.
Circumference to Radius: Worked Example
A circular running track has a circumference of 400 meters (1,312.34 feet). To find the radius of the track, divide 400 by 2π.
Running Track Orbit
A standard circular track has a running circumference of exactly 400 meters. Hover to measure the straight-line distance (radius) from the center grassy field to the runner.