Calculate circle radius from circumference (\(r = \frac{C}{2\pi}\)), diameter (\(d = \frac{C}{\pi}\)), and circle area (\(A = \frac{C^2}{4\pi}\)). Convert between radius, diameter, circumference, and area with inscribed polygon analytics.
Select known parameter and enter your measurement.
Diameter: 10.000 m • Area: 78.540 m² • r = C / 2π
| ⭕ Circle Radius (\(r\)) | 5.000 m |
| 📏 Circle Diameter (\(d\)) | 10.000 m (2r) |
| 🔄 Circumference (\(C\)) | 31.416 m (2πr) |
| 🍰 Circle Area (\(A\)) | 78.540 m² (πr²) |
| 🌓 Semicircle Perimeter | 25.708 m (πr + 2r) |
| ⏹️ Inscribed Square Side | 7.071 m (r√2) |
| 🔲 Circumscribed Square Side | 10.000 m (2r) |
| 🔺 Inscribed Equilateral Triangle | 8.660 m (r√3) |
In physical measurements, measuring straight through the center of a circular object to find its radius or diameter is frequently impossible. For existing tree trunks, large columns, sports balls, circular storage tanks, and pipelines, wrapping a flexible measuring tape around the outer perimeter to measure circumference (\(C\)) is the only practical option. Our Circumference to Radius Calculator solves essential real-world challenges:
Foresters measuring Diameter at Breast Height (DBH) of living timber cannot cut through the trunk. By measuring perimeter circumference (\(C\)), our tool instantly calculates exact radius (\(r = C / 2\pi\)), diameter (\(d = C / \pi\)), and cross-sectional basal area (\(A = C^2 / 4\pi\)).
Seamlessly switch between solving for radius from circumference, finding circumference from area, converting diameter to radius (\(r = d/2\)), or finding circle area from radius without multiple sequential calculator steps.
Woodworkers, machinists, and civil engineers can instantly extract the maximum square timber side length that can be milled from a circular log (\(s_{\text{in}} = r\sqrt{2} = \frac{C\sqrt{2}}{2\pi}\)) or the minimum circular pipe needed to encase a square conduit.
Converts freely between metric (millimeters, centimeters, meters, kilometers) and imperial measurements (inches, feet, yards, miles) with high-precision IEEE 754 floating-point accuracy.
Choose your given measurement: Circumference (\(C\)), Radius (\(r\)), Diameter (\(d\)), or Area (\(A\)).
Type your measured dimension and select your preferred unit (meters, centimeters, inches, feet, etc.).
Review instant calculations for radius (\(r = C / 2\pi\)), diameter (\(d = C / \pi\)), circle area (\(A = C^2 / 4\pi\)), and polygon metrics.
Click Copy Circle Telemetry Card to copy a formatted text summary for engineering logs, CAD, or homework.
Convert circumference to radius (\(C \to r\)), radius to circumference (\(r \to C\)), diameter to radius (\(d \to r\)), or area to circumference (\(A \to C\)).
Calculates inscribed square sides (\(r\sqrt{2}\)), circumscribed squares (\(2r\)), and equilateral triangles (\(r\sqrt{3}\)).
All calculations execute locally via JavaScript with zero server roundtrips, zero latency, and complete user privacy.
By definition, the mathematical constant Pi (\(\pi\)) is the ratio of any circle's circumference to its diameter (\(\pi = C / d\)). Because the diameter is twice the radius (\(d = 2r\)), substituting \(d\) yields the foundational relationship: $$C = 2\pi r \iff r = \frac{C}{2\pi} \approx \frac{C}{6.2831853}$$
A circular dining table has a diameter of \(d = 1.40\,\text{m}\). Find its radius and circumference.
Solution: \(r = d / 2 = 1.40 / 2 = \mathbf{0.70\,\text{m}}\); Circumference \(C = \pi d = 1.40\pi \approx \mathbf{4.398\,\text{m}}\).
A circular trampoline has an outer safety rim circumference of \(C = 12.566\,\text{m}\). Calculate its jumping mat area.
Solution: \(A = \frac{C^2}{4\pi} = \frac{(12.566)^2}{4\pi} = \frac{157.904}{12.566} \approx \mathbf{12.566\,\text{m}^2}\) (Radius \(r = 2.0\,\text{m}\)).
A 29-inch mountain bike tire has a radius of \(r = 14.5\,\text{in}\). How far does the bike travel in 100 wheel rotations?
Solution: One rotation \(C = 2\pi(14.5) \approx 91.106\,\text{in}\). Distance \(= 100 \times 91.106\,\text{in} = 9110.6\,\text{in} = \mathbf{759.2\,\text{ft}}\).
To calculate the radius and area of a circular container with circumference \(C = 31.42\,\text{cm}\): $$r = \frac{31.42}{2\pi} \approx \frac{31.42}{6.283185} \approx \mathbf{5.000\,\text{cm}}$$ $$d = \frac{31.42}{\pi} \approx \mathbf{10.001\,\text{cm}}, \quad A = \pi(5.000)^2 \approx \mathbf{78.540\,\text{cm}^2}$$
For a tree trunk with circumference \(C = 150.0\,\text{cm}\) measured at breast height: $$r = \frac{150.0}{2\pi} \approx \mathbf{23.873\,\text{cm}}, \quad d = \frac{150.0}{\pi} \approx \mathbf{47.746\,\text{cm}}$$ $$\text{Cross-Sectional Area } A = \frac{150.0^2}{4\pi} = \frac{22500}{12.56637} \approx \mathbf{1790.49\,\text{cm}^2}$$
Exact geometric dimensions from unit circles to planetary equators.
| Object / Preset | Circumference (\(C\)) | Radius (\(r\)) | Diameter (\(d\)) | Circle Area (\(A\)) | Inscribed Square Side |
|---|---|---|---|---|---|
| Unit Circle | \(2\pi \approx 6.283\) | \(1.000\) | \(2.000\) | \(\pi \approx 3.142\) | \(\sqrt{2} \approx 1.414\) |
| Basketball (Size 7) | \(29.50\,\text{in}\) | \(4.695\,\text{in}\) | \(9.390\,\text{in}\) | \(69.25\,\text{in}^2\) | \(6.640\,\text{in}\) |
| Soccer Ball (Size 5) | \(69.00\,\text{cm}\) | \(10.98\,\text{cm}\) | \(21.96\,\text{cm}\) | \(378.9\,\text{cm}^2\) | \(15.53\,\text{cm}\) |
| Bicycle Wheel 700c | \(2096\,\text{mm}\) | \(333.6\,\text{mm}\) | \(667.2\,\text{mm}\) | \(0.3496\,\text{m}^2\) | \(471.8\,\text{mm}\) |
| Tree Trunk DBH | \(150.0\,\text{cm}\) | \(23.87\,\text{cm}\) | \(47.75\,\text{cm}\) | \(1790.5\,\text{cm}^2\) | \(33.76\,\text{cm}\) |
| Earth Equator | \(40,075\,\text{km}\) | \(6,378.1\,\text{km}\) | \(12,756\,\text{km}\) | \(1.278 \times 10^8\,\text{km}^2\) | \(9,020\,\text{km}\) |
Authoritative answers to common questions about calculating radius from circumference, diameter conversions, and circle area calculations.
