Circle calculator: solve circumference, area, diameter, and radius from any one known value instantly. Free online tool, private, runs locally, no signup.
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Calculation details
Every figure above is calculated locally in your browser from the assumptions shown. No inputs are sent anywhere. See the methodology section below for the formulas used.
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Circle calculator: solve circumference, area, diameter, and radius from any one known value instantly. Free online tool, private, runs locally, no signup.
A radius-5 circle has area 78.5398 and circumference 31.4159.
Transparent methodology
How this calculator works
Reviewed August 2026 · BoringToolsKit Editorial Team
Formula
Diameter = 2r; circumference = 2 x pi x r; area = pi x r^2.
Worked example
A circle of radius 5: diameter 10, circumference 31.4159, area 78.5398.
BoringToolsKit. “Circle Calculator.” boringtoolskit.com/circle-calculator/ (reviewed August 2026). Free to reference in articles, syllabi, and answer posts with a link.
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Worked example: radius 5 through every formula
Enter known = radius, value = 5. The calculator takes r = 5 directly, then applies three formulas: d = 2r = 10, c = 2*pi*r = 2 * 3.141592653589793 * 5 = 31.41592653589793, and A = pi*r^2 = 3.141592653589793 * 25 = 78.53981633974483.
The formatter caps at 4 decimal places, so you see Diameter 10, Circumference 31.4159, Area 78.5398. Note the rounding: true circumference is 31.415926..., displayed as 31.4159, and true area is 78.539816..., displayed as 78.5398. If you need more precision than 4 decimals, take the displayed value as a starting point and extend by hand: the next digits are 2653 for circumference and 1633 for area.
The reverse direction works the same way. Enter known = circumference with value 10 and the calculator computes r = 10 / (2*pi) = 1.5915494309189535, shown as 1.5915. From that one input it rebuilds the full set: d = 3.1831, c = 10 (your input, recovered exactly), A = 7.9577. That round trip is the real test of consistency: area from r = 1.59155 is pi * 1.59155^2, which lands back on 7.9577.
Rounding drift and unit traps in practice
The calculator accepts a single positive number with no unit, so unit consistency is entirely on you. Measuring a pipe in inches but ordering insulation in centimeters means converting before or after, never mid-chain. A 4-inch diameter circle is 10.16 cm across and its area is 80.9308 square centimeters, not 80.93 square inches. Unit errors scale area by the square: 1 inch = 2.54 cm, but 1 square inch = 6.4516 square cm.
Practical measurements rarely give clean radii. A garden bed measured with a tape at 12.5 feet across is d = 12.5, so r = 6.25 and A = pi * 6.25^2 = 122.7185 square feet. Mulch sold in 2-cubic-foot bags covering that bed 3 inches (0.25 ft) deep needs 122.7185 * 0.25 = 30.6796 cubic feet, so 16 bags. Round up to 17: real beds are never perfect circles and edges eat the slack.
Precision limits matter too. This tool does not handle partial circles (arcs, sectors) or ellipses, and it treats pi as full double precision rather than 3.14. If your homework or spec requires 3.14, your hand answer will differ from the calculator's by about 0.05 percent on circumference, for example 31.4 versus 31.4159 on the radius-5 case. Both are correct within their stated precision.
