Enter radius, diameter, circumference, or area and get every circle measurement: inscribed square, hexagon, triangle sides, circumscribed square, area ratios, and more.
This circle measurements calculator goes beyond the basic radius-diameter-circumference-area set. Enter any one known property and the page computes every important circle dimension, including the side lengths of inscribed and circumscribed regular polygons.
The inscribed square — the largest square that fits inside a circle — has side s = r√2, where r is the radius. Its area is exactly 2r², which is always 2/π ≈ 63.66% of the circle's area. The circumscribed square — the smallest square that contains the entire circle — has side equal to the diameter, and its area is d² = 4r². The circle fills π/4 ≈ 78.54% of the circumscribed square — this is the classic "squaring the circle" ratio.
For regular hexagons, the inscribed hexagon has side length equal to the radius (a beautiful geometric fact), and its area is (3√3/2)r² ≈ 2.598r². The inscribed equilateral triangle has side r√3 and area (3√3/4)r².
These relationships are essential in engineering, packing problems, material cutting, and design. How much material is wasted when cutting circles from square sheets? What size circle do you need to inscribe a given square? The calculator answers those questions from a single starting value. Use the visual comparison bars to see how the different shapes relate in size, and the reference table to look up values for common radii.
Use this page when one circle measurement has to unlock many others. It keeps the core circle values together with inscribed and circumscribed polygon dimensions, which is useful for packing, design, and geometry problems where one radius drives several dependent quantities.
Basic: d = 2r, C = 2πr, A = πr²
Inscribed square side: s = r√2, area = 2r²
Circumscribed square side: s = d = 2r, area = 4r²
Inscribed regular hexagon side: s = r, area = (3√3/2)r²
Inscribed equilateral triangle side: s = r√3, area = (3√3/4)r²
Circle/circumscribed square area ratio: π/4 ≈ 0.7854
Circle/inscribed square area ratio: π/2 ≈ 1.5708Result: Radius-based circle and polygon measurements
With radius 12.13 mm, the calculator derives diameter, circumference, area, and the matching inscribed and circumscribed polygon measurements from that single starting value.
Enter radius, diameter, circumference, or area and get every circle measurement: inscribed square, hexagon, triangle sides, circumscribed square, area ratios, and more. Use it when you need a repeatable calculation in the math / geometry category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
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The inscribed square with side s = r√2 ≈ 1.414r, where r is the circle's radius. Its diagonal equals the circle's diameter.
The circumscribed square with side equal to the diameter (2r). The circle fits perfectly inside, touching all four sides.
A regular hexagon inscribed in a circle of radius r consists of 6 equilateral triangles. Each triangle has two sides equal to r (radii) and an angle of 60° between them, making the third side also r.
The waste is 1 − π/4 ≈ 21.46%. A circle uses about 78.54% of its circumscribed square's area.
For a circle of radius r, the inscribed equilateral triangle has side s = r√3 ≈ 1.732r and area (3√3/4)r².
Yes. Select "Area" as the input mode, enter the value, and the calculator derives the radius (r = √(A/π)) and all other measurements.
Comprehensive circle calculator: enter any one property (radius, diameter, circumference, or area) and compute all others plus sector area, arc length, segment area, and chord length.
Calculate the diameter of a circle from its radius, circumference, or area. Also computes radius, circumference, area, arc length, sector area, and chord length.
Calculate arc length, chord length, and circumference of a circle. Supports degrees and radians, with sagitta, sector area, and arc-to-chord ratio.