How this calculator works
A quarter disk occupies a right-angle corner in a square whose side equals the radius. Its area is one quarter of the full disk, and the spare square area is the square minus that sector. The chord connects the two arc endpoints but does not form part of the sector boundary. The boundary table counts the curved arc and the two straight radii separately. All six measurements can be used to recover the same radius.
Formula
A = πr²/4; spare = r² - A; chord = r√2; arc L = πr/2; perimeter P = 2r + L. Inverse examples: r = √(4A/π); r = P/(2 + π/2).
Worked example
For r = 2 m, the square covers 4 m² and the quarter disk covers π m². The spare area is 4 - π ≈ 0.858407 m². The arc is π m and the full perimeter is 4 + π ≈ 7.141593 m.
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Frequently asked questions
Is the perimeter one quarter of the circumference?
That is only the curved arc. The full sector perimeter also includes two radii, which the table lists separately.
What is the spare area?
It is the part of a square of side r outside the quarter disk placed at one corner. It is not the area of the circular segment between chord and arc.
Can the chord replace the two radii in the perimeter?
No. Doing so describes a circular segment instead of a quarter disk.