How this calculation works
Compare the compactness of a plane region with the circle of the same perimeter.
THE FORMULA
Q=4πA/P²A worked example
A unit square has quotient π/4.
Good to know
A value above one indicates inconsistent measurements for an ordinary plane region.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Compare the compactness of a plane region with the circle of the same perimeter.
The primary result is labeled “Compactness quotient”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A value above one indicates inconsistent measurements for an ordinary plane region.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A unit square has quotient π/4.
Which rule does this calculator apply?
Q=4πA/P²