Perimeter Calculator

Add every side. For a rectangle that is 2 × (length + width); for a circle it is the circumference, 2πr; for a triangle it is simply the three sides added.

Any two sides must together exceed the third. Lengths of 1, 2 and 5 cannot form a triangle, because 1 + 2 is less than 5 — the two short sides cannot reach across.

It gives a triangle's area from the three sides alone, with no height needed. Take the semi-perimeter s, then the area is the square root of s(s−a)(s−b)(s−c).

None mathematically — circumference is simply the word used for a circle's perimeter. The distinct name is a historical convention rather than a different concept.

The circle, always. It is why bubbles are round and why heat-loss calculations favour compact shapes — the circle encloses the most area per unit of boundary.

Measure and add every edge. There is no formula, which is exactly why irregular shapes are broken into regular ones for area but not for perimeter — the internal division lines are not part of the boundary.

The formal statement that among all shapes with a given perimeter, the circle encloses the greatest area. It is why bubbles are spherical and why compact shapes lose the least heat.

Two radii plus the arc, and the arc is the radius times the angle in radians. Forgetting the two straight edges is the usual mistake.

A boundary whose measured length grows without limit as the measuring stick shrinks — coastlines behave this way. It is why published coastline lengths vary enormously between sources.

In two dimensions, more perimeter per unit area means more boundary to lose heat through. It is the same reason a compact building loses less heat than a sprawling one of equal floor area.

Yes — the two quantities do not determine a shape between them. Many different shapes share any given pair.

With a flexible tape, or by approximating with straight segments. A map wheel does the same job on a drawing, and the answer depends on how finely the curve is followed.