How this instrument works
This quick-reference page covers the boundary-length formulas for four commonly needed shapes at once — a circle's circumference (2πr), a square's perimeter (4s), a rectangle's perimeter (2(l+w)), and an equilateral triangle's perimeter (3s) — selected with a simple shape number rather than navigating to four separate dedicated pages.
Circumference and perimeter are really the same underlying idea (the total distance around a shape's boundary), just with circumference reserved by convention for curved shapes like a circle. This page treats both under one roof, since the formula selection logic is identical either way: pick the shape, apply its own boundary-length formula.
Each of these four formulas has its own dedicated, more detailed page elsewhere on this site. This page trades that depth for speed — a single stop for whichever basic shape's boundary length happens to be needed right now.
- Enter the shape number into the Shape field: 1 for circle, 2 for square, 3 for rectangle, 4 for equilateral triangle.
- Enter the first dimension (radius or side) into Dimension 1.
- Enter the second dimension (width, rectangle only) into Dimension 2, if needed.
- Read Perimeter: the sheet applies the matching formula automatically.
Worked example — a square with side 4
Shape 2 (square) with dim1 = 4 gives a perimeter of 4×4=16, using the plain 4s formula automatically selected for that shape number.
Switch to shape 3 (rectangle) with dim1 = 6 (length) and dim2 = 4 (width), and the sheet applies 2(l+w) instead, giving a perimeter of 20 — the same page handling a different shape and formula just by changing the shape number.
Questions
How does the shape selector work?
Enter 1 for a circle, 2 for a square, 3 for a rectangle, or 4 for an equilateral triangle, and the sheet automatically applies that shape's own boundary-length formula to whatever dimensions are entered.
Is a circle's circumference the same thing as its perimeter?
Yes — circumference is simply the name reserved by convention for the perimeter of a circle or other curved shape. Both mean the total distance around the boundary.
Do I need to fill in both dimension fields?
Only for a rectangle, which needs both length and width. A circle only needs its radius, and both the square and equilateral triangle only need one side length; the second field is ignored for those shapes.
Why does the triangle option assume equilateral specifically?
Because an equilateral triangle's three equal sides let its perimeter collapse to a single-dimension formula, 3s — a general (non-equilateral) triangle needs all three side lengths individually, handled by this site's dedicated Triangle Perimeter page instead.
Where can I find a more detailed explanation for one specific shape?
Each of these shapes has its own dedicated page elsewhere on this site, with a fuller derivation and worked examples — this page trades that depth for a quick, single-stop reference across all four at once.