How this instrument works
This quick-reference page covers the area formulas for four of the most commonly needed shapes at once — a circle (πr²), a square (s²), a rectangle (l×w), and a triangle (½bh) — selected with a simple shape number rather than navigating to four separate dedicated pages. Enter the shape number and up to two dimensions, and the sheet applies whichever formula matches automatically.
Each of these four formulas has its own dedicated, more detailed page elsewhere on this site, with worked derivations and deeper context specific to that one shape. This page instead trades that depth for speed: a single stop for whichever basic shape's area happens to be needed right now, without deciding in advance which dedicated page to visit.
The second dimension field is simply ignored for shapes that don't need it — a circle only needs its radius, and a square only needs its side, so entering anything in the second field for those two shapes has no effect on the result at all.
- Enter the shape number into the Shape field: 1 for circle, 2 for square, 3 for rectangle, 4 for triangle.
- Enter the first dimension (radius, side, length, or base, depending on the shape) into Dimension 1.
- Enter the second dimension (width or height) into Dimension 2, if the chosen shape needs one.
- Read Area: the sheet applies the matching formula automatically.
Worked example — a circle of radius 5
Shape 1 (circle) with dim1 = 5 gives an area of π×25 ≈ 78.54, using the πr² formula automatically selected for that shape number.
Switch to shape 4 (triangle) with dim1 = 8 (the base) and dim2 = 5 (the height), and the sheet applies ½bh instead, giving an area of 20 — the same page handling a completely 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 a triangle, and the sheet automatically applies that shape's own area formula to whatever dimensions are entered.
Do I need to fill in both dimension fields?
Only for shapes that need two — a rectangle needs length and width, and a triangle needs base and height. A circle only needs its radius, and a square only needs its side; the second field is simply ignored for those two.
Where can I find a more detailed explanation for one specific shape?
Each of these four shapes has its own dedicated page elsewhere on this site, with a fuller derivation and worked examples specific to that shape — this page trades that depth for a quick, single-stop reference across all four at once.
Can this handle shapes other than these four?
Not on this page — it's scoped to the four most commonly needed basic shapes. Other shapes (polygons, ellipses, and more) each have their own dedicated pages elsewhere on this site.
What if I enter a shape number outside 1-4?
The formula has no matching case, so the result won't correspond to any real shape — the shape field is restricted to the valid range of 1 through 4 to prevent that.