Square Area Calculator

A = s × s = s²

s

A side length, in centimetres: any one of the four, since all four are equal. It is the only input this page needs, and it must not be negative. It may be any size from 0 up to a billion centimetres, which is ten thousand kilometres — the limit is there so that the squaring stays inside what a computer can count exactly, not because a square that large is unimaginable

A

The area of the square, in square centimetres: the side multiplied by itself. It is printed to four decimal places, the same width as the rest of the area pages in this subcategory, so that the answers here and the answers on the square calculator and the rectangle calculator read identically for the same shape

s × s

The multiplication, written out rather than as a power so that the two factors can be seen to be the same number. This is what makes the area grow with the square of the side: a side twice as long gives four times the area, a side three times as long gives nine times, and a side halved gives a quarter. It is the single most useful fact about this page, because it means a rough estimate of the side is a rough estimate of the area squared

cm²

Square centimetres, the unit the answer is printed in. A square centimetre is a square one centimetre on each side, so 25 of them tile a square of side 5 exactly — five rows of five. The little ² is not decoration: it is the marker that the unit was multiplied by itself along with the number, and it is why an area of 25 square centimetres is not the same kind of quantity as a perimeter of 20 centimetres, even though both are built from the same centimetre

square meters

What the answer becomes when the side is measured in metres: a side of 2 metres gives 4 square meters, a side of 3 gives 9. This page works in centimetres, so a side entered in metres is converted to centimetres before the squaring and the answer comes back in square centimetres — 4 square meters is 40,000 square centimetres. Converting the other way, square centimetres to square meters, divides by ten thousand rather than by a hundred, because both dimensions were converted

Use this page when you have measured one side of something square and want to know how much surface it covers: a tile, a pane of glass, a sheet of plywood, a patch of ground, a table top, a square of fabric. It is the shortest path from a tape measure to an area, and the table above it means that for the eight sizes it lists the answer is already on the screen. It is also the page to use when you are checking somebody else's number. Because the arithmetic is a single multiplication, an area that looks wrong can be checked by hand in seconds — a quoted figure of 25 square centimetres for a side of 5 is right, and a quoted figure of 25 for a side of 10 is not, since 10 × 10 is 100. That check is worth doing on any area quoted in square metres, because the factor between square centimetres and square meters is ten thousand and a decimal point moved the wrong number of places is the commonest error in this whole family of calculations. Use the square calculator instead when you have the perimeter or the diagonal rather than the side, or when you want all four readings in one place. Use the rectangle calculator when the two sides differ, which is the case for most real rooms and sheets — this page assumes they are equal, and a rectangle with sides of 5 and 6 covers 30 square centimetres, not 25.

1. A square with a side of 5 centimetres

   1. Multiply the side by itself: 5 × 5 = 25
   2. The answer is 25 square centimetres

   The row the page loads with, and the one to use as a sanity check whenever a square area looks wrong: the arithmetic is a single multiplication, so this can be verified without the page. It is also the row that lines up with two other tools in this subcategory — the square calculator entered with a side of 5 returns an area of 25, and the rectangle calculator entered with a length of 5 and a width of 5 returns the same 25, which is the clearest way to see that a square is a rectangle whose two sides happen to be equal.

2. A square with a side of 2.5 centimetres

   1. Multiply the side by itself: 2.5 × 2.5 = 6.25
   2. The answer is 6.25 square centimetres

   A side with one decimal place gives an area with two, and that is not an accident of this example: squaring multiplies the number of decimal places by two, so a measurement read to the nearest millimetre comes back as an area with two decimal places in centimetres. It also shows that the four decimals this page prints are a display width rather than a claim about accuracy — 6.25 is exact, and the two trailing zeros the page would print on a longer answer are not extra precision. If you are cutting a piece of material, the difference between 6.25 and 6.3 square centimetres is a sliver at the edge, and both are as good as the 2.5 you measured.

3. A square with a side of 12 centimetres

   1. Multiply the side by itself: 12 × 12 = 144
   2. The answer is 144 square centimetres

   Twelve is a common size because it divides a metre into whole numbers, and a square twelve centimetres on a side is a familiar tile. The number itself is worth noticing: 144 is a perfect square, so its own square root is the side you started with. A useful comparison is in the same table: a side of 10 gives 100, so two extra centimetres on the side — a fifth more — add nearly half again to the area, which is the growth rule at work on a pair of sizes you can picture.

4. A square with a side of 0.5 centimetres

   1. Multiply the side by itself: 0.5 × 0.5 = 0.25
   2. The answer is 0.25 square centimetres

   A side of half a centimetre gives an area of a quarter of a square centimetre, which surprises people the first time: the answer got smaller than the input, where every other example on this page makes it bigger. The rule has not changed — multiplying a number below 1 by itself always shrinks it — and the practical consequence is that areas of small things are genuinely tiny, so an area quoted in whole square centimetres for something a few millimetres across is worth a second look. It is also the row that shows what squaring does to a decimal point, since one decimal place on the way in becomes two on the way out.

This page computes one thing: the area of a square from the length of its side. It does not print the perimeter, which is four times the side, and it does not print the diagonal, which is the side times the square root of two — both follow from the input you already gave and both are on the square calculator, which is the page to use if you want them here. It does not work backwards. There is no box for an area that yields a side, so the question a tiler actually asks — how long a square tile do I need to cover 50 square centimetres — cannot be answered here, and it needs a square root rather than a squaring. The answer is always printed in square centimetres whatever the side was entered in, so a side in inches, feet or metres comes back as a square centimetre figure you have to convert yourself; the unit dropdowns convert the input, not the output. Converting square centimetres to square meters is a division by ten thousand, not by a hundred, and getting that wrong is the single most common way an area from this page ends up off by a factor of a hundred when it reaches a quote or an order form. A negative side is reported as an error rather than squared, since a square cannot have a negative edge, but a side of zero is answered with an area of zero rather than refused — a square with no size is a real answer to a real question and the page gives it. Side lengths above a billion centimetres are refused, which has nothing to do with geometry and everything to do with keeping the squaring inside the range of numbers a computer represents exactly; below that limit, areas are exact to the four decimals shown. The page does not check that your shape is square. It assumes the four sides are equal, as the name says, and it will happily compute the area of a rectangle you have mis-described — if the two sides differ, the rectangle calculator is the page you want, and it will show you the difference immediately. Nothing here accounts for waste, cutting kerf, edges, grout lines or the gaps between tiles, so the area this page returns is the area of the shape and not the quantity of material to buy.

What is the area formula for a square?

The side length multiplied by itself, written A = s × s or A = s². A square with a side of 5 centimetres covers 25 square centimetres, because 5 × 5 = 25. That is the whole formula — there is no factor of a half and no constant, which is what makes the square the simplest area to compute and the one worth remembering as a reference point for every other shape.

Why does doubling the side length give four times the area?

Because the square grows in two directions at once. Double the side and you have doubled both the width and the height, so the area is multiplied by two twice over: 2 × 2 = 4. A square of side 5 covers 25 square centimetres and a square of side 10 covers 100, not 50. The same rule runs the other way — halving the side divides the area by four, so a side of 2.5 covers 6.25, a quarter of 25. This is also the reason a small change in a measurement matters more than it looks like it should.

How many square centimetres are in a square meter?

Ten thousand, not one hundred. A metre is a hundred centimetres, and converting an area means converting both of its dimensions, so the factor is 100 × 100 = 10,000. One square meter is 10,000 square centimetres, and one square centimetre is 0.0001 square meters. The same trap appears between square centimetres and square millimetres, where the factor is a hundred, and between square meters and hectares, where it is ten thousand again. If an area from this page is going onto an order form quoted in square meters, divide by ten thousand.

Can I use this page for a rectangle?

No, not unless the rectangle is a square. This page multiplies one side by itself, which is only correct when all four sides are equal; a rectangle 5 centimetres by 6 covers 30 square centimetres, where this page would report 25 for that input. The rectangle calculator in the same subcategory takes the two different sides and multiplies them, and that is the page to use for a shape whose sides differ — the square calculator treats whatever it is given as a square, so feeding it a rectangle's perimeter or area only tells you about the square with the same perimeter or area, not about your rectangle. If the two sides differ by less than the width of your pencil line, either page will do.

What does a side of zero give?

An area of zero, printed rather than refused. A square with no size has no area, and that is a genuine answer rather than an error — the page reserves its error messages for negative sides, which cannot exist as lengths. Enter 0 and the table's last row shows the same thing. The neighbouring case is worth knowing too: a negative side is reported as an error, because the page has no way to tell whether you meant the length you typed or its sign.

Why does the answer come back with four decimal places?

Four decimals is a display width shared by the area pages in this subcategory, so that the same shape computed on this page, on the square calculator and on the rectangle calculator prints the same string. It is not a claim about precision. A side measured with a tape to the nearest millimetre is accurate to about one part in fifty, which is far coarser than the fourth decimal place of the answer; the extra digits are there so that exact answers — 6.25 for a side of 2.5, 0.25 for a side of 0.5 — come out clean rather than rounded.

• Square — the four-sided figure with equal sides and right angles that this page computes the area of, including the relation between the side, the diagonal and the area — Wolfram MathWorld (United States)
• Area — the general treatment of what an area is and how it behaves under scaling, which is where the rule that doubling a side quadruples the area comes from — Wolfram MathWorld (United States)
• 教育部关于印发义务教育课程方案和课程标准（2022 年版）的通知——The fifth item in the annex list of this notice is the Mathematics Curriculum Standards for Compulsory Education (2022 edition); the area of a rectangle and of a square and the units of area (square centimetre, square decimetre and square metre) are part of the primary school mathematics curriculum, and the wording of the standards and the grade-band breakdown are governed by that annex — 中华人民共和国教育部
• NIST Special Publication 811 — the United States guide to the metric system, including the rule that a unit raised to a power carries that power in its symbol, which is why an area in centimetres is written cm² — National Institute of Standards and Technology (United States)