Area Of Square Calculator

What this calculator does

A square has four equal sides, so it is the easiest area of all to work out. You only need one number, the length of a side.

Type the side, pick a unit, and the tool gives you the area inside the square: a floor tile, a chessboard square, a square room or garden bed.

Using the calculator

1. Type the side length.
2. Pick its unit.
3. Press Calculate.

There is just the one box, since every side of a square is the same length. The side has to be a positive number, and the area comes back in square units of the side's unit.

The formula | area = side × side

The area of a square is:

area = side × side

Multiply the side by itself. That is the whole formula, with nothing else to it.

This is also where the word squaring a number comes from. Multiplying a number by itself, like 5 × 5, literally measures the area of a square with that side, which is why we call it "5 squared" and write it 5². The shape and the operation share a name for a reason.

Squares and perfect square numbers

If the side is a whole number, the area lands on what are called the perfect squares: 1, 4, 9, 16, 25, 36, and on up. Each one is the area of a square that many units across, a 1 by 1, a 2 by 2, a 3 by 3, and so on.

So a square with a side of 6 has an area of 36, the sixth perfect square. You can see the whole run in the square numbers list.

Units and rounding

Because you multiply a length by a length, the area comes out in square units, matched to the side's unit: a side in centimetres gives an area in square centimetres. A tidy answer is shown in full, and a long decimal is rounded to three places.

A worked example | a 5 cm side

Say the side is 5 cm.

1. Multiply it by itself: 5 × 5 = 25.

So the area is 25 cm². Picture it as 25 little one-centimetre tiles, laid out in 5 rows of 5, filling the square exactly.

A square is a special rectangle

A square is just a rectangle that happens to have all four sides equal. The rectangle formula is length × width, and when the length and width are the same, that becomes side × side. So this is the rectangle's formula with one measurement standing in for both.

If your two sides are not equal, you have a rectangle rather than a square, and the area of rectangle calculator is the one to use.

Questions people ask

What is the area of a square with a 5 cm side?

It is 25 cm². Multiply the side by itself: 5 × 5.

Why is it side times side?

Because a square is a rectangle with equal sides, and a rectangle's area is length × width. With both the same, that is side × side, which is exactly what "squaring" a number means.

What is a perfect square?

A whole number that is the area of a square with a whole-number side, like 1, 4, 9, 16 and 25. They are the results of multiplying a whole number by itself.

Why is the answer in square units?

Because area is a length times a length. A side in centimetres gives an area in square centimetres.

What is the difference between this and the area of a rectangle?

A square has all sides equal, so it needs only one measurement. A rectangle has a different length and width, so it needs both.

References

A note on where this comes from. The square is the basic unit in which area is measured: the square metre, the standard unit of area in the International System of Units, is defined as the area of a square one metre on each side, as set out by the US National Institute of Standards and Technology. For further reading, see Square.

1. National Institute of Standards and Technology (NIST), guidance on the International System of Units (SI), where the square metre is defined as the unit of area, the area of a square one metre on each side.