Calculate Square Area: Formula and Examples

To calculate the area of a square, multiply the length of one side by itself: area = side × side, or A = s². Enter the side length and its unit in the calculator to get the square’s area in that unit squared, along with its perimeter and diagonal.

Formula

The standard formula for the area of a square is:

A = s² = s × s

• A is the area, measured in square units, such as square metres (m²), square centimetres (cm²), square feet (ft²), or square inches (in²).
• s is the length of one side, measured in a length unit such as metres, centimetres, feet, or inches.

The calculator also gives two related measurements. The perimeter is P = 4s, where P is the total distance around the square. The diagonal is d = s√2, the distance from one corner to the opposite corner. Both are lengths, not areas.

Worked Example

Using the calculator’s default side length of 5 m:

1. Area: A = 5 m × 5 m = 25.00 m².
2. Perimeter: P = 4 × 5 m = 20.00 m.
3. Diagonal: d = 5 m × √2 ≈ 7.07 m.

The area is 25 square metres. The square-metre unit comes from multiplying metres by metres: m × m = m². The perimeter and diagonal remain in metres because they measure length.

How to Calculate Square Area

Measure one side of the square, then multiply that measurement by itself. If a square has a side of 8 centimetres, its area is 8 × 8 = 64 cm². You do not need to measure all four sides if the shape is known to be a square, because all four sides are equal.

If the measurement uses a fraction or decimal, the same rule applies. For a side of 2.5 feet, the area is 2.5 × 2.5 = 6.25 ft². Keep the same unit for both factors; squaring a length also squares its unit.

For a real object, measure straight along a side rather than along a diagonal. Use a consistent unit and, when precision matters, record enough digits before rounding the final area.

Units and Conversions

Area units are two-dimensional. A result in square feet is not interchangeable with a result in feet, and converting the side length requires squaring the conversion factor when converting area.

• 1 m = 100 cm, so 1 m² = 10,000 cm².
• 1 ft = 12 in, so 1 ft² = 144 in².
• 1 m² is approximately 10.764 ft²; 1 ft² is approximately 0.0929 m².

For example, a square with a 1 m side has an area of 1 m², or 10,000 cm². It does not have an area of 100 cm²: 100 is the conversion for the side length, and that length must be multiplied by itself. If you are converting a square’s side from metres to feet, convert the side first and then square it, or convert the resulting area using an area conversion factor.

When This Formula Applies

The formula applies when the figure is a true square: it has four equal sides and four right angles. It is useful for estimating the surface area of square tiles, panels, plots, or other flat square regions. For a floor or wall made from several square sections, calculate each section’s area and add the results, provided the sections do not overlap.

A rectangle is different because its adjacent sides may have different lengths. Its area is length × width, not side × side unless it is also a square. For a triangle, circle, or irregular outline, use the formula for that shape or divide the region into simpler pieces. The square formula does not account for gaps, overlaps, thickness, or material waste.

Common Errors and Limits

• Using the perimeter as the area: multiplying a side by four gives a length around the boundary, not the area inside it.
• Using the diagonal as the side: the diagonal is longer than a side. If only the diagonal is known, the side is d ÷ √2, so the area is d² ÷ 2.
• Mixing units: convert all measurements to one unit before calculating. Multiplying a value in feet by one in inches gives a mixed-unit result that needs conversion.
• Rounding too early: keep the measured side’s available precision during the calculation, then round the area to a sensible number of decimal places.

The result is exact for a mathematically perfect square with an exact side length. Measurements of physical objects are approximate, and a slightly uneven or out-of-square object may need separate side measurements or a different method. The calculator assumes the side value is nonnegative and describes a square.

Frequently Asked Questions

What is the formula for the area of a square?
Multiply one side by itself: A = s². If the side is 6 inches, the area is 36 in².

How do I find the area if I know the perimeter?
Divide the perimeter by four to get the side, then square it. Equivalently, for perimeter P, area A = (P ÷ 4)². A perimeter of 20 cm gives a 5 cm side and an area of 25 cm².

How do I find the area from the diagonal?
For a square with diagonal d, A = d² ÷ 2. This follows because the diagonal is s√2, and squaring it gives d² = 2s².

Is square footage the same as feet?
No. Feet measure length; square feet measure area. A room 10 ft by 10 ft has an area of 100 ft², while each side is 10 ft.

Can I use the formula for a rectangle?
Only if the rectangle is a square. For other rectangles, multiply the length by the width; the sides do not have to be equal.

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in s | Side length | m | 5 | 0
out area | Area | m² | s ^ 2 | 2
out perimeter | Perimeter | m | 4 * s | 2
out diagonal | Diagonal | m | s * sqrt(2) | 2