What is the perimeter of a rectangle?

The perimeter is the total length around all four sides. P = 2 times (l plus w), where l is the length and w is the width. For a rectangle 12 cm by 8 cm: P = 2 times (12 plus 8) = 2 times 20 = 40 cm. The perimeter is always in the same linear unit as the inputs, while area is in square units.

How do I calculate how many tiles I need for a rectangular floor?

Find the floor area: length times width. Divide by the area of one tile. Add 10 to 15 percent for cuts and breakage. For a 4 m by 5 m floor (area 20 m squared) with 0.3 m by 0.3 m tiles (area 0.09 m squared): tiles needed = 20 divided by 0.09 = 223 tiles, plus 10 percent = 245 tiles.

Can a rectangle have the same area and perimeter number?

Yes. A rectangle has equal area and perimeter values when 2(l plus w) = l times w. One solution is l = 3 and w = 6: area = 18, perimeter = 18. Another is l = 4 and w = 4 (a square): area = 16, perimeter = 16. These are called equable rectangles.

Area of a Rectangle Calculator

Q: How do I find a missing side of a rectangle from its area?

Divide the area by the known side: missing side = area divided by known side. If the area is 96 square cm and one side is 12 cm, then the missing side is 96 divided by 12 = 8 cm. Use the Find Side tab on this calculator to enter the area and known side and get the missing dimension instantly.

Q: What is the diagonal of a rectangle?

The diagonal of a rectangle is d = the square root of (l squared plus w squared), derived from the Pythagorean theorem. For a rectangle 12 by 8: d = square root of (144 plus 64) = square root of 208 = 14.422 units. The diagonal is the straight-line distance between opposite corners.

Q: What is the difference between area and perimeter?

Area measures the two-dimensional space inside the shape, expressed in square units (cm squared, m squared, ft squared). Perimeter measures the total length of the boundary, expressed in linear units (cm, m, ft). For a 12 by 8 rectangle, area is 96 cm squared and perimeter is 40 cm. Doubling all sides quadruples the area but only doubles the perimeter.

Find rectangle area from length and width, or back-solve a missing side from the area. Perimeter and diagonal included.

▭ What is the Area of a Rectangle?

The area of a rectangle is the amount of two-dimensional space enclosed within its four right-angled sides. It is one of the most fundamental measurements in geometry and practical everyday life. The formula is simply length multiplied by width: A = l x w. Both the length and width must be in the same unit (centimetres, metres, feet, etc.), and the result is expressed in square units.

A rectangle is a quadrilateral with four right angles (90 degrees at every corner) and two pairs of parallel, equal-length sides. The longer side is conventionally called the length and the shorter side the width, though the formula works regardless of which is which. A square is a special rectangle in which length equals width; its area is the side length squared.

Rectangle area calculations appear in countless practical contexts. In construction and interior design, you calculate the floor area of a room (length times width) to determine how much flooring, carpet, or paint is needed. In agriculture, field area determines irrigation requirements and crop yield estimates. In packaging, the surface area of a box involves multiple rectangle calculations. In engineering, cross-sectional areas of rectangular beams appear in structural stress calculations. In printing, the area of a page or poster determines material and ink costs.

A common point of confusion is the difference between area and perimeter. Area measures the interior space in square units; perimeter measures the boundary length in linear units. A room 10 m by 5 m has area 50 square metres (the floor space) and perimeter 30 metres (the total length of the walls at floor level). These are distinct quantities with different units and different uses.

This calculator provides two modes. The Find Area mode computes the area, perimeter, diagonal, and aspect ratio from the length and width. The Find Missing Side mode back-solves a missing dimension when you know the area and one side, which is useful when you know the target area and one constraint (for example, the width of a room) and need to find the required length.

📐 Formula

A = l × w

A = area (square units)

l = length (any consistent unit)

w = width (same unit as length)

Example: l = 12, w = 8 → A = 12 × 8 = 96 sq units

P = 2(l + w)

P = perimeter (linear units)

Example: l = 12, w = 8 → P = 2(12 + 8) = 40 units

d = √(l² + w²)

d = diagonal length (Pythagorean theorem)

Example: l = 12, w = 8 → d = √(144 + 64) = √208 = 14.422 units

Missing side = A ÷ known side

To find a missing dimension when area is known

Example: A = 96, known side = 12 → missing side = 96 ÷ 12 = 8 units

📖 How to Use This Calculator

Steps

Choose the calculation mode - select Find Area to calculate area from length and width, or Find Missing Side to back-solve a missing dimension from the area.

Enter the length - type the rectangle length in the first input field, or drag the slider. Both inputs stay in sync automatically.

Enter the width or known side - for Find Area mode, type the width. For Find Side mode, type the target area and the known side length.

Click Calculate - the area, perimeter, diagonal, and aspect ratio (or the missing side) appear instantly below the button.

Try a worked example - click any Try this example link in the examples section to pre-fill the inputs and verify the result against the worked solution.

💡 Example Calculations

Example 1 - Standard Room: 12 m by 8 m

Find the floor area, perimeter, and diagonal of a room 12 metres long and 8 metres wide.

Rectangle: l = 12 m, w = 8 m

Area = l × w = 12 × 8 = 96 m²

Perimeter = 2(l + w) = 2(12 + 8) = 2 × 20 = 40 m

Diagonal = √(12² + 8²) = √(144 + 64) = √208 = 14.422 m

Aspect ratio = 12 ÷ 8 = 1.5 : 1

Area = 96 m² | Perimeter = 40 m | Diagonal = 14.422 m

Try this example →

Example 2 - A5 Paper Sheet: 14.8 cm by 21 cm

Find the area of an A5 sheet of paper (148 mm x 210 mm = 14.8 cm x 21 cm).

Rectangle: l = 21 cm, w = 14.8 cm

Area = 21 × 14.8 = 310.8 cm²

Perimeter = 2(21 + 14.8) = 2 × 35.8 = 71.6 cm

Diagonal = √(441 + 219.04) = √660.04 = 25.692 cm

Area = 310.8 cm² | Perimeter = 71.6 cm | Diagonal = 25.692 cm

Try this example →

Example 3 - Garden Plot: 200 m2 with Width 10 m

A garden plot has area 200 square metres and width 10 m. Find the length.

Find Side: A = 200 m², known side = 10 m

Missing side = A ÷ known side = 200 ÷ 10 = 20 m

Perimeter = 2(20 + 10) = 2 × 30 = 60 m

Diagonal = √(400 + 100) = √500 = 22.361 m

Missing side = 20 m | Perimeter = 60 m | Diagonal = 22.361 m

Try this example →

Example 4 - Basketball Court: 28 m by 15 m

An NBA basketball court is 28.65 m long and 15.24 m wide. Approximate it at 28 m by 15 m.

Rectangle: l = 28 m, w = 15 m

Area = 28 × 15 = 420 m²

Perimeter = 2(28 + 15) = 2 × 43 = 86 m

Diagonal = √(784 + 225) = √1009 = 31.765 m

Area = 420 m² | Perimeter = 86 m | Diagonal = 31.765 m

Try this example →

❓ Frequently Asked Questions

What is the formula for the area of a rectangle?+

The area of a rectangle is A = l times w, where l is the length and w is the width. Both measurements must use the same unit. For example, a rectangle 12 cm long and 8 cm wide has area = 12 times 8 = 96 square centimetres. The formula applies to all rectangles including squares, where l equals w and the area equals the side squared.

How do I calculate the perimeter of a rectangle?+

The perimeter is P = 2 times (l plus w). For a 12 by 8 rectangle: P = 2 times (12 plus 8) = 2 times 20 = 40 units. Perimeter is the total length around all four sides. Note that area is in square units while perimeter is in linear units. A fence around a rectangular yard uses the perimeter; grass seed or turf uses the area.

How do I find a missing side of a rectangle from its area?+

Rearrange the area formula: missing side = area divided by known side. If a rectangle has area 96 cm squared and one side is 12 cm, then the other side is 96 divided by 12 = 8 cm. Use the Find Missing Side tab on this calculator: enter the area and the known side, and the calculator returns the missing dimension together with the perimeter and diagonal.

What is the diagonal of a rectangle formula?+

The diagonal is d = square root of (l squared plus w squared), from the Pythagorean theorem. A rectangle's diagonal divides it into two equal right triangles with legs l and w. For a 12 by 8 rectangle: d = square root of (144 plus 64) = square root of 208 = 14.422 units. This is used in construction to verify square corners: if the diagonal matches the calculated value, the room is truly rectangular.

What is the difference between area and perimeter of a rectangle?+

Area measures the interior space in square units (m squared, ft squared). Perimeter measures the boundary length in linear units (m, ft). For a 12 by 8 rectangle, area = 96 m squared and perimeter = 40 m. Doubling both sides quadruples the area but only doubles the perimeter. Area is used for flooring, carpeting, and painting; perimeter is used for fencing, skirting boards, and framing.

How do I calculate room area in square metres for flooring?+

Measure the room length and width in metres, then multiply: area = l times w. For a 5 m by 4 m room, area = 20 m squared. Buy flooring for 20 m squared plus 10 to 15 percent for cuts and wastage (22 to 23 m squared). For rooms with alcoves or bays, split the room into rectangles, calculate each area separately, and add them together.

How many square feet is a 10 by 12 room?+

A 10 ft by 12 ft room has area = 10 times 12 = 120 square feet. To convert: 120 sq ft divided by 9 = 13.33 square yards. 120 sq ft times 0.0929 = 11.15 square metres. This is a common US bedroom size. For a 10 ft by 10 ft room: 100 square feet. For 12 by 12: 144 square feet.

What is the aspect ratio of a rectangle?+

The aspect ratio is the ratio of the longer side to the shorter side, expressed as N : 1. A 12 by 8 rectangle has aspect ratio 12 divided by 8 = 1.5 : 1. A square has ratio 1 : 1. Common screen aspect ratios are 16 : 9 (widescreen, ratio 1.778 : 1), 4 : 3 (old TVs, ratio 1.333 : 1), and 3 : 2 (camera sensors, ratio 1.5 : 1). Aspect ratio describes shape independently of size.

What is the area of a rectangle with length 15 and width 9?+

Area = 15 times 9 = 135 square units. Perimeter = 2 times (15 plus 9) = 48 units. Diagonal = square root of (225 plus 81) = square root of 306 = 17.493 units. Aspect ratio = 15 divided by 9 = 1.667 : 1. This is a rectangle close to a 5 : 3 ratio.

How does rectangle area relate to triangle area?+

A rectangle's diagonal divides it into two congruent right triangles. Each triangle has area = half the rectangle area = (l times w) divided by 2. This is also the general triangle formula: area = (base times height) divided by 2, where the base and height are the two sides of the right triangle. Any triangle can be shown to have area equal to half the area of its enclosing rectangle.

Can two rectangles have the same area but different perimeters?+

Yes. For example, a 1 by 36 rectangle and a 4 by 9 rectangle both have area 36 square units, but their perimeters are 74 and 26 units respectively. Among all rectangles with the same area, the square has the smallest perimeter. This is the isoperimetric inequality for rectangles: for fixed area, the shape closest to a square minimises the perimeter.

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📌 Quick Tips

💡Area = length times width. Both values must be in the same unit. If one is in centimetres and the other in metres, convert first.

💡The diagonal of a rectangle is the square root of (length squared plus width squared), using the Pythagorean theorem.

💡A square is a special rectangle where length equals width. Its area is the side length squared.

💡To find a missing side, divide the area by the known side: missing side = area divided by known side.

💡For flooring and tiling, calculate room area in square metres then divide by tile area (in square metres) to find tile count. Add 10 percent for cuts and waste.