The perimeter is the total distance around the outside of a shape

The perimeter is straightforward the sum of all the outer edges of a flat shape. If you walked around the border of a rectangle, a triangle, or a circle, the distance you travelled would be its perimeter. To find it, you measure or know the length of each side, then add them together.

The method changes slightly depending on the shape. A rectangle uses a different formula than a triangle, and a circle uses a completely different approach because it has no straight sides. Once you know which shape you are working with, the calculation itself is straightforward.

Key Takeaways

  • Perimeter means the total distance around the outside edge of a shape, measured in the same units as the sides themselves.
  • For rectangles, multiply the length by 2 and the width by 2, then add them together.
  • For triangles, add all three side lengths together with no formula needed.
  • For circles, multiply the diameter by pi (3.14159), or multiply the radius by 2 and then by pi.
  • Always make sure all measurements are in the same unit before you add them.

Perimeter of a rectangle

A rectangle has four sides: two long sides (length) and two short sides (width). Since opposite sides are always equal, you do not need to measure all four. Measure the length and the width, then use this formula:

Perimeter = (2 × length) + (2 × width)

For example, if a rectangle is 10 metres long and 5 metres wide, the perimeter is (2 × 10) + (2 × 5) = 20 + 10 = 30 metres. You can also think of it as adding all four sides: 10 + 5 + 10 + 5 = 30 metres. Both methods give the same answer.

Perimeter of a triangle

A triangle has three sides, and there is no shortcut. You must measure or know the length of all three sides, then add them together:

Perimeter = side 1 + side 2 + side 3

If a triangle has sides of 6 centimetres, 8 centimetres, and 10 centimetres, the perimeter is 6 + 8 + 10 = 24 centimetres. This works for any triangle, whether it is a right triangle, an equilateral triangle (all sides equal), or any other type.

Perimeter of a square

A square is a special rectangle where all four sides are exactly the same length. This makes the calculation even simpler:

Perimeter = 4 × side length

If each side of a square is 7 inches, the perimeter is 4 × 7 = 28 inches. You only need to measure one side because you know the other three are identical.

Perimeter of a circle

A circle has no straight sides, so the perimeter is called the circumference. Instead of adding sides, you use the radius or diameter and multiply by pi (π), which is approximately 3.14159.

If you know the diameter (the distance straight across the circle through the centre), use this formula:

Circumference = diameter × π

If you know the radius (the distance from the centre to the edge), use this formula instead:

Circumference = 2 × radius × π

For example, a circle with a diameter of 10 metres has a circumference of 10 × 3.14159 = 31.4159 metres. A circle with a radius of 5 metres has a circumference of 2 × 5 × 3.14159 = 31.4159 metres. Both give the same result because the diameter is always twice the radius.

Perimeter of other polygons

Any shape with straight sides — a pentagon (5 sides), hexagon (6 sides), or any other polygon — uses the same basic rule: add up the length of every side. There is no formula that works for all of them because the number of sides changes.

If a pentagon has sides of 4, 5, 6, 4, and 5 metres, the perimeter is 4 + 5 + 6 + 4 + 5 = 24 metres. The only requirement is that you measure or know every single side length before you add them.

Common mistakes to avoid

The most frequent error is mixing units. If one side is measured in metres and another in centimetres, you must convert them to the same unit before adding. Convert everything to the smaller unit (centimetres) or the larger unit (metres) first, then calculate.

Another mistake is forgetting to include all sides. With triangles and polygons, it is straightforward to miss one side if you are not careful. Count the sides, measure each one, and check your list before you add.

For circles, people sometimes confuse radius and diameter. The radius is half the diameter. If you are given the radius and you use the diameter formula by accident, your answer will be wrong. Double-check which measurement you have before you choose the formula.

Frequently Asked Questions

What is the difference between perimeter and area?

Perimeter is the distance around the outside edge of a shape. Area is the amount of space inside the shape. Perimeter is measured in units like metres or inches. Area is measured in square units like square metres or square inches. They are completely different measurements and use different formulas.

Do I need to use pi as 3.14159 or can I round it?

You can round pi to 3.14 for most everyday purposes, and your answer will be close enough. For more precise work, use 3.14159. Most calculators have a pi button that uses the full value. The more decimal places you use, the more accurate your answer will be.

What if I only know the area of a shape, not the side lengths?

You cannot find the perimeter from the area alone. You need to know the actual side lengths or at least enough information to work them out. For example, if you know a square's area is 25 square metres, you can figure out that each side is 5 metres, then calculate the perimeter. But for most shapes, area and perimeter are independent — you need the measurements themselves.

Can perimeter be a decimal or does it have to be a whole number?

Perimeter can absolutely be a decimal. If a rectangle is 5.5 metres long and 3.2 metres wide, the perimeter is (2 × 5.5) + (2 × 3.2) = 11 + 6.4 = 17.4 metres. Decimals are normal and correct whenever your measurements include decimals.