Perimeter formulas (with plain-English intuition)

The word perimeter comes from a Greek root meaning “measure around.” In practical terms, perimeter answers: “How far is it around the edge?” If you’re putting up a fence, adding trim, framing a border, or labeling a diagram, you usually care about perimeter. The good news: perimeter is almost always just adding side lengths — and the “formula” is basically a shortcut for that addition.

A rectangle has two pairs of equal sides: two lengths and two widths. If the length is L and the width is W, then going around the rectangle means adding L + W + L + W. Grouping like terms gives: P = 2L + 2W = 2(L + W).

• Use case: picture frames, yard borders, posters, tables.
• Why it’s viral: it’s the simplest “real life math” flex — quick, satisfying, and shareable.

A square is a special rectangle where all sides are equal. If the side length is s, then perimeter is P = s + s + s + s = 4s. If you can measure one side, you’re done.

Any triangle has three sides. If the side lengths are a, b, and c, then the perimeter is simply: P = a + b + c. No tricks. The only catch is that triangle side lengths must satisfy the triangle inequality: each side must be shorter than the sum of the other two. If not, those lengths can’t form a real triangle.

A circle is the “perimeter champion” because it has no sides. Instead of a polygon perimeter, we talk about circumference, which is still the distance around. If the radius is r, circumference is: C = 2πr. If you know the diameter d (which is twice the radius), then: C = πd. Both are the same fact written two ways.

• Rule of thumb: π ≈ 3.14159. So circumference is a little more than 3 times the diameter.
• Units: still linear units (cm, inches, feet), not square units.

A regular polygon has n equal sides (like a regular pentagon or hexagon). If each side length is s, then you’re just adding s a total of n times: P = n × s. This is especially handy for tiling, design patterns, and geometry homework where “regular” means “all sides equal.”

Sometimes you don’t have a “named” shape — you just have a path, border, or irregular polygon where the side lengths are known. In that case, perimeter is exactly what you think: add them all. Our custom-sides mode lets you enter a list like 3, 4, 5, 6.5 and it returns the total.

What this calculator does behind the scenes

This page is built to be fast and “no drama”: you choose a shape, type the measurements, and the calculator applies the correct perimeter formula. Everything runs client-side (inside your browser), so it feels instant.

• 1) Read inputs: the calculator collects your numbers (length, width, radius, etc.).
• 2) Validate: it checks that values are positive numbers. For triangles, it checks triangle inequality.
• 3) Compute: applies the formula for your shape (addition, multiplication, or 2πr).
• 4) Format: rounds based on your “Rounding” choice and appends your chosen unit.
• 5) Explain: prints the exact formula and substitutes your numbers so you can screenshot the “work.”

“Auto” rounding keeps the result clean without hiding accuracy. If your inputs are whole numbers, it will tend to show a tidy whole-number output. If your inputs include decimals, it will keep a reasonable number of decimals. You can override this (0–4 decimals) when you need exact formatting for assignments or reports.

Units here are purely labels: if you enter length in centimeters, the result is in centimeters. The calculator does not automatically convert between units. If you need conversions, use your unit converter tools and then re-calc perimeter.

Worked examples (copy these into notes)

Suppose a garden bed is 8 ft long and 3 ft wide. The perimeter tells you how much edging you need.
Formula: P = 2(L + W)
Plug in: P = 2(8 + 3) = 2(11) = 22 ft.
Practical tip: If you’re buying edging, add 5–10% for overlaps and cuts.

A square tile border has side length 12 cm.
Formula: P = 4s
Plug in: P = 4(12) = 48 cm.

A triangle has sides 5 m, 7 m, and 8 m.
Formula: P = a + b + c
Plug in: P = 5 + 7 + 8 = 20 m.
Reality check: 5 + 7 > 8 (true), 5 + 8 > 7 (true), 7 + 8 > 5 (true), so it’s a valid triangle.

A circular table has diameter 1.2 m. What’s the perimeter around the edge?
Formula: C = πd
Plug in: C ≈ 3.14159 × 1.2 ≈ 3.7699 m.
Rounded: about 3.77 m.

A regular hexagon has 6 equal sides, each 4 in.
Formula: P = n × s
Plug in: P = 6 × 4 = 24 in.

These examples cover most “perimeter” questions you’ll see in school or real life. If you’ve got a weird shape, use Custom sides: measure each segment and sum them.

Perimeter Calculator FAQ

• What’s the difference between perimeter and area?

  Perimeter measures the boundary length (around). Area measures the surface inside (filled-in region). Perimeter uses linear units (cm, ft). Area uses square units (cm², ft²).

• Is circle “perimeter” the same as circumference?

  Yes. Circumference is the special name for a circle’s perimeter. It’s calculated by C = 2πr or C = πd.

• Why does the calculator reject my triangle?

  If a + b ≤ c (or any side is too long compared to the others), those lengths can’t form a triangle in real space. The calculator checks this triangle inequality to prevent impossible results.

• Do I need to use the same unit for every input?

  Yes. Perimeter adds lengths. If you mix inches and centimeters, the sum won’t make sense. Convert first, then calculate.

• How accurate is π in this calculator?

  We use JavaScript’s built-in Math.PI, which is extremely accurate for everyday use. Your measurement accuracy (ruler, tape, rounding) usually matters more than π precision.

• Can I calculate the perimeter from area?

  Sometimes. For a square, if you know area A, then side s = √A and perimeter P = 4√A. For rectangles, many different rectangles can share the same area, so you need more info (like one side length).

• What perimeter should I use when buying materials?

  Use the calculated perimeter as a baseline, then add extra for waste, overlap, corners, and mistakes. In DIY projects, a 5–15% buffer is common depending on material type.

Make it shareable (without being cringe)

Perimeter isn’t “romantic,” but it can still be surprisingly shareable. People love quick challenges and “I never learned this” mini-lessons. Here are a few ways creators use simple math tools to get engagement:

• Story quiz: Post a photo of a rectangle with dimensions and ask, “Perimeter?” Then reveal the answer slide.
• DIY checklist: “How much trim do I need?” screenshot your result and use it as a shopping list.
• Homework helper: Show the formula substitution step — it’s what teachers want to see.
• Before/after: Share how changing one dimension changes perimeter but not always area.