Triangle Perimeter Calculator

P = a + b + c

Side a

Any one of the three sides, in centimetres. Which side you call a does not matter — the three are added, so the order changes nothing about the answer

Side b

The second side, in centimetres. It has to be the full length along the edge, not a horizontal or vertical projection of it, or the total will come out short

Side c

The third side, in centimetres. The three together must satisfy the triangle inequality, which the page checks before it answers anything

Perimeter

The distance all the way around the triangle, in centimetres. Walk the three edges once each and this is how far you have gone

a + b + c

One addition, done in order from left to right. There is no multiplication, no division and no rounding step, so the answer is exact for any inputs that are exactly representable

Four decimal places

How wide the reading is written. Three whole numbers always give a whole number, so the decimals only matter when a side is measured with a fraction in it

Centimetres

The unit of the answer whatever the dropdowns say. As with any perimeter this is a length, so the conversion is linear — a triangle measured in inches comes back as a centimetre figure, and you divide by 2.54 to read it in inches

Perimeter shows up wherever something has to go around the outside of a shape rather than fill it. Fencing a triangular paddock, running a coping or an edge strip along a triangular bed, cutting a border for a triangular pane of glass — all of those are priced and ordered by length, and the area, which is the number a survey will usually give you, is no help at all. Framing and fabrication bring a second family: a triangular gusset, a brace, a bracket, where the perimeter is the length of stock to cut, and an allowance for the corners is added on top. Sails, awnings and shade cloth are the same calculation in fabric. An equilateral triangle is the easiest case of all, since the perimeter is simply three times the side and the addition can be skipped entirely. Then there is the surveyor's use, which runs the other way: measure the three sides of a plot in the field, because those are the easy measurements to take, and the perimeter falls straight out of them while the area needs a formula on top. And there is the classroom version, where a triangle drawn on squared paper can be walked with a finger and the total checked against the answer — which is worth doing once with the 3, 4, 5 triangle, since the perimeter comes to 12 and the area to 6 and three separate memorable numbers come out of one small shape.

1. Sides of 3, 4 and 5

   1. Add the first two sides: 3 + 4 = 7
   2. Add the third: 7 + 5 = 12

   The pair the page loads with, and the shape to remember: 3, 4, 5 is the smallest right-angled triangle with whole-number sides, its area is 6 and its perimeter is 12. The herons page gives the same 12 for these three sides, which is the reconciliation between the two pages — they take identical inputs and answer different questions.

2. An equilateral triangle with sides of 6

   1. Add the first two sides: 6 + 6 = 12
   2. Add the third: 12 + 6 = 18

   An equilateral triangle, where the perimeter is just three times the side. Worth noting because it is the one case where you can skip the addition: for any regular polygon the perimeter is the side length times the number of sides, and the triangle is the smallest example of that.

3. An isosceles triangle with sides of 5, 5 and 6

   1. Add the first two sides: 5 + 5 = 10
   2. Add the third: 10 + 6 = 16

   An isosceles triangle with two equal sides, which is a shape that appears constantly in roofs and trusses. It is also the shape the isosceles triangle page opens with: its default is a base of 6 with two legs of 5, which returns a height of 4 and an area of 12 — the same triangle, two different questions asked about it.

4. Sides of 1, 1 and 2

   1. Add the first two sides: 1 + 1 = 2
   2. Add the third: 2 + 2 = 4

   The degenerate case, and the one that shows where the page draws the line: 1 + 1 is exactly 2, so the triangle has been flattened into a line segment rather than being impossible. The page answers 4, because walking a line of length 2 out and back is a real distance. Had the third side been 3, the page would have refused instead.

This page takes three side lengths and nothing else. It gives no area, no angles and no height — the area of the same triangle lives on its own page, and the two take identical inputs and answer different questions. The three sides must satisfy the triangle inequality; when the two shorter sides come to less than the longest, no triangle corresponds to the input and the page refuses rather than answering. When they come to exactly the longest, the triangle is degenerate, and the page accepts it and returns the perimeter of the line segment it has collapsed into. The answer is always in centimetres whatever the dropdowns are set to, and since a perimeter is a length the conversion is linear: a triangle measured in inches comes back as centimetres, and you divide by 2.54 rather than by 6.4516. Four decimal places is a display width rather than a claim about precision. Nothing here handles a curved side, a triangle drawn on a sphere, the thickness of a frame around the edge, or an allowance for waste when the sides are being cut from stock.

Does the order of the sides matter?

No. Addition is commutative, so 3, 4, 5 and 5, 3, 4 give the same 12. The boxes are labelled a, b and c for convenience, not because anything depends on which side goes where. The triangle inequality is checked in all three pairings regardless of the order you typed them in.

Why does the page refuse some sets of three numbers?

Because not every three lengths make a triangle. If the two shorter sides add up to less than the longest one, the two short sticks cannot reach across the long one however you tilt them, and there is no shape to measure. The page checks that condition and reports it rather than returning a total for something that does not exist.

What about a triangle that is exactly flat?

It is accepted. When the two shorter sides come to exactly the longest, the triangle has been squashed into a line segment rather than being impossible — a 1, 1, 2 triangle is a line of length 2 walked out and back. That has a real perimeter, which is 4, so the page answers. This is the one case people expect to be rejected and it is the one case that is not.

Where is the area of the same triangle?

On its own page. Three sides are enough to fix both the perimeter and the area, but the area needs a formula with a square root in it and the perimeter needs an addition, so they are kept apart. This page deliberately does one thing, and it takes exactly the same three numbers the other one takes.

Do the units matter?

The dropdowns change what you type in, not what comes out. The reading is always in centimetres, and since a perimeter is a length the conversion is linear — divide by 2.54 to read a centimetre answer in inches. Mixing units is handled rather than assumed away: each of the three boxes has its own dropdown, and whatever you pick there is converted into centimetres before the arithmetic runs, so a side in feet and a side in inches can be typed in as they are.

Is the perimeter useful on its own?

It is the number you need whenever something goes around a shape rather than filling it: fencing, edging, framing, binding, cutting stock to length. An area tells you how much paint a wall needs; a perimeter tells you how much skirting board goes along the bottom of it. Both are on this site, and for a triangle they are two different pages.

• Triangle — what a triangle is, the vocabulary of its sides, and the properties that follow from the three lengths alone — Wolfram MathWorld (United States)
• Triangle Inequality — the rule that any two sides must sum to more than the third, which is the check this page runs before answering — Wolfram MathWorld (United States)
• Perimeter — the general notion of the distance around a closed figure, of which the three-sided case on this page is the simplest instance — Wolfram MathWorld (United States)
• 教育部关于印发义务教育课程方案和课程标准（2022 年版）的通知——The fifth item in the annex list of this notice is the Mathematics Curriculum Standards for Compulsory Education (2022 edition); the perimeter of a triangle is part of the compulsory-education mathematics curriculum, and the wording of the standards and the grade-band breakdown are governed by that annex — 中华人民共和国教育部