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Triangle Perimeter Calculator

Enter the three side lengths to calculate the triangle's perimeter.

How it is calculated

The perimeter is the length of the boundary, found by adding the three sides:

P = a + b + c
semi-perimeter s = P ÷ 2

The tool also tests whether the three lengths can form a triangle: each side must be strictly smaller than the sum of the other two (a < b + c, b < a + c, c < a + b). If any one fails, the status reads Invalid, but the perimeter and semi-perimeter are still shown as a plain sum, so look at the status line before trusting the result. All three sides must be above zero and in the same length unit; the answer is in that unit, to two decimals.

Worked example

Take sides of 7, 8 and 9. The perimeter is 7 + 8 + 9 = 24.00, and the semi-perimeter is 24 ÷ 2 = 12.00. For the validity test, the longest side 9 is less than 7 + 8 = 15, and the other two sides pass too, so the status reads Valid triangle. Compare sides 3, 4 and 7: the sum is 14.00, but 7 is not less than 3 + 4, so the tool flags it Invalid (the sides just lie flat on a line).

Try this example →

Common mistakes

  • Ignoring the validity line. Sides 3, 4 and 7 still produce a perimeter of 14.00, but they cannot close into a triangle because 3 + 4 equals 7.
  • Mixing units, for example two sides in metres and one in centimetres. The sum is meaningless unless all three share a unit.
  • Entering a height or a diagonal in place of a side. Perimeter needs the three outer edges only.
  • Confusing perimeter with area. The perimeter is a length (24.00 here); area is a squared unit and needs a different formula such as Heron's.
  • Entering a side of 0, which is rejected, when a side is only very small. A degenerate sliver such as 1, 1, 2 is flagged Invalid because 2 equals 1 + 1.

About this calculator

A triangle’s perimeter is simply the sum of its three side lengths, P = a + b + c — but not every three lengths actually form a triangle. The triangle inequality theorem requires that the sum of any two sides be greater than the third; if it isn’t, the “triangle” can’t physically close.

This calculator adds your three sides to get the perimeter and checks that inequality automatically, flagging invalid combinations before you build on a wrong answer. It’s used in basic geometry coursework, and just as often in practical settings like construction and fencing layout, where knowing the total edge length of a triangular plot or truss is a quick first step in material estimating.

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