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Semiperimeter Calculator

Enter the three side lengths to find the semiperimeter of the triangle.

Result

21.00
42.00
13.00 + 14.00 + 15.00

How it is calculated

The semiperimeter s is half of the distance around the triangle:

s = (a + b + c) ÷ 2

Along with s the tool shows the full perimeter a + b + c and the sum written out with each side rounded to two decimals. All three sides must be greater than zero and in the same unit, and the answer is in that unit. The tool applies the strict triangle inequality: each side must be shorter than the other two combined, so sides such as 1, 1 and 100, or a flat triangle like 3, 4 and 7, show no result. The value is mainly a stepping stone to Heron's formula and the inradius.

Worked example

Take the triangle with sides 13, 14 and 15. The sum is 13 + 14 + 15 = 42.00, which is the perimeter, and half of it is the semiperimeter 21.00. This is the starting point for the area: s − a = 8, s − b = 7 and s − c = 6, so Heron's formula gives √(21 × 8 × 7 × 6) = √7056 = 84. The inradius is then 84 ÷ 21 = 4.

Try this example →

Common mistakes

  • Confusing the semiperimeter with the perimeter. Putting 21 (half) where 42 (the whole) belongs makes Heron's formula collapse, and the area comes out wrong.
  • Using the semiperimeter as if it were a side length or the height. It is a derived number, and it is always longer than any single side of a real triangle.
  • Entering sides that cannot form a triangle, such as 3, 4 and 8. The tool shows no result; a side exactly equal to the sum of the other two (3, 4, 7) is also rejected because the triangle would be flat.
  • Mixing units, such as one side in metres and the others in centimetres. The sum is only meaningful if all three are in the same unit.
  • Rounding the sides first. The tool shows two decimals (2.345, 3.456 and 4.567 appear as 2.35, 3.46 and 4.57), so for Heron's formula keep the exact sides and only round the final area.

About this calculator

The semiperimeter of a triangle, usually written s, is simply half the sum of its three side lengths: s = (a + b + c) / 2. On its own it is a modest quantity, but it is the key ingredient of Heron's formula for triangle area, Area = √[s(s−a)(s−b)(s−c)], which finds the area from side lengths alone with no need to know any angle.

The semiperimeter also appears in the formula for a triangle's inradius (r = Area / s, the radius of the circle inscribed inside the triangle touching all three sides) and in various other triangle-geometry identities, which is why it is computed as a standalone step before those formulas are applied.

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