Perimeter of a Triangle Calculator

Enter a triangle's three side lengths to get its perimeter (P = a + b + c), semi-perimeter, area (Heron's formula), and a triangle-validity check.

Quick Facts

Perimeter formula
P = a + b + c
Simply add the three side lengths together.
Triangle inequality
a + b > c (for every pair)
The sum of any two sides must exceed the third, or no triangle exists.
Heron's formula
Area = √(s(s−a)(s−b)(s−c))
Uses the semi-perimeter s = P / 2 — no angle or height needed.

Your Results

Calculated
Perimeter
-
P = a + b + c
Semi-perimeter
-
s = P / 2
Area (Heron's formula)
-
√(s(s−a)(s−b)(s−c))
Triangle Type
-
By side lengths

Ready

Enter three side lengths, then press Calculate.

Formula and Method for the Perimeter of a Triangle

A triangle's perimeter is the total distance around its boundary — the sum of the lengths of all three sides. If the sides are labeled a, b, and c, the formula is simply P = a + b + c. Unlike area, no angles, height, or special formula variant is needed — just add the three lengths. This calculator also checks that your three lengths can actually form a triangle, and derives the semi-perimeter and area from the same inputs.

How the calculation works

Enter the three side lengths and choose the unit they are measured in. The calculator first verifies the triangle inequality theorem: for three lengths to form a valid triangle, the sum of any two sides must be strictly greater than the third (a + b > c, a + c > b, and b + c > a). If all three checks pass, it adds the sides for the perimeter (P = a + b + c), halves that for the semi-perimeter (s = P / 2), and plugs s into Heron's formula, Area = √(s(s−a)(s−b)(s−c)), to get the area without needing an angle or height. It also classifies the triangle as equilateral (all sides equal), isosceles (exactly two sides equal), or scalene (all sides different).

Common mistakes

  • Ignoring the triangle inequality: not every trio of positive numbers forms a triangle — sides 2, 3, and 10 cannot close into a shape because 2 + 3 is less than 10.
  • Mixing units: keep all three side lengths in the same unit — convert inches to feet, or centimeters to meters, before entering values.
  • Confusing perimeter with area: perimeter (P = a + b + c) is a length in linear units (ft, m); area from Heron's formula is in square units (ft², m²) and is not simply half the perimeter times anything without the full formula.

Real-world applications

  • Fencing, edging, and trim projects use perimeter directly to determine how much linear material to buy.
  • Land surveying and construction layout use the triangle inequality and Heron's formula to verify staked-out triangular plots are geometrically valid.
  • Truss and structural design relies on triangle side lengths and area to compute load paths and material needs.
  • Geometry and trigonometry coursework use these same relationships to introduce the semi-perimeter before moving on to the law of cosines and other triangle formulas.

Frequently Asked Questions

What is the formula for the perimeter of a triangle?
The perimeter is simply the sum of the three side lengths: P = a + b + c. For example, a triangle with sides 3, 4, and 5 units has a perimeter of 3 + 4 + 5 = 12 units.
How do I know if three side lengths can form a valid triangle?
Apply the triangle inequality theorem: the sum of any two sides must be strictly greater than the third side (a + b > c, a + c > b, and b + c > a). If any of these fail, the three lengths cannot form a triangle.
How can I find a triangle's area from its three side lengths?
Use Heron's formula. First find the semi-perimeter s = (a + b + c) / 2, then compute Area = √(s(s−a)(s−b)(s−c)). This works for any triangle without needing to know an angle or height.
What is the difference between perimeter and semi-perimeter?
The semi-perimeter is exactly half the perimeter, s = P / 2. It is not a physical measurement on its own — it is an intermediate value used in Heron's formula and other triangle-geometry calculations.

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