Triangle Perimeter Calculator

P = a + b + c

Three sides, add them all. Trivial unless the side lengths aren’t actually valid for a triangle.

The triangle inequality says every side must be strictly SHORTER than the sum of the other two. Try to build a triangle with sides 3, 4 and 10 and it will not close: the 3 and the 4 together only reach 7, so the 10 has nothing to meet. This calculator refuses those values rather than adding them up.

Note the word strictly. Sides of 3, 7 and 10 fail too, even though 3 + 7 reaches 10 exactly, because the three points then lie on one straight line and the shape has no area at all.

Where this comes up in real work:

• Garden bed edging around an irregular triangular patch. A 4 ft × 5 ft × 6 ft bed needs 15 ft of border timbers.
• Sailmaking. A jib sail with luff (leading edge) 25 ft, foot (bottom) 12 ft, and leech (trailing edge) 22 ft has 59 ft of edge tape needed.
• Truss design. Trusses are triangles because a triangle cannot be deformed without changing a side length, and the perimeter gives the timber for the outer chords. A scalene truss measuring 30 ft, 18 ft and 22.5 ft takes 70.5 ft before the internal webs.
• Triangular plot fencing. For an odd-shaped lot the surveyor gives you three side measurements. Add them for the fence quantity.
• Yield, warning, and triangle road signs. A 36 in equilateral triangle needs 108 in, or 9 ft, of edge trim.

Worked example: sail patching

A storm jib measures 18 ft × 8 ft × 16 ft. You need to add bolt-rope along all three edges. P = 42 ft of bolt-rope. Order 45 ft to allow for the corner reinforcement laps.

Triangle inequality in practice:

If you measure three sticks meant to form a triangle and get 10, 4 and 4, you have measured something wrong. 4 + 4 = 8, which is less than 10, so those three lengths cannot meet.

Where a + b = c exactly, the triangle collapses to a straight line with zero area. Real measurements rarely land on it, but it is the boundary, and Heron’s formula obligingly returns 0 there rather than complaining.

Quick formulas for special triangles:

• Equilateral (all sides s): P = 3s
• Isosceles (base b, legs s): P = b + 2s
• Right triangle (legs a, b): hypotenuse = √(a² + b²), then P = a + b + √(a² + b²)
• 3-4-5 right triangle: P = 12 (scale up for larger versions: 6-8-10 has P = 24)