Triangle Perimeter Calculator
Compute the perimeter of any triangle from its three sides.
Validates the triangle inequality.
Multiple units supported.
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 no side can be longer than the sum of the other two. If you try to build a triangle with sides 3, 4, and 10, you can’t — the 3 and 4 together only reach 7, so the 10-cm side can’t close the loop. This calculator flags the violation if you enter impossible side values.
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. Roof trusses use triangles for rigidity — the perimeter tells you how much lumber is needed for the chord pieces (top, bottom, and webs). A 30 ft × 18 ft truss with diagonal 22.5 ft has 70.5 ft of chord.
- Triangular plot fencing. For an unusual lot, the surveyor gives you three side measurements. Add them for the fence quantity.
- Yield, warning, and triangle road signs. A 36 in side equilateral triangle needs 108 in (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’ve measured wrong somewhere. 4 + 4 = 8 < 10 — these can’t form a triangle.
For a degenerate case where a + b = c (exactly), the “triangle” collapses to a straight line with zero area. Real-world measurements rarely hit this exactly, but it’s the limiting case.
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)