Triangle Perimeter Calculator
Enter 3 side lengths or 3 coordinates — get the perimeter with honest triangle-inequality validation, a labeled diagram, and step-by-step working.
Is this the right tool?
This calculator finds the perimeter of a triangle only. Looking for something else?
- Perimeter of a trapezoid → area-of-a-trapezoid (includes a perimeter mode)
- Perimeter of a quarter circle → quarter-circle-perimeter
- Triangle area (not perimeter) → triangle-area-calculator
- Check if it is a right triangle → is-it-a-right-triangle
- Find a missing hypotenuse → hypotenuse
1. Choose input mode
Enter the three vertices. Each side is computed with the Euclidean distance formula d = √((x₂−x₁)² + (y₂−y₁)²).
2. Result
Worked examples
Example 1 — three sides: 3, 4, 5
- Triangle-inequality check: 3 + 4 = 7 > 5 ✓; 3 + 5 = 8 > 4 ✓; 4 + 5 = 9 > 3 ✓ — valid triangle.
- Perimeter:
P = 3 + 4 + 5 = 12.
Example 2 — three points: (0, 0), (3, 0), (0, 4)
- Side AB: d = √((3−0)² + (0−0)²) = √9 =
3. - Side BC: d = √((0−3)² + (4−0)²) = √(9 + 16) = √25 =
5. - Side CA: d = √((0−0)² + (4−0)²) = √16 =
4. - Triangle-inequality check: 3 + 4 > 5 ✓ — valid triangle.
- Perimeter:
P = 3 + 5 + 4 = 12.
Tip: the points (0, 0), (6, 0), (3, 4) give sides 6, 5, 5 and perimeter P = 6 + 5 + 5 = 16. A trickier one: (0, 0), (1, 0), (0, 2) gives sides 1, 2, and √5 ≈ 2.2360679775, so P = 1 + 2 + 2.2360679775 = 5.2360679775.
Frequently asked questions
The perimeter P of a triangle is the sum of its three side lengths: P = a + b + c. For example, a triangle with sides 3, 4, and 5 has perimeter P = 3 + 4 + 5 = 12.
Compute each side with the Euclidean distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2), then add the three sides. For example, the points (0, 0), (3, 0), and (0, 4) give sides 3, 4, and 5, so the perimeter is 3 + 4 + 5 = 12.
Three lengths form a real triangle only if each pair sums to more than the third side: a + b > c, a + c > b, and b + c > a (strictly greater). For example, 2, 3, and 10 fail because 2 + 3 = 5, which is not greater than 10, so they cannot form a triangle and this calculator reports them as invalid instead of returning a misleading perimeter.
Collinear points form a degenerate triangle with zero area. For example, (0, 0), (2, 0), and (5, 0) produce side lengths 2, 3, and 5, but 2 + 3 = 5 is not strictly greater than 5, so the triangle inequality fails. This calculator rejects such inputs honestly.
No. Addition is commutative, so P = a + b + c gives the same result whatever order you use. Entering 5, 3, 4 gives the same perimeter (12) as 3, 4, 5.
The same unit as your inputs. If the sides are in centimeters, the perimeter is in centimeters; if the coordinates are in inches, the perimeter is in inches. This calculator never converts units.
The perimeter is the total length around the triangle (a + b + c), while the area is the surface it encloses. For example, the 3-4-5 triangle has perimeter 12 but area 6. If you need the area, use a dedicated triangle area calculator instead.
Yes. It runs 100% in your browser with no server, no sign-up, and no data leaving your device. It also works offline once the page is loaded.
Free tool by NRTechStudio