Perimeter of Triangle Calculator
Enter three sides, a right triangle base and height, or two sides and an angle to find the perimeter.
Updated
Perimeter of Triangle Calculator
Our Perimeter of Triangle Calculator adds up the three sides of any triangle. Only know the base and height of a right triangle? It finds the hypotenuse with Pythagoras first. Know two sides and the angle between them? It finds the third side with the law of cosines. It also shows the working, the area, the angles and the type of triangle.
Quick answer
The perimeter of a triangle is a + b + c, the sum of its three sides: 5 + 6 + 7 = 18 cm.
- Right triangle: P = b + h + √(b² + h²), so 3 and 4 give 12
- Equilateral: 3 × side, so sides of 6 give 18
- Two sides and an angle: find c from c² = a² + b² − 2ab cos C, then add
- Units: a perimeter is a length (cm, m, ft), never cm²
What Is the Perimeter of a Triangle?
The perimeter of a triangle is the total distance around its edge: walk along all three sides and back to the start. It is a length, so it uses the same unit as the sides.
Perimeter of a Triangle Formula
- Measure the three sides. Call them a, b and c.
- Use one unit. Convert first if one side is in m and another in cm.
- Add them. 5 + 6 + 7 = 18.
- Write the unit. 18 cm, not 18 cm².
Half of the perimeter is the semi-perimeter, s = P ÷ 2. It is the first step of Heron’s formula for the area, so the calculator shows it in 3 sides mode.
Triangle Perimeter Examples
| Sides | Perimeter |
|---|---|
| 3, 4, 5 cm | 12 cm |
| 5, 12, 13 cm | 30 cm |
| 6, 8, 10 m | 24 m |
| 7, 24, 25 ft | 56 ft |
| 9, 9, 9 in | 27 in |
| 2.5, 3, 4 m | 9.5 m |
Perimeter of a Right Triangle
In a right triangle the base and height are two of the sides (the legs). The third side, the hypotenuse, comes from the Pythagorean theorem. Add all three:
P = b + h + c
P = 8 + 6 + 10 = 24
When b² + h² is not a perfect square, the answer has a root in it. Legs of 1 and 2 give c = √5 and P = 3 + √5 ≈ 5.236. The calculator shows both the exact form and the decimal.
Perimeter From Two Sides and an Angle
With two sides and the angle between them (the included angle), find the third side with the law of cosines, then add:
P = a + b + c
c = 7
P = 5 + 8 + 7 = 20
The angle must be the one between the two sides you know. At 90°, cos C is 0 and the rule becomes the right triangle formula above.
Equilateral, Isosceles and Scalene Triangles
| Triangle | Example |
|---|---|
EquilateralP = 3s | s = 6: 18 |
IsoscelesP = 2a + b | 5, 5, 6: 16 |
ScaleneP = a + b + c | 4, 6, 7: 17 |
Rightb + h + √(b² + h²) | 3, 4: 12 |
An equilateral triangle has three equal sides, an isosceles triangle has two, and a scalene triangle has none. The rule is always the same: add the three sides.
Missing Side From the Perimeter
Subtract the two sides you know from the perimeter:
30 − 8 − 10 = 12 cm
For an equilateral triangle, divide by 3: a perimeter of 27 in gives sides of 9 in.
Common Mistakes
- Adding the height: the height is only a side in a right triangle. In other triangles, use the slanted sides.
- Sides that cannot close: any two sides must add up to more than the third. 2, 3 and 6 is not a triangle.
- Mixed units: 1 m + 50 cm + 80 cm is 2.3 m, not 131.
- Square units: a perimeter is cm or m, not cm² or m².
- Wrong angle: the law of cosines needs the angle between the two known sides.
Key Terms
- Perimeter
- The distance around the triangle, P = a + b + c.
- Legs
- The two sides that meet at the right angle in a right triangle.
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Semi-perimeter
- Half the perimeter, s = P ÷ 2.
- Included angle
- The angle between two given sides.
How to Use the Perimeter of Triangle Calculator
- Choose what you know. Pick Right triangle (base and height), 3 sides, or 2 sides and the angle between them.
- Enter the values. Type the lengths, and the angle in degrees or radians if asked. Decimals and fractions such as 3/4 work. Choose a unit if you want one (mm, cm, m, km, in, ft, yd or mi).
- Read and copy the result. The perimeter appears as you type, with a drawing to scale, the working, the area, the angles and the type of triangle. Press Copy to copy it, or Clear or Esc to start again.
Example: a triangular garden bed has sides of 4 m, 6 m and 7 m. Pick 3 sides, enter 4, 6 and 7 and choose m. The perimeter is 17 m, so you need 17 m of edging.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a triangle?
Add the lengths of its three sides: P = a + b + c. A triangle with sides 5 cm, 6 cm and 7 cm has a perimeter of 18 cm.
How do you find the perimeter of a right triangle from the base and height?
Find the hypotenuse with Pythagoras, c = √(b² + h²), then add all three sides. A base of 3 and a height of 4 give c = 5 and P = 3 + 4 + 5 = 12.
How do you find the perimeter with two sides and an angle?
Use the law of cosines for the third side, c² = a² + b² − 2ab cos C, where C is the angle between a and b. Sides 5 and 8 with 60° between them give c = 7 and P = 20.
What is the perimeter of an equilateral triangle?
Three times the side length, P = 3s. Sides of 6 cm give a perimeter of 18 cm.
How do you find a missing side from the perimeter?
Subtract the two known sides from the perimeter: c = P − a − b. A perimeter of 30 cm with sides 8 cm and 10 cm leaves 12 cm.
Can any three lengths make a triangle?
No. Any two sides must add up to more than the third (the triangle inequality). 3, 4 and 5 works, but 2, 3 and 6 does not, because 2 + 3 is less than 6.
Is the Perimeter of Triangle Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Triangle Calculator to find the perimeter of any triangle from three sides, a right triangle’s base and height, or two sides and an angle.