What is the Perimeter of a Triangle?
The perimeter of a triangle is the total distance around the triangle — the sum of the lengths of all three sides. You can think of the perimeter as a path that surrounds the figure. In real-life applications, the perimeter of a triangle is useful for fencing a triangular plot of land, binding a triangular pennant with ribbon, or estimating the lace needed for a triangular piece of fabric.
How to Find the Perimeter of a Triangle?
The method depends on what information you have about the triangle. Our calculator supports three formulas:
Formula 1 — Three Sides (SSS)
If you know all three sides a, b, and c, the perimeter is simply their sum:
P = a + b + c
This is the most straightforward case. Just make sure the three side lengths satisfy the triangle inequality: each side must be less than the sum of the other two.
Formula 2 — Two Sides and the Included Angle (SAS)
If you know two sides a and b, and the angle γ (gamma) between them, use the Law of Cosines to find the third side:
c = √(a² + b² − 2ab · cos(γ))
Then compute the perimeter: P = a + b + c
Formula 3 — Two Angles and the Included Side (ASA)
If you know two angles β (beta) and γ (gamma), and the side a between them, first find the third angle:
α = 180° − β − γ
Then use the Law of Sines to find the other two sides and the perimeter:
P = a + a · (sin(β) + sin(γ)) / sin(β + γ)
Measurement Systems
Our perimeter of a triangle calculator supports both major measurement systems:
- Metric system: millimeters (mm), centimeters (cm), meters (m), kilometers (km)
- American (US) system: inches (in), feet (ft), yards (yd), miles (mi)
Enter the side lengths and angles in your preferred units. The perimeter result will be expressed in the same unit.
How to Use Our Perimeter of a Triangle Calculator?
- Choose the calculation method: Select SSS (three sides), SAS (two sides and angle), or ASA (two angles and side).
- Select the measurement system: Choose Metric or American (US), then pick the specific unit from the dropdown.
- Enter the values: Fill in the required sides and/or angles for the selected method.
- Click Calculate: The calculator instantly shows the perimeter, the step-by-step formula, and all intermediate results.
- Share or print: Use the Share button to send the result link, or Print to get a paper copy.
FAQs
What is the perimeter formula for a triangle?
The basic formula is P = a + b + c, where a, b, and c are the three side lengths. If you don't know all three sides, you can use the Law of Cosines (SAS method) or the Law of Sines (ASA method) to find the missing sides first.
Can a triangle have any combination of side lengths?
No. The three sides must satisfy the triangle inequality theorem: each side must be strictly less than the sum of the other two sides. For example, sides 1, 2, and 10 cannot form a triangle because 1 + 2 < 10.
What is the perimeter of an equilateral triangle?
For an equilateral triangle (all sides equal to a), the perimeter is P = 3a.
What is the perimeter of a right triangle?
For a right triangle with legs a and b and hypotenuse c, use the Pythagorean theorem: c = √(a² + b²), then P = a + b + c. Our SAS mode with a 90° angle automatically handles this calculation.
What units does this calculator support?
The calculator supports both the Metric system (mm, cm, m, km) and the American/Imperial system (in, ft, yd, mi). Angles are always entered in degrees.
What is the difference between SSS, SAS, and ASA?
SSS — you know all three sides. SAS — you know two sides and the angle between them. ASA — you know two angles and the side between them. Each method leads to the same perimeter when the inputs describe the same triangle.