📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

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Worked example

Data
Side A
\(b = {\color{#6c5ce7}{3\,\text{cm}}}\)
Side B
\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)
Side C
\(d = {\color{#6c5ce7}{5\,\text{cm}}}\)
Perimeter
\(a = \,?\)
Formula
\[a = {b}+{c}+{d}\]
Steps
1Substitute the values
\[a = {\color{#6c5ce7}{3\,\text{cm}}}+{\color{#6c5ce7}{4\,\text{cm}}}+{\color{#6c5ce7}{5\,\text{cm}}}\]
Each letter is replaced by its value.
2Add
\[a = {\color{#6c5ce7}{3\,\text{cm}}}+{\color{#6c5ce7}{4\,\text{cm}}}+{\color{#6c5ce7}{5\,\text{cm}}} = 12\,\text{cm}\]
\(3+4 = 7\)\(7+5 = 12\)
Perimeter: 12 cm
Check

If we use the result to calculate Side A, we should get the value you entered:

\[b = {a}-{c}-{d}\]
\[b = 12\,\text{cm}-4\,\text{cm}-5\,\text{cm} = 3\,\text{cm}\]
It gives 3 cm, the same as the value entered.
Calculate the Perimeter
Please fill in the fields:
Side_A Side_B Side_C
And leave empty
Perimeter
Calculate the Side_A
Please fill in the fields:
Perimeter Side_B Side_C
And leave empty
Side_A
Calculate the Side_B
Please fill in the fields:
Perimeter Side_A Side_C
And leave empty
Side_B
Calculate the Side_C
Please fill in the fields:
Perimeter Side_A Side_B
And leave empty
Side_C

How to calculate the perimeter of a triangle

The perimeter of a triangle is the sum of its three sides:

\[ P = \text{Side}_A + \text{Side}_B + \text{Side}_C \]

If you know the perimeter and two sides, the third one is:

\[ \text{Side}_C = P - \text{Side}_A - \text{Side}_B \]

How to use the calculator

  1. Enter three of the four values.
  2. Leave empty the one you want to find.
  3. Press Calculate. Use the same unit for all the sides.

Worked examples

1. Sides of 5, 7 and 9 cm

\[ P = 5 + 7 + 9 = 21\ \text{cm} \]

2. Third side with a perimeter of 30 m

Sides of 8 m and 12 m: \( 30 - 8 - 12 = 10 \) m.

3. Right triangle with only the legs

If you only know the legs of a right triangle, find the hypotenuse first with the Pythagorean theorem. With legs of 6 and 8, the hypotenuse is \( \sqrt{36 + 64} = 10 \) and the perimeter is \( 6 + 8 + 10 = 24 \).

Special triangles

  • Equilateral (three equal sides): \( P = 3 \times \text{Side} \).
  • Isosceles (two equal sides): \( P = 2 \times \text{Equal side} + \text{Base} \).
  • Scalene (three different sides): add the three.

Can these three sides form a triangle?

Each side must be shorter than the sum of the other two (the triangle inequality). With 3, 4 and 9 there is no triangle, because 3 + 4 = 7 is less than 9. Check it before trusting a perimeter.

Area from the three sides (Heron's formula)

With the perimeter you can also get the area. Call \( s \) half the perimeter:

\[ A = \sqrt{s(s - a)(s - b)(s - c)} \]

For sides of 5, 7 and 9: \( s = 10.5 \) and \( A = \sqrt{10.5 \times 5.5 \times 3.5 \times 1.5} \approx 17.41 \).

When Do You Need to Calculate the Perimeter of a Triangle?

🏡 Fencing Triangular Plots

Corner lots and plots between roads are often triangular. Adding the three sides gives the length of fence or wall to enclose them.

Accurate fencing for corner and wedge-shaped lots
⛺ Tents, Sails and Pennants

Triangular sails, pennants and tent panels get a hem or a rope along their edges. The perimeter tells how much tape or rope you need.

Buy the right length of edging or rope
🏠 Gables and Roof Trusses

The gable end of a roof and each roof truss form a triangle. The perimeter gives the length of timber or trim needed to build or finish it.

Material lists for roof framing
🌱 Triangular Garden Beds

Beds in corners are often triangular. The perimeter gives the edging, and the area (with Heron's formula) the soil.

Plan edging and soil for corner beds
🚴 Routes With Three Stops

A trip between three points and back to the start is the perimeter of the triangle they form. It helps estimate the length of a delivery or a training loop.

Estimate the length of a closed route
📚 Geometry and the Triangle Inequality

Perimeter problems often check whether three lengths can form a triangle, or combine the perimeter with the Pythagorean theorem.

Practice with sums and inequalities

Common Mistakes

⚠️ Leaving Out a Side
Common Error: Adding only the two sides labeled in a drawing; the third one is often the base or the hypotenuse.
✅ Solution: Always add three sides
⚠️ Impossible Triangles
Common Error: Using three lengths where one is longer than the sum of the other two. No triangle exists, so the perimeter means nothing.
✅ Solution: Check that each side is shorter than the sum of the other two
⚠️ Using the Height as a Side
Common Error: The height of a triangle is not one of its sides, except in a right triangle, where it can be a leg.
✅ Solution: Measure along the edges
⚠️ Confusing Perimeter and Area
Common Error: Using base × height ÷ 2, which is the area.
✅ Solution: The perimeter only adds lengths
⚠️ Missing Hypotenuse
Common Error: In a right triangle where only the legs are known, adding just the two legs.
✅ Solution: Find the hypotenuse with √(a² + b²) and add it
⚠️ Mixed Units
Common Error: Sides measured in meters and in centimeters on the same plan.
✅ Solution: Convert all the sides to one unit

Applications by Industry

Construction
  • Trusses: Timber length for triangular roof trusses
  • Gables: Trim along the edges of gable ends
  • Bracing: Triangular bracing in frames
Surveying
  • Triangulation: Measuring land by splitting it into triangles
  • Corner lots: Fence length for triangular plots
  • Traffic islands: Curbs around triangular islands
Sailing & Outdoor Gear
  • Sails: Edge tape and bolt rope for triangular sails
  • Tents: Seams of triangular tent panels
  • Shade sails: Cable along the edges of shade sails
Manufacturing
  • Sheet metal: Weld length on triangular gussets
  • Signs: Border of triangular warning signs
  • Packaging: Edges of triangular prism boxes
Design & Crafts
  • Bunting: Ribbon for triangular flags
  • Quilting: Edges of triangle quilt pieces
  • Jewelry: Wire for triangular frames
Education
  • Geometry: Types of triangles and their perimeters
  • Inequalities: The triangle inequality
  • Heron's formula: Area from the three sides

External Resources

Other calculators

Perimeter of a Square
Perimeter of a Square
Perimeter of a Trapezoid
Perimeter of a Trapezoid
Perimeter of a Rhomboid
Perimeter of a Rhomboid
Perimeter of a Rectangle
Perimeter of a Rectangle
Perimeter of a Circle
Perimeter of a Circle
Perimeter of a Rhombus
Perimeter of a Rhombus
Area of a Rectangle
Area of a Rectangle
Surface Area of a Sphere
Surface Area of a Sphere

Geometry Calculators

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