30-60-90 Triangle Calculator
Use this calculator to find the sides, area and perimeter of a special right triangle. Enter any side and the calculator will compute the remaining values automatically.
30-60-90 Triangle Calculator
The 30-60-90 triangle calculator helps you quickly find the sides, area, and perimeter of a special right triangle whose angles are 30°, 60°, and 90°. By entering any one side, the calculator automatically computes the remaining sides using the well-known 1 : √3 : 2 ratio.
This triangle appears frequently in geometry, trigonometry, architecture, and engineering, so understanding its properties can make many math problems easier to solve.
What Is a 30-60-90 Triangle?
A 30-60-90 triangle is a special right triangle where the three interior angles measure:
- 30°
- 60°
- 90°
Since it contains a right angle, the triangle follows thePythagorean theorem.
30-60-90 Triangle Formula
A 30-60-90 triangle is a special right triangle where the side lengths always follow a fixed ratio.
- Short leg (a) – opposite 30°
- Long leg (b) = a × √3
- Hypotenuse (c) = 2a
Example Calculation
If the short leg is a = 5
b = a × √3 = 5 × 1.732 = 8.66
c = 2a = 2 × 5 = 10
Area = ½ × a × b = ½ × 5 × 8.66 = 21.65
30-60-90 Triangle Side Ratio
The sides follow this fixed ratio:
1 : √3 : 2
| Side | Description |
|---|---|
| a | Short leg (opposite 30°) |
| b | Long leg (opposite 60°) |
| c | Hypotenuse (opposite 90°) |
Area and Perimeter
Area Formula
Area = ½ × a × b
Area = (√3 / 2)a²
Perimeter Formula
Perimeter = a + b + c
Perimeter = a(3 + √3)
FAQ
The side ratio is 1 : √3 : 2.
Multiply the shortest side by 2.
Multiply the short leg by √3.
They appear in geometry, engineering, architecture, and trigonometry problems.