30-60-90 Triangle Calculator

Last Updated on March 2, 2026 | 1 : 42 pm by Anas Brittany

Use this 30-60-90 triangle calculator to solve a special right triangle where the angles are 30°, 60°, and 90°. Enter any one side length and the calculator will find the other two sides using the standard 30-60-90 ratio.

What Is a 30-60-90 Triangle?

A 30-60-90 triangle is a special right triangle with angles of 30°, 60°, and 90°. Because the angles are fixed, the side lengths always follow a predictable ratio. This makes it faster to solve than using the full Pythagorean theorem every time.

30-60-90 Triangle Side Ratio

The side lengths always follow this pattern:

Short leg : Long leg : Hypotenuse = 1 : √3 : 2

• The short leg is opposite the 30° angle
• The long leg is opposite the 60° angle
• The hypotenuse is opposite the 90° angle

If the short leg is x:

• Long leg = x√3
• Hypotenuse = 2x

How to Solve a 30-60-90 Triangle

To find missing sides:

• If you know the short leg, multiply by √3 to get the long leg, and multiply by 2 to get the hypotenuse.
• If you know the hypotenuse, divide by 2 to get the short leg, then multiply by √3 to get the long leg.
• If you know the long leg, divide by √3 to get the short leg, then multiply the short leg by 2 to get the hypotenuse.

30-60-90 Triangle Formulas

Let the short leg be x:

• Long leg = x√3
• Hypotenuse = 2x
• Area = (x · x√3) ÷ 2 = (x²√3) ÷ 2
• Perimeter = x + x√3 + 2x = 3x + x√3

Example

If the hypotenuse is 14:

• Short leg = 14 ÷ 2 = 7
• Long leg = 7√3 ≈ 12.124

So the triangle sides are approximately 7, 12.124, and 14.

Frequently Asked Questions

Why is the ratio always the same?

The angles are fixed at 30° and 60°, so the triangle is always similar no matter the size. Similar triangles always keep the same side ratios.

Is this triangle used in real life?

Yes. It appears in geometry, trigonometry, construction layouts, design, and engineering whenever a 30° angle is involved.

Can I use any unit?

Yes. The ratio works for inches, feet, meters, or any other unit, as long as all sides use the same unit.