30-60-90 Triangle Calculator
Enter any one side of a 30-60-90 triangle to find the other sides, area, and perimeter.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the 30-60-90 Triangle Calculator
A 30-60-90 triangle has sides in the fixed ratio 1 : sqrt(3) : 2. This calculator lets you find all three sides plus the area and perimeter from any single known side.
- Select the known side. Choose whether you know the short side (opposite 30 degrees), the long side (opposite 60 degrees), or the hypotenuse.
- Enter the length. Type the value of the known side.
- Read the results. All three sides, the area, and the perimeter appear instantly.
About 30-60-90 Triangles
The 30-60-90 triangle is one of two special right triangles (the other is 45-45-90). It appears when you bisect an equilateral triangle. The side ratios are always 1 : sqrt(3) : 2. The short leg is half the hypotenuse, and the long leg is sqrt(3) times the short leg. These relationships make it one of the most commonly tested triangles in geometry and standardized tests.
Frequently Asked Questions
What is the ratio of sides in a 30-60-90 triangle?
The sides are always in the ratio 1 : sqrt(3) : 2. The shortest side is opposite the 30-degree angle, the medium side (sqrt(3) times the short side) is opposite the 60-degree angle, and the hypotenuse (twice the short side) is opposite the 90-degree angle.
How do I find the hypotenuse of a 30-60-90 triangle?
The hypotenuse is exactly twice the length of the short side. If the short side is 5, the hypotenuse is 10. If you know the long side, divide it by sqrt(3) to get the short side, then multiply by 2.
Where does the 30-60-90 triangle come from?
It is formed by cutting an equilateral triangle in half along its altitude. Each half is a 30-60-90 triangle. This is why the short side is half the original equilateral side (the hypotenuse).