30-60-90 triangle calculator
A 30-60-90 triangle is half of an equilateral triangle, so its sides always keep the same ratio. Pick the side you know and enter its length.
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How to use it
- Enter known side and side length.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Short leg x (opposite 30°), long leg x√3 (opposite 60°), hypotenuse 2x. Area = x × x√3 / 2.
Example
Inputs: Known side = Short leg (opposite 30°), Side length = 5. Result: Long leg: 8.6603; Short leg: 5; Hypotenuse: 10.
Limits and caveats
- Only for a triangle with angles of exactly 30, 60 and 90 degrees.
- Use one length unit; the area is in that unit squared.
Questions about this tool
What is the side ratio of a 30-60-90 triangle?
1 : √3 : 2. The hypotenuse is twice the short leg and the long leg is the short leg times about 1.732.
Why is the hypotenuse twice the short leg?
The triangle is half of an equilateral triangle, so the short leg is half a side and the hypotenuse is a full side.
How do I get the short leg from the long leg?
Divide the long leg by √3, for example 6 / 1.732 ≈ 3.464.