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30-60-90 Triangle Calculator — result sheet
Find every side, area, perimeter, and trigonometric ratio of a 30-60-90 right triangle from any one known side.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Short:long:hypotenuse = 1:√3:2; area = ½(short)(long); perimeter = short + long + hypotenuse.
The 30-60-90 triangle is a special right triangle. Once one side is known, the fixed 1:√3:2 ratio determines the other two sides; the calculator keeps the side label explicit so a long leg is not accidentally treated as the short leg.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Known side length — length units; minimum 1.0E-6; maximum 1000000000000
- Known side — 3 choices
Worked example
| Input | Value |
|---|---|
| Known side length | 6 |
| Known side | short |
If the short leg is 6, the long leg is about 10.3923, the hypotenuse is 12, the area is about 31.1769, and the perimeter is about 28.3923 length units.
Assumptions and limits
- The triangle has angles 30°, 60°, and 90° in the standard special-triangle arrangement.
- The entered known side is positive and all lengths use the same unit.
- The displayed trigonometric ratios use the 30° angle as the reference angle.
- This tool does not solve an arbitrary triangle, account for drawing scale, or validate measured survey uncertainty.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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