30-60-90 Triangle Calculator
Enter any one side of a 30-60-90 triangle and get the other two instantly from the 1 : √3 : 2 ratio.
The 1 : √3 : 2 Ratio
In a 30-60-90 triangle the sides always keep the same proportions: the hypotenuse is twice the short leg, and the long leg is the short leg times √3. Knowing any one side therefore pins down the whole triangle — no trigonometry needed.
Frequently Asked Questions
Which leg is opposite which angle?
The shortest side faces the smallest angle (30°); the long leg faces 60°; the hypotenuse faces 90°.
Where does √3 come from?
Split an equilateral triangle down the middle — the altitude is (side × √3)/2, which becomes the long leg.
Are answers exact?
They are shown as decimals (5 places). For exact form, keep √3 symbolic: e.g. short leg 5 → long leg 5√3.