30-60-90 Triangle Calculator
Enter any one side, the height, area or perimeter of a 30-60-90 triangle to find the rest.
Change the values and press Calculate to work out your own figures.
Enter any one measurement.
Show the working
- From the short leg a
- The shape is fixed, so every measurement is a fixed multiple of the side
How to use it
Enter any one measurement.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
sides in the ratio 1 : √3 : 2
Half an equilateral triangle
Cutting an equilateral triangle in half gives a 30-60-90 triangle, which is why the hypotenuse is twice the short leg.
Questions
What are the sides if the short leg is 3?
3, 3√3 ≈ 5.196 and 6.
Which side is opposite 30°?
The short leg.
Formulas
sides in the ratio 1 : √3 : 2
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).