# 30 60 90 Special Right Triangle Calculator

Enter any known value for a 30 60 90 triangle to calculate the edge lengths, altitude, area, perimeter, inradius, and circumradius.

## Solution:

## On this page:

## What is a 30 60 90 Triangle?

A 30 60 90 triangle is a special right triangle that has interior angles measuring 30°, 60°, and 90°.

You can also think of a 30 60 90 triangle as half of an equilateral triangle divided from any point to halfway along the opposite leg.

In a 30 60 90 triangle the shortest leg will be opposite the 30° angle and the longest leg, or hypotenuse, will be opposite the 90° angle.

## Formulas to Solve a 30 60 90 Triangle

Because a 30 60 90 triangle is a right triangle the formulas for a right triangle can also be used on them. However, there are also a few simplified formulas that can be used on a 30 60 90 triangle as well.

### Solve Leg A

Given leg *b*, the formula to solve leg *a* is:

a = b × √3 / 3

Thus, leg *a* is equal to leg *b* times the square root of 3, divided by 3.

### Solve Leg B

Given leg *a*, the formula to solve leg *b* is:

b = a√3

So, leg *b* is equal to leg *a* times the square root of 3.

### Calculate the Hypotenuse

In a 30 60 90 special right triangle the hypotenuse is always equal to twice the length of the shortest leg. Thus, the formula to calculate the hypotenuse *c* is simply c = 2a.

### Find the Area

Given the side lengths of a 30 60 90 triangle, the formula to find the area is:

T = ab / 2

The area *T* is equal to leg *a* times leg *b*, divided by 2.

### Calculate Perimeter

Like any triangle, the perimeter is equal to the sum of the edges.

p = a + b + c

So, perimeter *p* is simply leg *a* plus leg *b* plus hypotenuse *c*.

Like special right triangles? You might also like our 45 45 90 calculator.