Special Right Triangle Calculator
30 60 90 Triangle Calculator
Use this 30-60-90 triangle calculator to easily find the short leg, long leg, hypotenuse, area, and perimeter using the exact 30 60 90 triangle formula and ratio.
Calculator Mode
Special Right Triangle CalculatorFind long leg from short leg
This calculator finds Long Leg using long leg = a × √3.
Enter inputs to calculate Long Leg.
Long Leg
Result-
Solution Steps
Formula: long leg = a × √3
Find hypotenuse from short leg
This calculator finds Hypotenuse c using c = 2a.
Enter inputs to calculate Hypotenuse c.
Hypotenuse c
Result-
Solution Steps
Formula: c = 2a
Find short leg from hypotenuse
This calculator finds Short leg a using a = c / 2.
Enter inputs to calculate Short leg a.
Short leg a
Result-
Solution Steps
Formula: a = c / 2
Find short leg from long leg
This calculator finds Short leg a using a = long leg / √3.
Enter inputs to calculate Short leg a.
Short leg a
Result-
Solution Steps
Formula: a = long leg / √3
Find long leg from hypotenuse
This calculator finds Long leg using long leg = (c × √3) / 2.
Enter inputs to calculate Long leg.
Long leg
Result-
Solution Steps
Formula: long leg = (c × √3) / 2
Find area from short leg
This calculator finds Area using Area = (short leg × long leg) / 2.
Enter inputs to calculate Area.
Area
Result-
Solution Steps
Formula: Area = (short leg × long leg) / 2
Find perimeter from short leg
This calculator finds Perimeter P using P = a + a√3 + 2a.
Enter inputs to calculate Perimeter P.
Perimeter P
Result-
Solution Steps
Formula: P = a + a√3 + 2a
All input values must be greater than 0.
Formula
Triangle Diagram
Triangle Diagram Key
- Short leg a is opposite the 30-degree angle.
- Long leg a√3 is opposite the 60-degree angle.
- Hypotenuse c is exactly twice the length of the short leg a.
How to Use This Calculator
- Select what you want to find from the 30 60 90 calculator modes.
- Enter your known side length (short leg, long leg, or hypotenuse).
- Verify the number is positive and greater than zero.
- Check the result box for your perfectly scaled answer from our 30 60 90 triangle solver.
Step-by-Step Examples
Example 1: Find long leg and hypotenuse when short leg a = 5.
Example 2: Find short leg when c = 14.
Example 3: Find long leg from hypotenuse c = 10.
What the Result Means
The calculated 30 60 90 triangle sides show exactly how long each part of the triangle needs to be to maintain the 30 and 60 degree angles. They are perfectly proportional.
The 30 60 90 area calculator and 30 60 90 perimeter calculator results give you the exact bounded 2D size and the total outline length of your triangle.
Side Ratio
The standard side ratio for a 30 60 90 triangle is a : a√3 : 2a.
The short leg is a, the long leg is a times the square root of 3, and the hypotenuse is exactly twice the short leg.
When to Use This Calculator
- Checking trigonometry assignments involving special right triangles as a 30 60 90 missing side calculator.
- Determining the height of an equilateral triangle using the 30 60 90 long leg calculator.
- Drafting angles and structural supports in engineering or architecture.
- Solving complex vector problems in physics with the 30 60 90 hypotenuse calculator.
Common Mistakes
- Mixing up the short leg and the long leg.
- Using √2 instead of √3 for the long leg calculation.
- Thinking the hypotenuse equals a√3 instead of 2a.
- Using the long leg value as the short leg by accident.
- Forgetting that the hypotenuse is exactly double the short leg.
FAQs
Answers to the most common right-triangle solving questions.
01 How do I use this 30 60 90 triangle calculator? expand_more
Simply choose the value you want to calculate, enter the side you already know, and the tool will use the correct ratio to find the answer.
02 Which side is the short leg and the long leg? expand_more
The short leg is always opposite the 30-degree angle, while the long leg is always opposite the 60-degree angle.
03 What is the formula to find the hypotenuse from the short leg? expand_more
The formula is c = 2a, meaning the hypotenuse is exactly double the length of the short leg.
04 What does the long leg result mean? expand_more
The long leg result tells you the exact height or base required to match the other sides while keeping the 30 and 60 degree angles intact.
05 Can I find the short leg from the long leg? expand_more
Yes, you can find the short leg by dividing the long leg by the square root of 3.
06 Why do we multiply by the square root of 3? expand_more
Multiplying by the square root of 3 is a fixed geometric rule for this triangle type, linking the short leg to the long leg mathematically.