Special Right Triangle Calculator
45 45 90 Triangle Calculator
Use this 45-45-90 triangle calculator to quickly find the hypotenuse, leg, area, and perimeter of any isosceles right triangle using standard 45 45 90 triangle formulas and ratios.
Calculator Mode
Special Right Triangle CalculatorFind hypotenuse from leg
This calculator finds Hypotenuse c using c = a × √2.
Enter inputs to calculate Hypotenuse c.
Hypotenuse c
Result-
Solution Steps
Formula: c = a × √2
Find leg from hypotenuse
This calculator finds Leg a using a = c / √2.
Enter inputs to calculate Leg a.
Leg a
Result-
Solution Steps
Formula: a = c / √2
Find area from leg
This calculator finds Area using Area = a² / 2.
Enter inputs to calculate Area.
Area
Result-
Solution Steps
Formula: Area = a² / 2
Find perimeter from leg
This calculator finds Perimeter P using P = 2a + a√2.
Enter inputs to calculate Perimeter P.
Perimeter P
Result-
Solution Steps
Formula: P = 2a + a√2
All input values must be greater than 0.
Formula
Triangle Diagram
Triangle Diagram Key
- Leg a represents the two equal sides of the isosceles right triangle.
- Hypotenuse c is the longest side opposite the 90° angle.
- Both acute angles are exactly 45 degrees.
How to Use This Calculator
- Choose the 45 45 90 calculator mode based on what you already know.
- Enter the known value (either the leg or the hypotenuse).
- Ensure your input is greater than 0.
- Read the calculated result directly from the isosceles right triangle calculator output field.
Step-by-Step Examples
Example 1: Find hypotenuse when a = 5.
Example 2: Find leg when c = 10.
Example 3: Find area when a = 6.
What the Result Means
The results you get represent the physical dimensions of your triangle. A calculated leg or hypotenuse is the exact side length needed to maintain the 45-degree angles.
Using our 45 45 90 area calculator and 45 45 90 perimeter calculator features helps you understand the total 2D space inside the triangle and the total distance around its edges.
Side Ratio
The side ratio for every 45 45 90 triangle is a : a : a√2.
This means both legs are always exactly the same length, and the hypotenuse is always the leg length multiplied by the square root of 2.
When to Use This Calculator
- Solving geometry and trigonometry homework problems as a 45 45 90 missing side calculator.
- Calculating dimensions for square-based constructions or diagonal cuts with the isosceles right triangle formula.
- Designing isometric grids and drafting standard angles.
- Finding the shortest distance across a square diagonal using the 45 45 90 hypotenuse calculator.
Common Mistakes
- Using 30 60 90 ratios by mistake.
- Forgetting that both legs are equal.
- Using c = 2a instead of c = a × √2.
- Dividing by 2 instead of √2 when finding the leg.
- Forgetting to square the leg when calculating area.
FAQs
Answers to the most common right-triangle solving questions.
01 What is a 45 45 90 triangle calculator? expand_more
It is a specific tool designed to solve an isosceles right triangle by finding the hypotenuse, leg, area, or perimeter based on the fixed side ratios.
02 What is an isosceles right triangle? expand_more
An isosceles right triangle is a right triangle where both legs are identical in length, and both non-right angles are exactly 45 degrees.
03 What is the formula for the hypotenuse of a 45 45 90 triangle? expand_more
The formula to find the hypotenuse is c = a × √2, where a is the length of one leg.
04 What does the calculated area mean? expand_more
The area result means the total amount of flat space contained inside the three sides of the triangle.
05 Can I find the leg if I only know the hypotenuse? expand_more
Yes, you can easily find the leg by taking the hypotenuse and dividing it by the square root of 2.
06 Why are the legs always equal? expand_more
Because the opposite angles are both 45 degrees, the sides opposite those angles must also be equal to each other.