45-45-90 Triangle Calculator
Enter any one side, the height, area or perimeter of a 45-45-90 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 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 : 1 : √2
Half a square
A square's diagonal splits it into two 45-45-90 triangles.
Questions
What is the hypotenuse if each leg is 3?
3√2 ≈ 4.242640687.
What is the area?
Half a leg squared: 4.5.
Formulas
sides in the ratio 1 : 1 : √2
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).