Quick answer
A 45-45-90 triangle has equal legs a and a hypotenuse of a√2. A leg of 10 gives a hypotenuse of 14.1421.
Enter the leg length. The calculator returns the leg and hypotenuse. Use this forty-five ninety triangle calculator to check your own figures.
Related tools: Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides. 45-45-90 Triangle Calculator: Sides of a 45°-45°-90° triangle from one leg. 30-60-90 Triangle Calculator: Sides of a 30°-60°-90° triangle from the short leg.
How to use the Forty-Five Ninety Triangle Calculator
- Enter leg length (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Leg length | A number | > 0 |
Formula and method
Formula
legs = a; hypotenuse = a√2
IEEE-754 double precision; shown to at most 6 decimal places.
Fixed side ratios of the special right triangle.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Leg length = 10.
| Result | Value |
|---|---|
| Leg | 10 |
| Hypotenuse | 14.142136 |
The first line is the headline result (leg). Below it the forty-Five Ninety Triangle Calculator lists hypotenuse, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Isosceles right triangle
The angles are 45°, 45° and 90°, and the sides are in the ratio 1 : 1 : √2. It's the shape of a set square and of a square cut along its diagonal.
Quick use
Hypotenuse ≈ 1.414 × leg. A 10 cm leg gives 14.14 cm; if you know the hypotenuse, divide by 1.414 to get the leg. The Forty-Five Ninety page and the 45-45-90 calculator share this formula.
How the result changes with leg length
Holding every other input at the first worked example, this table changes only leg length. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Leg length | Leg | Hypotenuse |
|---|---|---|
| 5 | 5 | 7.071068 |
| 10 | 10 | 14.142136 |
| 20 | 20 | 28.284271 |
| 40 | 40 | 56.568542 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Leg length: entering "0" shows "Leg length must be greater than 0." beside that field and no result.
Choosing between the Forty-Five Ninety Triangle Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [45-45-90 Triangle Calculator](/math/45-45-90-triangle-calculator/) | leg length | Leg |
| [30-60-90 Triangle Calculator](/math/30-60-90-triangle-calculator/) | short leg length | Short leg |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive length
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for leg length to confirm this.
Frequently asked questions
What is the leg if the hypotenuse is 10?
With hypotenuse 10 each leg is 10 ÷ √2 ≈ 7.071.
What is its area?
a² ÷ 2, 50 for a leg of 10.
Are the two acute angles equal?
Yes. The two acute angles are both 45° in this isosceles right triangle.
What does the Forty-Five Ninety Triangle Calculator calculate?
Sides of a 45-45-90 triangle from one leg. It returns Leg and Hypotenuse.
What formula does the Forty-Five Ninety Triangle Calculator use?
legs = a; hypotenuse = a√2. Fixed side ratios of the special right triangle.
What do I need to enter in the forty-Five Ninety Triangle Calculator?
You enter Leg length.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive length.
What is an example of a forty-Five Ninety Triangle result?
With leg length 10, the leg is 10.
Related calculators
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- 45-45-90 Triangle Calculator — Sides of a 45°-45°-90° triangle from one leg.
- 30-60-90 Triangle Calculator — Sides of a 30°-60°-90° triangle from the short leg.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Triangle Area Calculator — Area of a triangle from base and height.
- SAS Triangle Calculator — Solve a triangle from two sides and the included angle.
- SSS Triangle Calculator — Angles and area of a triangle from its three sides.
- Isosceles Triangle Calculator — Height, area and angles of an isosceles triangle from its base and equal sides.
- Triangle Height Calculator — Height of a triangle from its area and base.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.