You are here:

This online Pythagorean Theorem Calculator (Pythagoras calculator) allows you to compute the output based on Pythagoras theory. Details of how to use the calculator and how to calculate Pythagoras theory are below the calculator for first time users.

**Please provide a rating**, it takes seconds and helps us to keep this resource free for all to use

^{1} Changing Angle 1, measured in degrees, will change Angle 2, the Adjacent side, the Hypoteneuse and Area of the triangle.

^{2} Changing Angle 2, measured in degrees, will change Angle 1, the Opposite side, the Hypoteneuse and Area of the triangle.

^{3} Changing the length of the Opposite side, measured in units, will change Angle 1, Angle2, the Hypoteneuse and Area of the triangle.

^{4} Changing the length of the Adjacent side, measured in units, will change Angle 1, Angle2, the Hypoteneuse and Area of the triangle.

^{5} Changing the length of the Hypoteneuse measured in units, will change the Opposite side, the Adjacent side and Area of the triangle.

The Pythagoras calculator is used to calculate geometrical expression based on the Pythagoras theorem. It was given by Pythagoras of Samos, an ancient Ionian Greek philosopher who also founded Pythagoreanism. The wise philosopher was an ardent follower of geometry and gave us many theorems, the most notable being the Pythagorean theorem, or simply, the Pythagoras theorem.

Applicable to a simple, 2-dimensional right-angled triangle, Pythagoras theorem is a relatively simple expression that established a harmonious balance between the base, the perpendicular and the hypotenuse of a right-angled triangle.

Consider a right-angled triangle ABC with base of length 'b', a perpendicular height 'a' and a hypotenuse of length 'h'.

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the square of base and perpendicular.

h² = b² + a²

The right-angled triangle may look as simple as any other triangle, but it has few properties that make it special. They are:

- A right-angled triangle can never be equilateral, because then none of the angles will be 60°.
- The hypotenuse is the longest side of a right-angled triangle.
- An isosceles right-angled triangle will have two identical angles (45°) and one right angle.

The Pythagoras calculator developed by icalculator does more than simply calculate the length of the hypotenuse or any other side when the other two are given. It also gives you accurate values of other two angles as well as the area of the right-angled triangle formed by the given measurements.

For example, consider a right-angled triangle with base 3cm and perpendicular 4cm. The Pythagoras calculator automatically generates the following results:

Hypotenuse | 5 |
---|---|

Angle1 | 36.87° |

Angle2 | 53.13° |

Area | 6 square units |

And the best thing is that all this happens instantly.

Put Pythagoras theorem in the world of physics, and you'll see the right-angle triangle above can give an idea of distance and displacement. Displacement is the shortest distance between two points.

With the above information in mind, consider you are meeting two friends in a playground. One is 300 meters away from you and the other one is 400 meters away from you. Instead of travelling a total of 700 meters, you can simply start walking towards the other friend, who will be 500 meters away from you. That's displacement for you, saves time, saves effort.

Oh, and whenever you place a ladder against a wall, the ladder acts as the hypotenuse, while the wall and the floor are the perpendicular and base respectively. You judge how far the ladder must be from the base of the vertical wall so you can reach the desired height easily, without making the ladder tip over.

However, as you place the ladder away from the base, its effective height starts decreasing. This is where the Pythagoras calculator will help you choose what length of ladder will be your right fit.

And then there's a case of buying a new television. It's a common misconception that the size of a television relates to the width of the television screen or the total width of the television. The size of a television is actually the length of the diagonal running from one corner of the screen to the other corner. This diagonal is also the hypotenuse traveling across the horizontal and vertical sides of the television, which means a 56" television measures so across the diagonal.

Pythagoras calculators are also important in surveying, navigation and architecture.

As you can see from the examples cited above, Pythagoras theorem is all around us without us realizing it consciously. The Pythagoras calculator was developed with these facts in mind, to help users make fast calculations without wasting a single second of their precious time.

You may also find the following Math calculators useful.