Pythagorean Theorem Calculator
Created by
Eon CalculatorThe pythagorean theorem calculator helps you find the missing side of a right-angled triangle. Whether you are working on a school assignment, design work, project this tool provides you with instant results with no need for manual calculations. All you have to do is enter the length of two sides and the calculator will solve for the third side instantly.
What is the Pythagorean Theorem?
The Pythagorean Theorem is a fundamental rule in geometry. It refers to right-angled triangles (triangles where one angle is 90 degrees).
The theorem describes the relationship between three sides of a right-angled triangle. The formula is:
Where;
A and B are the lengths of the two shorter sides (called the legs),
C is the length of the hypotenuse, which is the longest side opposite the right angle.
The theorem tells us that the sum of the square value of the two legs (a² + b²) is always equal to the square of the hypotenuse (c²). This theorem helps us find the length of one side if we know the length of the other two sides.
For example: If side a = 6 cm and side b = 8 cm; 6² + 8² = c². So, 36 + 64 = √100 = 10 cm.How to use the Pythagorean Theorem?
Using the Pythagorean Theorem is simple, but it is very important to understand the sides of a right triangle. Follow these simple steps to use the Pythagorean Theorem.
1.Confirm that the triangle is a right-angled triangle. This means the angle must be 90°. The Pythagorean Theorem only works for right triangles.
2.Next step is to label the side of the triangle. The two shorter sides (legs) are labelled as a and b. The longest side is the hypotenuse (c).
3.If you are solving for the c, use the formula: c = √(a² + b²). If you need to find A or B, rearrange the formula to: a = √(c² - b²) or b = √(c² - a²).
4.If you are solving for c, input the length both a and b into the formula. If you are solving for a or b, enter the value of the c and a or b into the formula.
5.Square the known values. Add the square values if you're solving for c or subtract the values if you are solving for a or b. Take the square root of the result to get the missing side length.
Using Pythagorean theorem calculator
This Pythagorean theorem calculator is one of the easiest calculators you can find on the internet. All you need to do is enter any two sides of a right triangle, and the calculator will figure out the third side as well as the area of the triangle. Here are the steps you need to follow to use our Pythagorean theorem calculator.
1.If you are missing c, enter the a and b values. If you are missing one of the legs (a or b), enter the hypotenuse (c) and the other leg (a or b).
2.Click Calculate after you've put in the numbers. The calculator will use the Pythagorean Theorem and find the missing side.
3.The default triangle length unit is centimeter (cm), and the area unit is cm². These units can be changed to any of the given units depending on your needs.
Finding the length of the hypotenuse?
If you want to find the length of the hypotenuse in a right-angled triangle, use the formula: c = √(a² + b²).
The Hypotenuse formula is a direct form of the Pythagorean Theorem. a² + b² = c² is just solve it for c by taking the square root of both sides. For example: if side a = 3 cm and side b = 4 cm, then: c = √(3² + 4²) = √(9 + 16) = √25 = 5.
| Side | Formula | When to Use |
|---|---|---|
Hypotenuse (c) | c = √(a² + b²) | a and b |
Leg a | a = √(c² - b²) | (c) and leg b |
Leg b | b = √(c² - a²) | (c) and leg a |
Apart from the hypotenuse formula, the pythagorean theorem can also be rearranged to find value for a or b. If you already know hypotenuse and one leg value; To find a: a = √(c² - b²) and to find b: b = √(c² - a²).
Units of measurement for the sides
When using Pythagorean Theorem, it is very important all the sides of the triangle are measured in the same unit. If one side of the triangle is centimeters the other sides must also be in centimeters. If the other side uses different units you need to convert them before applying the Pythagorean Theorem.
Real-life applications of this theorem
This theorem is not just any mathematical concept, it has several practical applications. Here are some practical applications;
Civil engineers use it to ensure the corners are square (90°), calculate roof slopes, and determine ladder heights.
Navigation and GPS:
This theorem is used by pilots and sailors to find the shortest paths and distances between two points.
It is also helpful in surveying and map-making, computer graphics and animation, sports and home improvement.
Pythagorean Theorem Calculator
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