Calculate the sides of a right triangle using the Pythagorean Theorem: a² + b² = c².Find the length of any side when you know the other two.
For a right triangle with sides a, b and hypotenuse c:
a² + b² = c²To find side c: c = √(a² + b²)
To find side a: a = √(c² - b²)
To find side b: b = √(c² - a²)
Using the Pythagorean theorem:
Verifying the Pythagorean theorem:
Find answers to common questions about Online Calculator.
The Pythagorean Theorem Calculator helps find the missing side of a right triangle using the formula: a² + b² = c², where c is the hypotenuse.
The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
While the theorem is named after the Greek mathematician Pythagoras (c. 570–495 BCE), evidence suggests that the principle was known and used by the Babylonians and ancient Egyptians long before Pythagoras. Pythagoras is credited with providing the first proof of the theorem.
Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c². Examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17). These represent the sides of right triangles with whole number lengths.
The Pythagorean Theorem has countless practical applications, including architecture and construction (ensuring corners are square), navigation (calculating distances), surveying, physics, and even in computer graphics and game development for calculating distances and detecting collisions.
Enter the values of two sides of a right triangle, and the calculator will compute the missing side using the Pythagorean theorem formula.
Yes, whether you need to find the hypotenuse (c) or a leg (a or b), the calculator can compute the missing value.
Triangle sides cannot be negative. The calculator will prompt you to enter valid positive values.
Yes, the calculator allows you to enter decimal and fractional values for precise calculations.
This calculator works for 2D right triangles. For 3D problems, you may need an extended version using the distance formula.
Some versions of the calculator show step-by-step calculations, including squaring, summing, and taking the square root.
If you enter non-numeric or missing values, the calculator will show an error message and ask for valid inputs.
Absolutely! The Pythagorean theorem is widely used in construction, navigation, and engineering for measuring distances and angles.
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