Pythagorean Theorem
c = √(a² + b²)
Pythagorean Theorem Calculator
Discover the power of our Pythagorean Theorem Calculator, an essential online tool for solving right-angled triangle problems. Whether you’re a student tackling geometry homework or a professional needing quick calculations, this calculator simplifies the process using the famous formula a² + b² = c². Optimize your math tasks with accurate results in seconds.
About
The Pythagorean Theorem is a fundamental principle in geometry, stating that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Named after the ancient Greek mathematician Pythagoras, this theorem has applications in fields like architecture, engineering, and physics. Our Pythagorean Theorem Calculator leverages this formula to compute unknown sides effortlessly. Input two known sides, and it calculates the third, making it ideal for verifying distances, constructing buildings, or even in navigation. With user-friendly interface and instant results, it’s perfect for educational purposes and real-world problem-solving. Explore how this timeless theorem meets modern technology in our free tool.
How to Use
Using the Pythagorean Theorem Calculator is straightforward. Start by identifying the sides of your right-angled triangle: ‘a’ and ‘b’ are the legs, and ‘c’ is the hypotenuse. To find the hypotenuse, enter values for ‘a’ and ‘b’, then click ‘Calculate’. The tool computes c using √(a² + b²). If you know the hypotenuse and one leg, input those to find the missing leg. For example, to find ‘b’, enter ‘a’ and ‘c’, and it solves b = √(c² – a²). Ensure all inputs are positive numbers. The calculator handles decimals for precision. It’s mobile-friendly, so use it anywhere. No downloads required – just visit our page and start calculating. This tool saves time and reduces errors in manual computations.
Examples
Let’s look at practical examples. Suppose you have a triangle with legs a=3 and b=4. The calculator computes c=√(9+16)=√25=5. This classic 3-4-5 triangle is common in construction. Another example: a=5, b=12, then c=√(25+144)=√169=13, forming a 5-12-13 triangle. If you know c=10 and a=6, find b=√(100-36)=√64=8. For real-world use, imagine measuring a ladder against a wall: base 8 feet, height 15 feet – hypotenuse is √(64+225)=√289=17 feet. Or in coordinates: distance between (0,0) and (3,4) is 5 units. These examples show the calculator’s versatility for everyday math problems.
FAQ
1. What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
2. Can the calculator handle non-integer values?
Yes, it supports decimals and fractions for precise calculations.
3. Is this tool free to use?
Absolutely, our Pythagorean Theorem Calculator is completely free with no sign-up required.
4. What if I enter invalid inputs?
The calculator validates inputs and alerts you if values are negative or if c is smaller than a or b when solving for legs.
5. How accurate are the results?
Results are highly accurate, using advanced algorithms to minimize rounding errors in square roots.