Pythagorean Theorem Calculator – Free Tool with Steps & Examples

Q: 2. What is the formula for the Pythagorean Theorem?

The formula for the Pythagorean Theorem is: a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides (legs) of a right-angled triangle, and 'c' is the length of the hypotenuse.

Q: 4. How do I find the hypotenuse using the Pythagorean Theorem?

To find the hypotenuse (c), use the formula: c = √(a² + b²). Substitute the values of 'a' and 'b' (the lengths of the other two sides) into this equation and calculate the square root of the result.

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How to Use the Pythagorean Theorem Calculator to Find the Hypotenuse or Missing Side

Side a (Base): Side b (Perpendicular): Side c (Hypotenuse):

What is Pythagorean Theorem Calculator?

A Pythagorean Theorem Calculator instantly finds any missing side (base, perpendicular, or hypotenuse) of a right-angled triangle using the Pythagorean formula. Just enter any two known sides and leave the unknown blank.

This tool quickly provides correct results along with step-by-step calculation, making geometry and coordinate problems much easier for students, parents, and teachers. It's simple to use and saves valuable calculation time.

Formula Behind Pythagorean Theorem Calculator

The Pythagorean theorem states that in a right triangle, (Hypotenuse)² = (Base)² + (Perpendicular)², or c² = a² + b². If any two side lengths (a, b, or c) are known, the third side can be found by rearranging and using a square root for the unknown side.

Pythagorean Theorem Example Table

Given Sides	Missing Side
a=3, b=4	c = 5
a=6, b=8	c = 10
b=12, c=13	a = 5
a=7, c=25	b = 24
b=15, c=17	a = 8
a=9, b=12	c = 15

Steps to Use Pythagorean Theorem Calculator

Enter exactly two side lengths (base, perpendicular, or hypotenuse), leaving the side to find blank.
Click "Calculate".
See the missing side and full working instantly.

Why Use Vedantu’s Pythagorean Theorem Calculator?

This calculator is designed for the fastest, most accurate solution of right triangle problems, showing all calculation steps. It's mobile friendly, and trusted by lakhs of students for quick homework help.

You no longer have to remember complex formulas or perform repeated manual calculations. Cut errors and gain deeper understanding with stepwise breakdowns for each case, right from your phone or PC.

Applications of Pythagorean Theorem Calculator

Use this calculator to solve exam questions, construction planning, navigation, mapping distances between two points, or in science projects where right triangles appear, such as ladders, ramps, or measuring height using shadows.

It's useful in coordinate geometry for finding the straight-line distance between two points. You can also use it for physics, design work, or any field that involves right-angled triangle measurements.

For more maths practice, explore Vedantu’s HCF calculator, our smart prime numbers tool, and detailed concept guides on algebra and multiples in maths for strong exam prep.

FAQs on Pythagorean Theorem Calculator – Free Tool with Steps & Examples

1. What is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental concept in geometry that describes the relationship between the sides of a right-angled triangle. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (called legs or cathetus). This theorem has numerous applications in various fields, including construction, navigation, and computer graphics.

2. What is the formula for the Pythagorean Theorem?

The formula for the Pythagorean Theorem is: a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides (legs) of a right-angled triangle, and 'c' is the length of the hypotenuse.

3. How do I use the Pythagorean Theorem Calculator?

Vedantu's Pythagorean Theorem Calculator simplifies the process. Simply input the lengths of any two sides of your right-angled triangle into the designated fields. Then click the 'Calculate' button; the calculator will instantly compute the length of the missing side, along with the step-by-step solution.

4. How do I find the hypotenuse using the Pythagorean Theorem?

To find the hypotenuse (c), use the formula: c = √(a² + b²). Substitute the values of 'a' and 'b' (the lengths of the other two sides) into this equation and calculate the square root of the result.

5. How can I find the length of a leg (side) in a right-angled triangle using the Pythagorean Theorem?

If you know the hypotenuse (c) and one leg (a or b), you can find the length of the other leg using these formulas:
a = √(c² - b²)
b = √(c² - a²)
Substitute the known values and solve for the unknown leg.

6. What are some real-world applications of the Pythagorean Theorem?

The Pythagorean Theorem has numerous real-world applications. For example, it is used in:
• Construction (calculating diagonal lengths)
• Surveying (measuring distances)
• Navigation (finding shortest routes)
• Computer graphics (determining distances between points).

7. What are Pythagorean triples?

Pythagorean triples are sets of three whole numbers (a, b, c) that satisfy the Pythagorean Theorem (a² + b² = c²). Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17). These triples are useful for quickly solving certain right-angled triangle problems.

8. Can the Pythagorean Theorem be used on a coordinate plane?

Yes, the Pythagorean Theorem forms the basis of the distance formula in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) on a coordinate plane is given by:
d = √[(x2 - x1)² + (y2 - y1)²]

9. Why is the Pythagorean Theorem important in mathematics?

The Pythagorean Theorem is a cornerstone of geometry and trigonometry. It provides a fundamental relationship between the sides of a right-angled triangle and forms the basis for many other mathematical concepts and formulas. It's essential for understanding and solving problems in various branches of mathematics.

10. How accurate is Vedantu's Pythagorean Theorem Calculator?

Vedantu's Pythagorean Theorem Calculator is designed for accuracy. It's built using robust algorithms and regularly tested to ensure reliable results. However, minor discrepancies may occur due to rounding errors in calculations, especially with very large numbers.

11. What if I enter incorrect values into the Pythagorean Theorem Calculator?

The calculator will attempt to process the inputs, but if the values provided don't represent a valid right-angled triangle (for instance, if the sum of the squares of two sides is less than the square of the third), it might display an error message or an unexpected result. Always double-check your input values for accuracy.