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Pythagorean Theorem Calculator for Right Triangles
Calculate the missing side of a right triangle using our free Pythagorean Theorem Calculator. Get fast, accurate results with clear step-by-step calculations based on the formula a² + b² = c².
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Accuracy
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Right Triangle & Geometry Calculator
Enter any 2 known values to instantly find the missing side, angles, area, and perimeter with full step-by-step solutions.
Features
Everything you need in a pythagoras solver
The most complete pythagorean calc on the web - designed for clarity, speed, and learning.
Instant Calculation
This smart online calculator delivers results the moment you type - no page reload, no waiting.
Step-by-Step Solutions
See every value substitution in the right triangle equation with a clear algebraic breakdown.
Educational Content
Learn how to work out the hypotenuse, prove the fundamental formula, and explore real-world examples.
Validated & Accurate
Our pythagoras solver validates inputs and reports precise floating-point results in real time.
Find Any Side
Use our tool to easily solve for side A, find side B, or compute the missing hypotenuse all in one place.
Free Forever
No sign-ups, no ads blocking the view - the math solver is 100% free to use anywhere.
Benefits
Built for every learner and professional
From classroom math problems to real-world jobsite measurements, our interactive geometry solver adapts to your workflow seamlessly.
For Teachers
Display interactive math examples and solutions live in class using a projector-friendly, dark-mode-ready interface.
For Engineers
Rapidly compute hypotenuse lengths, verify right angles on site, and validate design geometry.
For DIY & Trades
Square up floors, roofs, and framing instantly with practical 3-4-5 rule and geometry examples.
Learn
Master the Pythagorean Theorem
From a2 plus b2 c2 to advanced pythagorean triple theorem concepts.
What is the Theorem?
The formula describes the relationship between the three sides of a right-angled triangle. For any right triangle with legs a, b and hypotenuse c:
a² + b² = c²
Our online tool is built around this rule. Enter any two known sides and the solver instantly finds the third.
How to Find the Hypotenuse
- Square both legs (a² and b²).
- Add them together.
- Take the square root of the sum to get the longest side.
This is the fastest way to compute missing side lengths or solve right triangle problems.
Triples & Formulas
An integer triple consists of three positive integers (a, b, c) that satisfy a² + b² = c². Using Euclid's formula (a = m² − n², b = 2mn, c = m² + n²), you can generate every primitive triple set:
(20, 21, 29)
(3, 4, 5) – the classic ratio
(5, 12, 13)
(8, 15, 17)
(7, 24, 25)
Real Life Applications
Where is this formula used in daily life? Everywhere:
- Construction - squaring foundations & roof pitches.
- Navigation - computing shortest paths.
- Screens - diagonal size from width & height.
- Sports - field diagonal distances.
Proofs
Discover Garfield's classic geometric proof, step-by-step algebraic derivations, and interactive visual proofs. Learn how to master and prove this core formula on your own.
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Loved by learners
What people say about our pythagoras calculator
It is a fundamental geometric rule stating that in any right-angled triangle, the square of the longest side (hypotenuse c) equals the sum of the squares of the other two sides (a and b). The relation is written as a² + b² = c².
To answer how to find the hypotenuse of a triangle, square both legs, add them, and take the square root. Try our finding the hypotenuse calculator above — it also handles how to calculate hypotenuse of right triangle.
Yes — switch tabs to use the pythagorean theorem find b calculator or find side a. It's a complete find the missing side of a right triangle calculator.
A pythagorean triple is a set of three positive integers a, b, c that satisfy a² + b² = c², such as (3,4,5). See our pythagorean triples list from 1 to 100 or generate more with the pythagorean triple calculator.
Historically credited to Pythagoras of Samos (~570 BCE), though ancient Babylonians used it much earlier. Learn more about its origins in our blog.
There are 300+ proofs including garfield's proof of pythagorean theorem, algebraic proof pythagorean theorem, and a proof of pythagorean theorem with proofs vectors.
From construction work to GPS mapping — see real-life practical examples and practical math word problems below.
Yes. This pythagoras theorem calculator is mobile-first, works offline once loaded, and supports keyboard, dark mode, and copy/download of every result.
Blog
Latest Guides & Geometry Insights
Explore our step-by-step tutorials, formulas, and practical examples to master right-triangle calculations effortlessly.
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What Is the Pythagorean Theorem? Formula, Examples, and Uses
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Pythagorean Theorem Calculator: How to Calculate Right Triangles
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How to Calculate Pythagorean Theorem: Easy Formula & Steps
Learning how to calculate Pythagorean theorem equations is an essential math skill for geometry, algebra, engineering, construction, and real-world problem-solving. This fundamental rule provides a quick, reliable way to find the missing side length of any right triangle. Whether you…
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Pythagorean Theorem Equation: Formula, Steps, and Easy Examples
Understanding right-angled triangles becomes straight forward once you learn the pythagorean theorem equation. Whether you are solving algebra problems, designing 2D graphics, or measuring distances in real-life construction, this fundamental geometry rule provides a quick way to find any missing…
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Pythagorean Triple: Definition, Formula, and Easy Examples
If you have ever worked with right-angled triangles, you already know the famous Pythagorean theorem: a² + b² = c². However, working with decimals or square roots can get messy very quickly. This is where a pythagorean triple makes geometry…
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Calculating Right Triangle Sides, Angles, and Area: The Complete Mathematical Guide
Calculating Right Triangle is simple and accurate with our free online calculator. Whether you need to find a missing side, determine an angle, or calculate the hypotenuse, this tool provides instant and reliable results using proven mathematical formulas. It is…
Solve Any Right Triangle in Second
Jump back to the top and try our dedicated modes to calculate the hypotenuse, find side B, or solve for side C instantly.