Use this calculator to find the hypotenuse of a right triangle using the Pythagorean Theorem.
The Pythagorean Theorem Calculator is a free, easy-to-use tool designed to calculate the length of any side of a right triangle using the classic Pythagorean theorem. Whether you're a student, engineer, carpenter, or DIY enthusiast, this calculator helps you solve triangle problems accurately in seconds using the formula a² + b² = c².
The Pythagorean Theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides:
Formula: c² = a² + b²
A right triangle has one angle that is exactly 90 degrees. The side opposite this angle is the hypotenuse (c), and the two adjacent sides are known as the legs (a and b). The Pythagorean theorem works only for right-angled triangles.
Depending on which side you're solving for, rearrange the formula:
The theorem is also used to find the distance between two points (x₁, y₁) and (x₂, y₂) using the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
This is directly derived from the Pythagorean theorem and used in GPS systems, mapping, and physics.
In 3D geometry, the formula extends to:
d = √(x² + y² + z²)
This calculates the diagonal distance between opposite corners of a rectangular prism or space.
No. It only applies to right-angled triangles.
Any unit—meters, feet, inches—as long as you use the same unit for all sides.
Yes! It's widely used in engineering, architecture, design, computer graphics, and more.
The calculator will return accurate decimal values. You can round them based on your needs.
import math
def hypotenuse(a, b):
return math.sqrt(a**2 + b**2)
function findHypotenuse(a, b) {
return Math.sqrt(a * a + b * b);
}
Named after the ancient Greek mathematician Pythagoras, this theorem was known to Babylonian and Indian mathematicians long before his time. It remains one of the most famous and frequently used theorems in all of mathematics.
A Pythagorean triple consists of three positive integers that satisfy the theorem.
Use this free Pythagorean Theorem Calculator to find the missing side of a right triangle. Enter two known sides to calculate the third instantly using a² + b² = c².
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While most people associate the Pythagorean theorem with school math, it's actually used in a variety of industries and technical fields. Here are some common examples:
Learning how to apply the Pythagorean theorem has practical advantages that go beyond academic achievement. It builds foundational skills for problem-solving, logic, and spatial understanding.
If a triangle has sides where a² + b² = c², then the triangle must be a right triangle. This principle is useful in verifying right angles during construction and geometry proofs.
The Pythagorean theorem can be extended to three dimensions:
d = √(x² + y² + z²)
This calculates the space diagonal inside a cube or cuboid, often used in physics and computer science.
Some versions of this calculator can even help generate Pythagorean triples for exercises and number theory analysis. Here's a simple trick:
Example: m = 2, n = 1 → a = 3, b = 4, c = 5 (a classic Pythagorean triple)
Teachers, tutors, and students can benefit from printable worksheets that test knowledge of the Pythagorean theorem with real-world word problems, triangle diagrams, and missing-side puzzles.
Typical problem types include:
The Pythagorean theorem is powerful, but it only works in specific contexts. Avoid using it when:
Although named after Pythagoras (circa 570–495 BCE), historical evidence shows that the Babylonians and Indians knew of the theorem over 1000 years earlier. The oldest record appears in the Babylonian clay tablet Plimpton 322, which lists Pythagorean triples dating back to 1800 BCE.
The theorem remains one of the most important and timeless discoveries in the history of mathematics.
Scenario: You want to build a rectangular garden with diagonal support lines. If the garden is 20 meters long and 15 meters wide, what length should the diagonal support be?
Solution: c = √(20² + 15²) = √(400 + 225) = √625 = 25 meters
This helps ensure proper tension and shape for the structure.
Trigonometric functions like sine, cosine, and tangent also help solve triangles, but they require knowledge of angles. The Pythagorean theorem is simpler when only side lengths are involved.
For angle-based problems, try our Trigonometry Calculator.
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The Pythagorean Theorem Calculator is not only a mathematical aid—it's a practical tool used in everyday life and high-level professions. Whether you're solving homework, building something, or coding a navigation algorithm, this calculator makes triangle math effortless and error-free.
Try it now to solve any right triangle problem in seconds and deepen your understanding of one of geometry’s greatest tools.