What is the Pythagorean Theorem formula?

The formula is `a² + b² = c²`, where `a` and `b` are the two perpendicular legs and `c` is the hypotenuse.

What are common Pythagorean Triples?

Pythagorean triples are sets of three positive integers that satisfy the theorem, including (3, 4, 5), (5, 12, 13), (7, 24, 25), and (8, 15, 17).

Can the Pythagorean Theorem be used on non-right triangles?

No. The Pythagorean theorem strictly applies to right-angled (90°) triangles. For non-right triangles, use the Law of Cosines (`c² = a² + b² - 2ab cos(C)`).

How do you check if a triangle is a right triangle?

If the square of the longest side equals the sum of the squares of the other two sides (`c² = a² + b²`), the triangle is confirmed right-angled (converse of Pythagorean theorem).

How do you find the acute angles of a right triangle?

Use inverse trigonometric functions: `Angle A = arcsin(a / c)` and `Angle B = 90° - Angle A`.

Can I use the Pythagorean Theorem on non-right triangles?

No. The standard Pythagorean Theorem `a² + b² = c²` applies strictly to right-angled triangles (90°). For acute or obtuse triangles, use the Law of Cosines.

Math & Statistics Cluster

Pythagorean Theorem Calculator ($a^2 + b^2 = c^2$)

Calculate hypotenuse and leg lengths of right-angled triangles with step-by-step solutions.

TL;DR: Pythagorean Theorem Calculator solves for any side of a right-angled triangle using the fundamental theorem $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

Solve for

Leg a

Leg b

What Is the Pythagorean Theorem and What Is the Formula for the Hypotenuse?

The Pythagorean Theorem states that in any right-angled triangle, the square of the hypotenuse (the longest side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². To solve for hypotenuse: c = √(a² + b²). To solve for a leg: a = √(c² - b²).

How to Use the Pythagorean Theorem Calculator

Our Pythagorean Theorem Calculator performs high-precision mathematical operations directly in your browser with zero latency and complete client-side privacy.

Select what you are solving for: Hypotenuse ($c$), Leg $a$, or Leg $b$.
Enter the lengths of the two known triangle sides.
Click 'Calculate Side' to compute the missing dimension.
Review the step-by-step squaring, addition/subtraction, and square root operations.
View triangle perimeter, area, and acute angles in degrees/radians.

Mathematical Formula & Equations

Solves right-triangle hypotenuse $c$ and legs $a, b$ along with interior trigonometric angles.

\[ a^2 + b^2 = c^2 \implies c = \sqrt{a^2 + b^2}, \quad a = \sqrt{c^2 - b^2} \]

Calculation Example

With legs $a = 9$ and $b = 12$: $$\text{Hypotenuse } c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$$

100% Client-Side Privacy & Data Security

All calculations, amortization schedules, variables, and sensitive numerical datasets execute 100% locally in your web browser memory. Your financial, medical, and personal values are never transmitted, logged, or uploaded to any external server.

Frequently Asked Questions

: The formula is `a² + b² = c²`, where `a` and `b` are the two perpendicular legs and `c` is the hypotenuse.
: Pythagorean triples are sets of three positive integers that satisfy the theorem, including (3, 4, 5), (5, 12, 13), (7, 24, 25), and (8, 15, 17).
: No. The Pythagorean theorem strictly applies to right-angled (90°) triangles. For non-right triangles, use the Law of Cosines (`c² = a² + b² - 2ab cos(C)`).
: If the square of the longest side equals the sum of the squares of the other two sides (`c² = a² + b²`), the triangle is confirmed right-angled (converse of Pythagorean theorem).
: Use inverse trigonometric functions: `Angle A = arcsin(a / c)` and `Angle B = 90° - Angle A`.
: No. The standard Pythagorean Theorem `a² + b² = c²` applies strictly to right-angled triangles (90°). For acute or obtuse triangles, use the Law of Cosines.

Cite This Calculator

Need to reference this online calculator in a financial proposal, academic paper, blog post, or classroom curriculum? Copy a citation below.

NexLove.org. (2026). Pythagorean Theorem Calculator [Online Calculation Tool]. https://nexlove.org/tools/pythagorean-theorem-calculator

“Pythagorean Theorem Calculator.” NexLove.org, 2026, nexlove.org/tools/pythagorean-theorem-calculator.

NexLove.org (2026) Pythagorean Theorem Calculator. Available at: https://nexlove.org/tools/pythagorean-theorem-calculator (Accessed: 2026).

@misc{nexlove_pythagorean_theorem_calculator,
  title = {Pythagorean Theorem Calculator},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/pythagorean-theorem-calculator}
}

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