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Pythagorean Theorem Calculator

Solve for any side of a right triangle — with steps and a labeled diagram.

a=3b=4c=5
c = 5

Step 1: a² + b² = c² → 3² + 4² = c²

Step 2: c² = 9 + 16 = 25

Step 3: c = √25 = 5

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Using a² + b² = c²

In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. It is one of the oldest and most useful facts in mathematics — builders use the 3-4-5 triangle to square up foundations, and GPS systems solve millions of triangle problems per second.

Solving for Each Side

  • Hypotenuse: c = √(a² + b²) — square, add, square-root.
  • A leg: a = √(c² − b²) — subtract first, then square-root. The hypotenuse must be the longest side.

Famous Triples

Some integer sets fit perfectly: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Spotting a multiple of one of these triples lets you answer without a calculator — a favorite trick in timed exams.

Need all sides and angles? Try our triangle calculator.

Frequently Asked Questions

What is the Pythagorean theorem formula?

a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse (the side opposite the right angle).

How do you find the hypotenuse with two sides?

Square both legs, add them, and take the square root. For legs 3 and 4: c = √(9 + 16) = √25 = 5.

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

Plug the three sides into a² + b² = c² with the longest side as c. If both sides of the equation match, the triangle is right-angled.

Is this Pythagorean calculator free?

Yes — every tool on Math Solver Free is free with no sign-up, and all calculations run in your browser.