← Math & statistics

Pythagorean theorem (right triangle) calculator

See a right triangle diagram and the three square area model side by side. Solve for any side, check if three sides form a right triangle, or find the distance between two points—always with exact radicals plus an optional decimal approximation.

The tool highlights a²+b²=c² visually and keeps your steps for copying as LaTeX or SVG. Calculations stay in your browser.

Other languages ja | en | zh-CN | es | pt-BR | id | fr | hi-IN | ar
Solve for

We sort the largest value as c (hypotenuse) before checking a²+b²=c².

dx = x2 - x1, dy = y2 - y1, distance d = √(dx² + dy²).

How to use
  1. Pick a mode (solve, check, or distance).
  2. Enter two sides or two points; example chips fill them for you.
  3. Results, diagrams, and steps update automatically. Copy the URL, LaTeX, or SVG for class use.
Display & accessibility settings

Result

Enter two sides to solve for the third, or load an example.

Exact radicals are kept internally; decimals are for display only.

Diagrams

Right triangle (a, b, c)
Right triangle diagram Shows legs a and b with a right angle and hypotenuse c.
Square area model (a², b², c²)
Area model for a² + b² = c² Three squares built on each side; a² and b² combine to c².

Steps

What this means

FAQ

Which side is the hypotenuse?

The hypotenuse is opposite the right angle and is always the longest side. If your c is shorter than a or b, the triangle is impossible.

Why do we square the legs in a²+b²=c²?

Squaring converts each side length into the area of a square on that side. The two smaller square areas add up exactly to the big square on c.

Why does a square root appear at the end?

You add areas (a²+b²) first, then take the square root to get back to a length. That is why radicals show up in the answer.

How do I handle decimals or fractions?

Type 0.3 or 1/2. Internally we keep an exact fraction and only round for display, so you avoid accumulated error.

How strict is the right-triangle check?

Fractions are compared exactly. Decimal-only inputs use a tiny tolerance; the difference is shown so you can judge \"almost\" cases.

Is my input sent anywhere?

No. Everything runs locally, including the diagrams and exports.

Related calculators