Pythagorean Theorem Calculator

A carpenter checking a corner, a network engineer sizing a diagonal cable run, and a student staring at a homework diagram are all asking the same question: does a² + b² = c² hold, or what does the missing number have to be so that it does. Pythagorean Theorem Calculator takes any two of the three sides and solves for the third, or takes all three and tells you whether they actually describe a right triangle.

Fields are always labelled the same way: a and b are the legs, c is the hypotenuse, so the tool never has to guess which side you mean. Leave exactly one blank and it gets solved. Fill all three and the page checks them against each other instead of assuming you already know they fit.

Getting a Missing Side

1. a and b open on 6 and 8 with c blank; Load Sample steps through further leg pairs such as 5 and 12.
2. The hypotenuse resolves to 10 the moment both legs are valid. There is no separate calculate button, since every keystroke re-solves live.
3. Four result cards appear: the solved side, the perimeter (24 for the sample), the area (also 24, a coincidence of this particular triangle) and all three angles.
4. A purple callout below the cards flags that 6-8-10 is 2 × the primitive triple 3-4-5 — a fact the solver checks against a table of every primitive triple with a hypotenuse under 100, not something guessed from rounding.

The Formula Behind the Square-on-a-Side Proof

• Solving for a leg rearranges the same identity: with the hypotenuse and one leg known, the other is √(c² − known leg²), never the other way around.
• The diagram beneath the cards draws an actual square on each side, sized in proportion to the triangle, and captions the arithmetic underneath: a² + b² = c² with the real numbers substituted in, not a generic illustration reused across every result.
• Angles come from inverse sine, not a lookup table: asin(a / c) gives the angle opposite a in degrees, and the angle opposite b is whatever is left of 90.

What Happens When the Triangle Doesn't Close

• Typing a leg equal to or longer than the hypotenuse raises A leg must be shorter than the hypotenuse — 13 can't be a leg if 5 is the hypotenuse. before it ever reaches a square root of a negative number.
• With all three sides filled, a mismatch doesn't just say “wrong.” It reports the triangle as Not a right triangle and states exactly how far off the typed hypotenuse is from the one the two legs actually produce.
• Inputs are capped at 1,000,000,000 per side, which keeps every squared value comfortably inside what a JavaScript double represents exactly.
• Two blanks at once stop the solver rather than guessing which pair you meant, with Enter at least two sides — leave the one you want solved for blank. shown until one is filled back in.