We sort the largest value as c (hypotenuse) before checking a²+b²=c².
dx = x2 - x1, dy = y2 - y1, distance d = √(dx² + dy²).
- Pick a mode (solve, check, or distance).
- Enter two sides or two points; example chips fill them for you.
- Results, diagrams, and steps update automatically. Copy the URL, LaTeX, or SVG for class use.
Display & accessibility settings
Results
Exact radicals are kept internally; decimals are for display only.
Diagrams
Steps
What this means
- a² and b² are the areas of the squares on each leg; their sum equals the square on c.
- The square root at the end simply turns area back into length.
- If c is not the longest side, the triangle cannot be right-angled.
- Integer sets like 3-4-5 are called Pythagorean triples; the tool shows a badge when it happens.
- Decimals and fractions are accepted; your input never leaves the browser.
How to use this calculator effectively
Use this page when you know two sides of a right triangle and need the missing side, area, perimeter, altitude, angles, or a quick validity check.
How it works
The calculator applies a^2 + b^2 = c^2 and keeps full precision internally until the final display. Enter the two known sides, confirm that c is the hypotenuse, and use the steps to see each square, subtraction, and square-root operation.
When to use
It is useful for geometry homework, construction sketches, screen or diagonal measurements, and checking whether a side set forms a valid right triangle before using it elsewhere.
Common mistakes to avoid
- Putting a leg value in the hypotenuse field when it is not the longest side.
- Mixing units such as inches and centimeters without converting first.
- Rounding an intermediate square root before using it in another calculation.
- Using the theorem for non-right triangles; use the triangle solver instead.
Interpretation and worked example
For a 3-4-? triangle, the tool squares both legs, adds 9 + 16, and takes sqrt(25) = 5. If your computed c is shorter than a or b, re-check which side is the hypotenuse.
See also
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.