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
This guide helps you use Pythagorean theorem (right triangle) calculator in a repeatable way: define a baseline, change one variable at a time, and explain each output using explicit assumptions before sharing results.
How it works
The calculator applies deterministic formulas to your input values and only rounds at the final display layer. This makes it useful for comparative analysis: keep one scenario as a baseline, then vary assumptions and measure the delta in both absolute terms and percentage terms. If a change appears too large or too small, verify units, period conventions, and sign direction before interpreting the result.
When to use
Use this page when you need a fast planning estimate, a classroom check, or a reproducible scenario that teammates can review. It is most effective at the decision-prep stage, where you need to compare options quickly and decide which assumptions deserve deeper modeling or external validation.
Common mistakes to avoid
- Mixing units such as percent vs decimal, or monthly vs yearly settings.
- Changing multiple fields at once, which hides the real cause of result movement.
- Comparing outputs across tools without aligning constants and default conventions.
- Treating rounded display values as exact inputs for downstream calculations.
Interpretation and worked example
Start with a baseline case and save that output. Next, edit one assumption to reflect your realistic alternative, then compare both the direction and size of change. If the direction matches domain intuition and magnitude is plausible, your setup is likely coherent. If not, check hidden defaults, unit conversions, boundary conditions, and date logic before drawing conclusions.
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.