Find hypotenuse, legs, perimeter, and area from measurements. Review formulas, units, examples, and calculation steps. Download neat reports for homework, construction, and classroom checks.
| Case | Side a | Side b | Side c | Area | Perimeter |
|---|---|---|---|---|---|
| Classic 3 4 5 | 3 | 4 | 5 | 6 | 12 |
| Scaled triple | 6 | 8 | 10 | 24 | 24 |
| Large build check | 9 | 12 | 15 | 54 | 36 |
| Diagonal estimate | 5 | 12 | 13 | 30 | 30 |
| Non right example | 4 | 5 | 8 | Not right | 17 |
Main theorem: a² + b² = c²
Find hypotenuse: c = √(a² + b²)
Find missing leg: a = √(c² - b²) or b = √(c² - a²)
Area of the right triangle: Area = (a × b) / 2
Perimeter: P = a + b + c
Check mode: sort the sides and test whether smaller² + smaller² equals largest² within the chosen tolerance.
The Pythagorean theorem helps you measure right triangles with confidence. It links the two legs and the hypotenuse. This calculator speeds up routine work. It also reduces manual mistakes.
Right triangles appear in geometry, construction, navigation, surveying, design, and screen layouts. You may need a roof slope length. You may check a wall brace. You may verify a diagonal on a floor plan. The theorem gives a direct answer when two sides are known.
This page solves several common tasks. It can find the hypotenuse from two legs. It can find a missing leg from one leg and the hypotenuse. It can also test whether three sides form a right triangle. Along with the missing side, it reports area, perimeter, and acute angles when possible. Step text explains the logic clearly.
The main rule is a² + b² = c². Here, a and b are the legs. The value c is the hypotenuse. When the hypotenuse is unknown, square both legs, add them, and take the square root. When a leg is unknown, subtract the known leg square from the hypotenuse square, then take the square root.
Use the same unit for every side. Do not mix meters with inches. Set the decimal precision you want before calculating. For checking mode, enter all three sides and compare the squared values. Small rounding differences can happen. The tolerance field helps handle that.
Measure carefully before entering values. Keep enough decimal places for technical tasks. Review the generated steps, not only the final number. Exporting to CSV helps record jobs. Exporting to PDF helps share results with clients, teachers, or team members. The example table below shows sample triangle values for quick comparison.
Students can confirm homework and exam practice. Carpenters can verify corners and framing cuts. Engineers can estimate diagonals, clearances, and braces. DIY users can check ladders, ramps, and shelf supports. Because the layout is simple, the page works well for fast field entry. The included validation also prevents impossible side combinations, which saves time during repeated calculations. It also improves confidence when reviewing measurements.
It solves the hypotenuse, either missing leg, and right triangle checks. It also reports area, perimeter, and acute angles when the triangle values allow those results.
Use check mode when you already know all three sides. The calculator sorts them, compares the squared values, and tells you whether they satisfy the theorem within your chosen tolerance.
In a right triangle, the hypotenuse lies opposite the right angle. That side is always longer than either leg, so any valid input must keep c larger than the other two sides.
Measured values often contain rounding. A small tolerance lets the calculator treat tiny squared differences as acceptable. This is useful for field measurements, decimal inputs, and imported values.
Yes. Enter any unit label you want, but keep every side in the same unit. The calculator does not convert units automatically, so consistency matters for accurate results.
For a right triangle, area equals one half times leg a times leg b. The calculator uses the two perpendicular sides as base and height after solving any missing value.
The CSV file includes the selected mode, solved sides, area, perimeter, angles, and status text. It is useful for saving results, sharing records, or importing into spreadsheet software.
The PDF export creates a simple report with the main result values and step summary. It works well for printing, sending to clients, or attaching to homework notes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.