Enter three side lengths to check whether they form a right triangle using the Pythagorean theorem. See all angles, deviation from 90°, area, perimeter, and a table of Pythagorean triples.
How do you know if three side lengths form a right triangle? The Pythagorean theorem gives the definitive test: a triangle is a right triangle if and only if the square of the longest side equals the sum of the squares of the other two sides (a² + b² = c²).
This calculator does much more than a simple pass/fail check. Enter any three positive side lengths and it immediately tells you whether the triangle is right-angled, classifies it as acute or obtuse if not, and computes every interior angle using the law of cosines. It highlights which angle is closest to 90° and shows the exact deviation, which is especially useful for real-world measurements that are nearly—but not perfectly—right-angled.
You also get the triangle's area (via Heron's formula), perimeter, semi-perimeter, and a side classification (equilateral, isosceles, or scalene). A tolerance field lets you account for rounding or measurement error. Eight presets include classic Pythagorean triples like 3-4-5, 5-12-13, and 8-15-17, plus non-right examples for comparison. A reference table of the twelve most common Pythagorean triples rounds out the tool, making it ideal for students, teachers, carpenters, and anyone who needs to verify right angles quickly.
Is It a Right Triangle? problems often require several dependent steps, and a small arithmetic slip can propagate through every derived value. This calculator is tailored to that workflow: you enter side a, side b, side c, and it returns pythagorean check, triangle type (sides), triangle type (angles), angle a in one consistent pass. It is useful for homework checks, worksheet generation, tutoring walkthroughs, and fast field/design estimates where you need reliable geometry results without rebuilding the full derivation each time.
A triangle with sides a ≤ b ≤ c is right-angled iff a² + b² = c². Angles via law of cosines: cos(A) = (b² + c² − a²) / (2bc). Area via Heron: √[s(s−a)(s−b)(s−c)].
Result: YES — Right triangle
3² + 4² = 9 + 16 = 25 = 5², so it satisfies the Pythagorean theorem exactly. Angles: 36.87°, 53.13°, 90°.
This is it a right triangle? tool links the entered values (side a, side b, side c, tolerance) to the target geometry relationships used in class and practice problems. Instead of solving each intermediate step manually, you can validate setup and arithmetic quickly while still tracing which measurements drive the final result.
Formula focus: the calculator formula
Is It a Right Triangle? shows up in school geometry, technical drafting, construction layout checks, and early engineering design estimates. When values are changed repeatedly, the calculator helps you compare scenarios quickly and see how sensitive the shape is to each dimension.
Start with the primary outputs (pythagorean check, triangle type (sides), triangle type (angles), angle a) and then use the remaining cards/tables to confirm consistency with your diagram. Keep units consistent across inputs, and round only at the end if your assignment or project specifies a fixed precision.
It states that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². Use this as a practical reminder before finalizing the result.
Increase the tolerance value. The calculator flags it as right if the difference between a²+b² and c² is within the tolerance.
Yes — the calculator automatically sorts them to identify the hypotenuse (longest side) for the Pythagorean check. Keep this note short and outcome-focused for reuse.
Three positive integers (a, b, c) that satisfy a² + b² = c². The smallest is (3, 4, 5).
Using the law of cosines: cos(A) = (b² + c² − a²)/(2bc), then A = arccos of that value, converted to degrees. Apply this check where your workflow is most sensitive.
If the three sides violate the triangle inequality (any side ≥ sum of the other two), no results are shown. Use this checkpoint when values look unexpected.