Find the missing side of a right triangle using the Pythagorean theorem. Enter any two sides, get the third plus area, angles, perimeter, inradius, and more.
The Missing Side of a Right Triangle Calculator uses the Pythagorean theorem to find any missing side when you know the other two. Select which side is unknown — leg a, leg b, or hypotenuse c — enter the two known values, and instantly get the missing side along with a full set of triangle properties.
The Pythagorean theorem (a² + b² = c²) is one of the most fundamental relationships in mathematics. It applies to every right triangle and forms the basis of distance calculations in two and three dimensions, trigonometry, and countless engineering applications.
Beyond finding the missing side, this calculator computes the triangle's area (½ab), perimeter (a+b+c), both acute angles using inverse tangent, the inradius (radius of the inscribed circle), the circumradius (half the hypotenuse), and the altitude to the hypotenuse. It also identifies whether your triangle forms a Pythagorean triple — a set of three positive integers where a² + b² = c² — and whether that triple is primitive (no common factor).
Eight preset buttons load classic Pythagorean triples like (3,4,5), (5,12,13), and (8,15,17) so you can explore results immediately. A comprehensive reference table lists twelve common Pythagorean triples, and visual comparison bars show how sides and angles relate to each other.
Missing Side of 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 decimal places, which side is missing?, unit, and it returns side a (leg), side b (leg), hypotenuse c, area 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.
c = √(a² + b²) to find the hypotenuse. a = √(c² − b²) or b = √(c² − a²) to find a missing leg.
Result: c = 5
c = √(3² + 4²) = √(9 + 16) = √25 = 5. This is the classic (3, 4, 5) Pythagorean triple. Area = ½×3×4 = 6, perimeter = 12.
This missing side of a right triangle tool links the entered values (decimal places, which side is missing?, unit) 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
Missing Side of 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 (side a (leg), side b (leg), hypotenuse c, area) 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 any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². Use this as a practical reminder before finalizing the result.
Square both legs, add them together, and take the square root: c = √(a² + b²). Keep this note short and outcome-focused for reuse.
Subtract the known leg squared from the hypotenuse squared, then take the square root: a = √(c² − b²). Apply this check where your workflow is most sensitive.
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². Examples: (3,4,5), (5,12,13).
A primitive triple is one where a, b, and c have no common factor greater than 1. For example, (3,4,5) is primitive but (6,8,10) is not.
The inradius is (a + b − c)/2, where a and b are legs and c is the hypotenuse. It is the radius of the largest circle that fits inside the triangle.
No — the Pythagorean theorem only applies to right triangles. For other triangles, use the Law of Cosines.