Calculate the perimeter of a right triangle from any two sides. Find all three sides, area, angles, inradius, circumradius, and altitude. Includes Pythagorean triples table.
A right triangle is a triangle with one 90-degree angle. Its three sides are the two legs (the sides forming the right angle) and the hypotenuse (the longest side, opposite the right angle). The Pythagorean theorem — a² + b² = c² — links all three, so knowing any two sides immediately gives the third.
The perimeter is simply the sum of all three sides: P = a + b + c. While the formula is straightforward, computing c = √(a² + b²) by hand is tedious, and situations like knowing one leg and the hypotenuse (requiring c² − a² under the radical) add extra steps. This calculator handles both cases and does far more than just perimeter.
Enter any two sides — either both legs or one leg and the hypotenuse — and the tool instantly computes the perimeter, all three side lengths, the area (½ab), both acute angles via inverse tangent, the inradius r = (a + b − c)/2, the circumradius R = c/2, and the altitude to the hypotenuse h = ab/c. Visual bars compare side lengths and angles at a glance.
Eight presets load classic Pythagorean triples (3-4-5, 5-12-13, 8-15-17, …) so you can explore integer-sided right triangles instantly. A reference table lists ten common triples with their perimeters and areas. Whether you are solving geometry homework, designing a ramp, or checking construction measurements, this tool gives you every property of a right triangle in one place.
Perimeter 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 unit label, show pythagorean triples, known sides, and it returns perimeter, leg a, leg b, hypotenuse c 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.
Perimeter = a + b + c, where c = √(a² + b²) (both legs known) or b = √(c² − a²) (leg + hypotenuse known). Area = ½ab. Inradius r = (a + b − c)/2. Circumradius R = c/2.
Result: Perimeter = 12
Hypotenuse c = √(9 + 16) = √25 = 5. Perimeter = 3 + 4 + 5 = 12. Area = ½ × 3 × 4 = 6. Angles ≈ 36.87° and 53.13°.
This perimeter of a right triangle tool links the entered values (unit label, show pythagorean triples, known sides) 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
Perimeter 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 (perimeter, leg a, leg b, hypotenuse c) 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.
A set of three positive integers (a, b, c) satisfying a² + b² = c², meaning they form a right triangle with integer sides. Use this as a practical reminder before finalizing the result.
Not without additional information. You need at least two of the three sides, or one side plus an acute angle.
It is the radius of the inscribed circle, computed as r = (a + b − c)/2, where c is the hypotenuse. Keep this note short and outcome-focused for reuse.
Because the hypotenuse of a right triangle is always a diameter of the circumscribed circle (Thales' theorem). Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
Use inverse tangent: angle A = arctan(a/b), angle B = arctan(b/a). The right angle is always 90°.
No. For general triangles, use the law of cosines to find the third side and then add all three sides.