Solve right triangles with the Pythagorean theorem. Find any side, angles, area, perimeter, altitude, inradius, circumradius, and detect special triples.
The **Pythagorean Theorem Calculator** solves any right triangle using the timeless relationship a² + b² = c², where c is the hypotenuse. Choose one of three modes — find the hypotenuse from two legs, or find either leg when the hypotenuse and the other leg are known — and get a complete breakdown of every measurement.
Beyond the basic side calculation, this tool computes both acute angles using inverse trigonometry, the area (½ab), the perimeter, the semi-perimeter, the altitude from the right-angle vertex to the hypotenuse (h = ab/c), the inradius of the inscribed circle, and the circumradius, which for right triangles always equals half the hypotenuse. Medians to each side are also displayed.
Proportion bars give you an instant visual comparison of all three side lengths, making the triangle's shape immediately apparent. The tool also automatically detects well-known Pythagorean triples — 3-4-5, 5-12-13, 8-15-17, and more — as well as multiples of those primitives. A comprehensive reference table lists twelve common triples, highlights matches, and notes whether each is primitive.
Eight preset buttons load classic right triangles in one click, including all four modes of solving. A precision slider lets you control the number of decimal places from 0 to 10. Whether you are studying geometry, checking a construction layout, or validating survey measurements, this calculator provides every number you need from a single right triangle.
Pythagorean Theorem Calculator — Right Triangle Solver helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like Side a, Side b, Hypotenuse c in one pass.
c = √(a² + b²). Angle A = arctan(a/b). Area = ½ab. Altitude h = ab/c. Inradius r = (a + b − c)/2. Circumradius R = c/2.
Result: c = 5, A ≈ 36.87°, B ≈ 53.13°, Area = 6, Perimeter = 12
Using a=3, b=4, the calculator returns c = 5, A ≈ 36.87°, B ≈ 53.13°, Area = 6, Perimeter = 12. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to pythagorean theorem calculator — right triangle solver workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
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. It is one of the most fundamental results in all of geometry.
Rearrange the formula: a = √(c² − b²). Enter the hypotenuse and the known leg, select the "Find Leg" mode, and the calculator does the rest.
A Pythagorean triple is a set of three positive integers (a, b, c) such that a² + b² = c². The simplest is 3-4-5. A triple is "primitive" if gcd(a, b, c) = 1.
Yes. Enter any positive decimal values and the calculator computes exact results to the chosen precision. Special-triple detection works on integer values and their multiples.
It is the perpendicular distance from the right-angle vertex to the hypotenuse. Its length equals ab/c, and it divides the hypotenuse into two segments whose lengths have a geometric mean equal to the altitude.
By Thales' theorem, any triangle inscribed in a semicircle with the diameter as one side is a right triangle. So the hypotenuse is a diameter and the circumradius is half of it.