MathematicsGeometry
Pythagorean Theorem & Right Triangle Calculator
Calculate missing side lengths (leg a, leg b, or hypotenuse c), interior angles, area, and perimeter of any right-angled triangle.
Right Triangle Sides: a² + b² = c²
Enter any two known values. Leave the unknown third field blank to solve.
Solved Triangle Metrics
c = 5
Leg a: 3 | Leg b: 4
Triangle Area (½ab):6
Perimeter (a + b + c):12
Interior Angles:∠A: 36.87°, ∠B: 53.13°, ∠C: 90°
Mathematical Formula: Pythagorean Theorem
a² + b² = c² ⟹ c = √(a² + b²)
The fundamental relation among the three sides of a right triangle in Euclidean geometry.
How to Use This Calculator
- 1Enter any two known side lengths (Side A, Side B, or Hypotenuse C).
- 2Leave the unknown field blank.
- 3Click Calculate to find the missing side, exact angles (in degrees), area, and perimeter.
Practical Example: Classic 3-4-5 Triangle
Scenario: Leg A = 3, Leg B = 4
Side A:3
Side B:4
Result: Hypotenuse C: 5.0 | Area: 6.0 | Angles: 36.87°, 53.13°, 90.0°
3² + 4² = 9 + 16 = 25, and √25 = 5.
Frequently Asked Questions
The hypotenuse (c) is always the longest side of a right triangle and is directly opposite the 90-degree right angle.
Pro Calculation Tips
- Common Pythagorean triples to memorize: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Model Assumptions
- Only applies to right-angled (90 degree) triangles.