Geometry
Enter the two legs of a right triangle to find the hypotenuse, angles, area, and perimeter.
Hypotenuse (c)
5.00 units
Uses the Pythagorean theorem: c = √(a² + b²). Angles are calculated with inverse tangent (arctan). Area = ½ab.
A right triangle calculator computes all key measurements of a right triangle given its two legs (the sides that form the 90° angle). It calculates the hypotenuse using the Pythagorean theorem, derives both acute angles using inverse tangent, determines the area (half the product of the legs), and sums all three sides for the perimeter. The calculator handles any positive leg lengths and instantly displays results with two decimal precision.
Enter the length of leg A and leg B (the two sides meeting at the right angle). The calculator applies the Pythagorean theorem to find the hypotenuse, uses arctan (inverse tangent) to compute each acute angle, multiplies the legs and divides by two for area, and adds all three sides for perimeter. Results update live as you type.
Hypotenuse: c = √(a² + b²) | Angle A: α = arctan(b/a) × (180/π) | Angle B: β = arctan(a/b) × (180/π) | Area: A = ½ab | Perimeter: P = a + b + cThe Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the two legs. Inverse tangent (arctan) relates the opposite and adjacent sides to find acute angles in degrees. Area is simply half the base times height. Perimeter is the sum of all three sides.
| Input | Result | Notes |
|---|---|---|
| Legs: a = 3, b = 4 | Hypotenuse: 5 | Angle A: 53.13° | Angle B: 36.87° | Area: 6 | Perimeter: 12 | The classic 3-4-5 Pythagorean triple; angles sum to 90° |
| Legs: a = 5, b = 12 | Hypotenuse: 13 | Angle A: 67.38° | Angle B: 22.62° | Area: 30 | Perimeter: 30 | Another famous triple (5-12-13); commonly used in construction |
| Legs: a = 7.5, b = 10 | Hypotenuse: 12.50 | Angle A: 36.87° | Angle B: 53.13° | Area: 37.50 | Perimeter: 30.00 | Demonstrates the calculator with decimal inputs; angles are supplementary to the 5-12-13 triangle |
The Pythagorean theorem states that in any right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse. This is one of the most fundamental relationships in mathematics and applies to all right triangles, regardless of size.
No—this calculator specifically uses properties of right triangles. For oblique triangles (no right angle), use the law of cosines or law of sines instead.
Pythagorean triples are sets of three positive integers that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17). Any multiple of a Pythagorean triple is also a triple—e.g., (6, 8, 10) is a multiple of (3, 4, 5).
The acute angles are found using inverse tangent (arctan). For angle A: arctan(opposite/adjacent) = arctan(b/a). The two acute angles always sum to exactly 90°.
Real-world measurements contain errors from tools, human error, or rounding. Small differences (within 1-2%) are normal. If the difference is larger, double-check that your angle is truly 90° using a level or square.
Any unit works (feet, meters, inches, centimeters, etc.)—just be consistent. The calculator returns results in the same units as your input.