PythLab

Pythagorean Theorem Calculator

Right-triangle hypotenuse in one step.

Leg a

Leg b

Hypotenuse c

a² + b² = c²

What you entered

Leg a: 3Leg b: 4

1
Square leg a
3²= 9
2
Square leg b
4²= 16
3
Sum of squares
9 + 16= 25
4
Hypotenuse (square root)
√25= 5

Result

Hypotenuse c: 5

For a right triangle with legs 3 and 4, the hypotenuse is 5 — the longest side, opposite the right angle.

Hypotenuse for common right triangles

The hypotenuse is the square root of a squared plus b squared. The first seven rows are Pythagorean triples, where all three sides are whole numbers.

Side a	Side b	Hypotenuse c
3	4	5.000
5	12	13.000
6	8	10.000
7	24	25.000
8	15	17.000
9	12	15.000
20	21	29.000
1	1	1.414
2	3	3.606

The 6-8-10 and 9-12-15 rows are just the 3-4-5 triangle scaled by 2 and 3, which is why builders use the 3-4-5 method to check a corner is square: measure 3 units along one wall, 4 along the other, and the diagonal must be exactly 5. The last two rows show the usual case - most right triangles have an irrational hypotenuse, and 1,1 gives the square root of 2. The formula only applies to right-angled triangles; for any other triangle you need the law of cosines.

One of the oldest, most-used formulas in math

a² + b² = c² relates the two legs of any right triangle to its hypotenuse — it works because the squares built on each leg literally tile to cover the square built on the hypotenuse, a relationship provable with nothing more than rearranged shapes.

Where it shows up outside the classroom

Carpenters use it to confirm a corner is truly square (the 3-4-5 rule), and it's the basis for finding the shortest distance between two points — GPS, TV screen sizes, and construction diagonals all lean on this same relationship.

Frequently asked questions

How do I find the hypotenuse of a right triangle?

c = √(a² + b²). For legs 3 and 4: c = √(9 + 16) = √25 = 5. Common Pythagorean triples to remember: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Any multiple of a triple also works (6-8-10, 9-12-15).

How do I find a missing leg?

Rearrange: a = √(c² − b²). If the hypotenuse is 13 and one leg is 5: a = √(169 − 25) = √144 = 12. The missing leg is always shorter than the hypotenuse.

What is the 3-4-5 rule in construction?

Measure 3 feet along one wall and 4 feet along the perpendicular wall. If the diagonal between those points is exactly 5 feet, the corner is a perfect 90° angle. Any multiple works too: 6-8-10 for larger spaces, 9-12-15 for even bigger ones.