Pythagorean Theorem Calculator
Find a missing side of a right triangle with a² + b² = c². Also returns area, perimeter and angles. Free and private.
🔒 Runs entirely in your browser — nothing is uploadedThe Pythagorean theorem
The Pythagorean theorem states that in any right triangle the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². The hypotenuse c is the side opposite the 90° angle and is always the longest. If the legs are 3 and 4, then c² = 9 + 16 = 25, so c = 5. This calculator solves for whichever side you leave blank and shows the formula with your numbers filled in.
Rearranging the formula gives the other two cases: a = √(c² − b²) and b = √(c² − a²). Because a square root of a negative number is not real, the hypotenuse must be longer than the known leg, and the tool warns you if it is not.
Extra values for the triangle
Once all three sides are known the calculator also gives the area (a × b ÷ 2), the perimeter (a + b + c) and the two acute angles, found with the arctangent of the legs. In the 3-4-5 triangle the angles are about 36.87° and 53.13°, which always add up to 90°. These extras are useful for roof pitches, ramps, ladders, screen diagonals and any layout problem where you need a straight-line distance.
Practical uses
Carpenters use the 3-4-5 rule to check that a corner is square: measure 3 units along one edge and 4 along the other, and the diagonal should be exactly 5. You can also find the diagonal of a rectangular room, the length of a ladder needed to reach a window, or the straight-line distance between two points on a grid. Keep both inputs in the same unit, and the answers will be in that unit too. All calculations run locally in your browser, and no values are sent anywhere.
How to use
- Enter two sidesFill in any two of the three sides: leg a, leg b or the hypotenuse c.
- Leave one blankThe empty field is the side the calculator solves for.
- Review the triangleRead the missing side plus the area, perimeter and both acute angles.