Complete guide
Pythagorean theorem calculator for a missing side
Choose the missing side and enter the other two. Calculator24 rearranges a²+b²=c², reports the missing length, perimeter, area and acute angles.
Pythagorean theorem
For a right triangle, the sum of the squared leg lengths equals the squared hypotenuse. The relationship applies only when the angle opposite c is 90°.
Solve for the hypotenuse
Square both legs, add them and take the positive square root.
c = √(a²+b²)Solve for a leg
Subtract the known leg square from the hypotenuse square. A nonpositive remainder cannot form a triangle.
a = √(c²−b²)b = √(c²−a²)Angles, area and perimeter
After all sides are known, inverse tangent finds an acute angle, area equals ab/2 and perimeter equals a+b+c.
Common triples
Integer triples such as 3-4-5 and 5-12-13 satisfy the equation exactly. Scaled versions remain right triangles.
Common Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Frequently asked questions
What is the Pythagorean theorem?
For a right triangle, a²+b²=c².
Which side is c?
c is the hypotenuse opposite the right angle.
Can the theorem solve a leg?
Yes. Subtract the other leg square from c² and take the square root.
Does it work for every triangle?
The equality applies to right triangles.
What is a Pythagorean triple?
It is a set of three positive integers that satisfies a²+b²=c².
What to keep in mind
The selected missing field is ignored and replaced by the result. A hypotenuse must be longer than either leg.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.