Pythagorean theorem calculator for a missing side
Choose the missing side and enter the other two. HitEquals rearranges a²+b²=c², reports the missing length, perimeter, area and acute angles.
Inputs used by this calculator
Pythagorean Theorem Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Missing side | Hypotenuse c | Hypotenuse c · Leg a · Leg b | Chooses which Pythagorean Theorem Calculator method or unknown the engine evaluates. |
| Leg a | 3 | 1e-9 to 1000000000000 | Supplies the leg a quantity used by the published equation or result breakdown. |
| Leg b | 4 | 1e-9 to 1000000000000 | Supplies the leg b quantity used by the published equation or result breakdown. |
| Hypotenuse c | 5 | 1e-9 to 1000000000000 | Supplies the hypotenuse c quantity used by the published equation or result breakdown. |
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.
What the Pythagorean Theorem Calculator answers
Find a missing right-triangle side from the other two sides and inspect the Pythagorean substitution, squares and final root.
Use Pythagorean Theorem Calculator when you know Missing side, Leg a, Leg b and Hypotenuse c and need the relationship expressed by the published equation.
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 question does this Pythagorean Theorem Calculator answer?
Find a missing right-triangle side from the other two sides and inspect the Pythagorean substitution, squares and final root.
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 are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.