Pythagorean Theorem Calculator
Solve a missing side of a right triangle or verify three entered sides using a squared plus b squared equals c squared.
- Solve any one missing side
- Verify whether three sides satisfy a²+b²=c²
- Also shows angles, area and perimeter
Calculator workspace
Enter the known values, calculate, and review the supporting figures and formula instead of relying on a single unexplained number.
What this Pythagorean Theorem Calculator does
The Pythagorean theorem is one of the most useful relationships in geometry: for a right triangle, the square of the hypotenuse equals the sum of the squares of the two perpendicular legs. This calculator lets you enter any two positive side lengths and solve the third. You can also enter all three sides to check whether they satisfy the right-triangle relationship within normal floating-point tolerance.
The workspace is designed for quick checking as well as repeatable planning. Inputs remain editable, the supporting figures are shown with the headline result, and the calculation runs locally in the browser. That makes it easy to change one assumption at a time, compare scenarios and copy or save a result together with the values that explain it.
Formula and calculation method
a² + b² = c², with c as the hypotenuse.
The calculator uses the convention that c is the hypotenuse, so c must be the longest side. If c is missing, it computes √(a²+b²). If a or b is missing, it rearranges the equation to √(c²−known leg²). Once all sides are available, the tool calculates the two acute angles with inverse trigonometric functions, then derives area and perimeter. When all three sides are supplied, the Pythagorean residual a²+b²−c² is displayed so you can see the size and direction of any mismatch.
How to use the calculator
- Choose the calculation mode, shape, unit or known-value combination when the page provides one.
- Enter values that belong to the same problem or measurement scenario and keep units consistent with the field labels.
- Select Calculate and review both the main answer and the supporting metrics shown with it.
- Change one assumption at a time when comparing scenarios; this makes the effect of each input easier to understand.
- Use Copy Result, Share Result or Save Result Image when you need a portable record of the calculation.
Worked example
For a = 3 and b = 4, the calculator solves c = 5 because 3² + 4² = 9 + 16 = 25 and √25 = 5. The area is 6 square units, the perimeter is 12 units, and the acute angles are approximately 36.87° and 53.13°.
How to interpret the result
When measuring a physical corner, a small non-zero residual may result from rounding or measurement uncertainty rather than a truly non-square corner. For layout work, compare the calculated diagonal with the measured diagonal using the same units and precision. The calculator does not convert units automatically because the Pythagorean relationship is unit-consistent: all three sides simply need to use the same unit.
A calculator result is only as useful as the values entered. For measurements, use appropriately precise source data; for costs, use prices that match the same currency and period; for technical work, compare the output with drawings, equipment data or other authoritative information. The supporting metrics on this page are included specifically to make cross-checking easier.
Important assumptions and limitations
This tool is specifically for Euclidean right triangles. It is not a general triangle solver and does not use the law of sines or law of cosines for arbitrary angles. If you know a side and an acute angle instead of two sides, use the Right Triangle Calculator, which provides dedicated trigonometric modes.
This calculator is provided for planning, checking, education and general informational use. It makes the formula and assumptions visible, but it does not replace project specifications, professional engineering, financial or medical advice, contractual documents, equipment ratings or applicable standards.
Frequently asked questions
Which side is c?
c is the hypotenuse: the side opposite the 90-degree angle and the longest side of a right triangle.
Can I enter all three sides?
Yes. The calculator will check the Pythagorean residual and indicate whether the sides form a right triangle within numerical tolerance.
Do the side units matter?
All side values must use the same unit, but that unit can be feet, meters, inches or any other consistent length unit.