Pythagorean Theorem (a² + b² = c²) Calculator
Use our free online Pythagorean Theorem Calculator to perform fast, accurate calculations with instant formulas, step-by-step arithmetic, and verified reference benchmarks.
Pythagorean Theorem Calculator
Instant Live Computation • Zero Waiting
Adjust inputs on the left for instantaneous live computation.
How to Calculate: The Pythagorean Theorem Calculator Formula
In any Euclidean right triangle (90° angle), the square of the hypotenuse (c) equals the sum of the squares of the other two legs (a and b).
Step-by-Step Calculation Guide
- Input known lengths for side a and side b (or hypotenuse c and one leg).
- Calculate squares of the known lengths.
- Take the square root to find missing side.
- Review perimeter, area, and internal angles.
Practical Pythagorean Theorem Calculator Examples
Leg a = 3, Leg b = 4.
Screen width = 48 inches, height = 27 inches.
Famous Pythagorean Integer Triples (a² + b² =
Official reference values and benchmark classifications based on standard institutional guidelines.
| Triple Name | Side a | Side b | Hypotenuse c | Ratio Scaling |
|---|---|---|---|---|
| Smallest Primitive Triple | 3 | 4 | 5 | 3 : 4 : 5 (Scales to 6-8-10, 30-40-50) |
| Second Primitive Triple | 5 | 12 | 13 | 5 : 12 : 13 |
| Third Primitive Triple | 8 | 15 | 17 | 8 : 15 : 17 |
| Fourth Primitive Triple | 7 | 24 | 25 | 7 : 24 : 25 |
| Fifth Primitive Triple | 9 | 40 | 41 | 9 : 40 : 41 |
Frequently Asked Questions about Pythagorean Theorem Calculator
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle, situated directly opposite the 90-degree right angle.
How do carpenters use the 3-4-5 rule?
Carpenters measure 3 feet along one wall and 4 feet along an adjacent wall; if the diagonal distance between the marks is exactly 5 feet, the corner is confirmed square (90 degrees).
Does the Pythagorean theorem work on non-right triangles?
No. For oblique triangles without a 90° angle, use the generalized Law of Cosines: c² = a² + b² - 2ab·cos(C).
Can hypotenuse c be shorter than a or b?
No. The hypotenuse is mathematically guaranteed to be the longest side in any Euclidean right triangle.