A walkthrough, end to end.
- 1
Enter two sides of the right triangle (legs a, b) or one leg + hypotenuse.
- 2
Pick which side you want to solve for.
- 3
The calculator returns the missing side using a² + b² = c².
Pythagorean theorem
In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Discovered ~500 BCE; remains the cornerstone of Euclidean geometry.
What you can do with this.
Solve for hypotenuse
Legs 3 and 4 → hypotenuse = √(9 + 16) = 5. The classic 3-4-5 right triangle. Used in carpentry to verify square corners.
Solve for missing leg
Hypotenuse 13, leg 5 → other leg = √(169 − 25) = 12. Pythagorean triples (3-4-5, 5-12-13, 8-15-17, 7-24-25) appear regularly in geometry problems.
Diagonal of a TV / monitor
55-inch TV's diagonal: width and height satisfy 16:9 aspect → solve for the actual width and height that gives 55-inch diagonal. The calculator can do this with reverse engineering.
Diagonal of a square / rectangle
Room diagonal 12 ft × 16 ft → diagonal = √(144 + 256) = 20 ft. Useful for moving large furniture through doorways.
Verify square corners
Carpenters use 3-4-5 (or any Pythagorean triple) to verify a corner is exactly 90°. Mark 3 ft along one side, 4 ft along the other; if the diagonal is exactly 5 ft, the corner is square.
Distance to base of a tower
Wire from ground to top of pole. If pole is 10 m tall and wire is 12 m long, the distance from base = √(144 − 100) = 6.6 m. Practical engineering math.
Pythagorean theorem in 3D
Generalizes: a² + b² + c² = d² for box diagonal. The calculator does 2D right triangle; for 3D box diagonal, square each dimension separately and sum.
Pythagorean calculator 2026 — what's current
One of the oldest and most-used theorems in mathematics. Calculator wins for speed and verification; AI tools also handle reliably.
Frequently asked.
Yes — Pythagorean theorem is specifically for right triangles. For any other triangle, use the law of cosines instead (Triangle Calculator).
Three positive integers (a, b, c) with a² + b² = c². Famous examples: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Useful for verifying square corners exactly.
Side lengths must be positive. Pythagorean theorem applies to magnitudes only.
No. Calculations run entirely in your browser.