Is It a Right Triangle?
Enter any three side lengths. The checker tests the Pythagorean theorem (a² + b² = c²) with float-safe tolerance, then classifies the triangle as acute, right, or obtuse — with all three angles, Heron area, perimeter, and a live diagram.
Right-triangle checker
Order doesn't matter — the longest side is tested as the hypotenuse. Measurements use a relative tolerance of 1e-9, so 0.3, 0.4, 0.5 still checks out.
Result
- Classification
- Pythagoras check
- Angles (sorted)
- Largest angle
- Area (Heron)
- Perimeter
- Hypotenuse
Worked examples
3, 4, 5 → RIGHT ✓
3² + 4² = 9 + 16 = 25 = 5². Angles 36.87°, 53.13°, 90°. Area = 6, perimeter = 12. The classic Pythagorean triple.
3² + 4² = 9 + 16 = 25 = 5². Angles 36.87°, 53.13°, 90°. Area = 6, perimeter = 12. The classic Pythagorean triple.
5, 5, 5 → NOT right (acute)
Equilateral: 5² + 5² = 50 > 25 = 5², so a² + b² > c² — all angles 60°. Area ≈ 10.8253, perimeter = 15.
Equilateral: 5² + 5² = 50 > 25 = 5², so a² + b² > c² — all angles 60°. Area ≈ 10.8253, perimeter = 15.
2, 3, 4 → NOT right (obtuse)
2² + 3² = 13 < 16 = 4², so a² + b² < c² — largest angle ≈ 104.48°. Area ≈ 2.9047, perimeter = 9.
2² + 3² = 13 < 16 = 4², so a² + b² < c² — largest angle ≈ 104.48°. Area ≈ 2.9047, perimeter = 9.
1, 1, √2 ≈ 1.4142 → RIGHT ✓
1² + 1² = 2 = (√2)². Isosceles right triangle: angles 45°, 45°, 90°. Area = 0.5, perimeter ≈ 3.4142.
1² + 1² = 2 = (√2)². Isosceles right triangle: angles 45°, 45°, 90°. Area = 0.5, perimeter ≈ 3.4142.
FAQ
How do you check if three sides form a right triangle?
Sort the sides so c is the longest, then compare a² + b² with c². If they match (within a tiny 1e-9 relative tolerance for floating-point rounding), it is a right triangle. For example, 3, 4, 5 gives 3² + 4² = 9 + 16 = 25 = 5², so it is a right triangle.
What is the difference between an acute, right, and obtuse triangle?
It depends on the largest angle: under 90° is acute, exactly 90° is right, over 90° is obtuse. Equivalently, with c the longest side: a² + b² > c² means acute, = c² means right, < c² means obtuse.
Is 5, 5, 5 a right triangle?
No — 5, 5, 5 is an equilateral triangle, which is acute: 5² + 5² = 50 > 25 = 5², so a² + b² > c². All three angles are 60°, the area is about 10.8253, and the perimeter is 15.
Is 1, 1, √2 a right triangle?
Yes — 1, 1, √2 (≈1.4142) is an isosceles right triangle: 1² + 1² = 2 = (√2)². Its angles are 45°, 45°, 90°, its area is 0.5, and its perimeter is about 3.4142.
What if my side measurements are not exact?
The checker uses a relative tolerance of 1e-9 when comparing a² + b² to c², so ordinary floating-point inputs like 0.3, 0.4, 0.5 still verify as right triangles. If the mismatch is bigger than the tolerance, the triangle is honestly classified acute or obtuse instead — e.g. 3, 4, 4.999 is acute and 3, 4, 5.001 is obtuse.
Does the order of the sides or the unit matter?
No. The sides are sorted internally, so 5, 3, 4 checks the same as 3, 4, 5. Any consistent length unit works (cm, inches, meters) because the test only compares ratios of squares.
Scope note: this is a dedicated yes/no right-triangle checker (Pythagorean test with tolerance). For a general solver — any side/angle from partial data, medians, altitudes — use the Triangle Area Calculator & Triangle Calculator instead.
Free tool by NRTechStudio