Instantly calculate the hypotenuse or a leg of a right triangle using the Pythagorean theorem: a² + b² = c².
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The hypotenuse is the side opposite the right angle: c = √(a² + b²).
√(3² + 4²) = 5
Hypotenuse c = 5Standard geometry formulas. Instant in-browser calculation, no account. Exact results for the dimensions you enter.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. From this you get any missing side:
With legs 3 and 4: hypotenuse = √(9 + 16) = √25 = 5. Reverse, with hypotenuse 13 and leg 5: the other leg = √(169 − 25) = 12.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
The hypotenuse c = √(a² + b²). For legs 3 and 4: c = √(9 + 16) = √25 = 5.
The leg b = √(c² − a²). For hypotenuse 13 and leg 5: b = √(169 − 25) = √144 = 12.
Three whole numbers satisfying a² + b² = c², for example (3, 4, 5), (5, 12, 13) and (8, 15, 17).
Only in right triangles (with a 90° angle). For other triangles the law of cosines is used.
Check whether a² + b² = c², where c is the longest side. If the equality holds, the triangle is right-angled.
In construction (checking right angles, the “3-4-5” corner), navigation, graphics and for computing distances.
Distance = √((x₂−x₁)² + (y₂−y₁)²), a direct application of the Pythagorean theorem in the plane.