Pythagorean Theorem Calculator

For any right triangle, a^2 + b^2 = c^2, where a and b are the two legs and c is the hypotenuse - the side opposite the right angle. Rearranged to solve for each side: c = sqrt(a^2 + b^2), a = sqrt(c^2 - b^2), b = sqrt(c^2 - a^2). Enter any two sides and the calculator finds the third.

Construction workers use the 3-4-5 rule to confirm a right angle. The same formula finds a screen diagonal from width and height or a roof rafter length from run and rise. For maps, it applies directly to projected Cartesian coordinates and short local offsets. Latitude and longitude over larger distances require a spherical or ellipsoidal distance formula.

A 3-4-5 triangle is the smallest right triangle with all-integer sides: 3^2 + 4^2 = 9 + 16 = 25 = 5^2. Builders use it to square corners - measure 3 ft along one wall, 4 ft along the other, and adjust until the diagonal reads exactly 5 ft. Scaled versions like 6-8-10 or 9-12-15 work equally well.

Pythagorean triples are sets of three positive integers (a, b, c) satisfying a^2 + b^2 = c^2. Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and (20, 21, 29). Multiplying any triple by the same integer produces another valid triple - for example, doubling (3, 4, 5) gives (6, 8, 10).

No - it applies only to right triangles. For triangles with any angle, use the Law of Cosines: c^2 = a^2 + b^2 - 2ab x cos(C). When C equals 90 degrees, the cosine term drops to zero and you get the Pythagorean theorem back. Note: the calculator returns no result if the hypotenuse you enter is not longer than each leg, since that input cannot form a valid right triangle.