Pythagorean Theorem Calculator

Find the missing side of a right triangle from the other two, with its angles and area.

Result

Enter your values and select Calculate to see the result.

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How the Pythagorean Theorem Calculator works

In a right triangle the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides. Enter any two sides and leave the third empty: you get the missing side, both acute angles, the area and the perimeter.

Formula

a² + b² = c²

Area = a × b ÷ 2; the angle opposite a is sin⁻¹(a ÷ c).

Examples

The 3-4-5 triangle

Sides 3 and 4 give a hypotenuse of 5, an area of 6, a perimeter of 12 and angles of about 36.87° and 53.13°.

A missing leg

A hypotenuse of 13 and a side of 5 give the other side: 12.

Frequently asked questions

Does it work for any triangle?

Only right triangles. For others, use the Triangle Calculator (law of cosines).

How do builders use it?

To check a right angle: measure 3 units along one side and 4 along the other; the diagonal should be exactly 5.

Why must the hypotenuse be the longest side?

c² = a² + b² is larger than either a² or b², so c is always longer than each leg.

Triangle Calculator

Solve any triangle from three sides or angles: SSS, SAS, ASA, AAS and the two-triangle SSA case.

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