Pythagorean Theorem Calculator
Solve right-triangle sides, angles, area, perimeter, and side ratios.
Used only for labels and result suffixes.
One side touching the right angle.
The other side touching the right angle.
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How Right-Triangle Solving Works
The theorem handles side lengths; trig relationships handle side plus angle cases.
Pythagorean theorem
If the two legs are a and b, and the hypotenuse is c, then a^2 + b^2 = c^2. The same relationship can be rearranged to solve a missing leg.
Side plus angle
With one side and one acute angle, sine, cosine, and tangent fill in the missing sides. The third angle is always 90 degrees minus the acute angle you entered.
Area and slope
Right-triangle area is a x b / 2. The slope value compares vertical rise to horizontal run, which is useful for ramps, roof pitch, and layout checks.
Pythagorean Calculator Examples
Common right-triangle setups and what each mode solves.
3-4-5 triangle
Enter legs 3 and 4 to get hypotenuse 5, area 6, and perimeter 12.
Missing ladder distance
With a 13 ft hypotenuse and 5 ft ground distance, the vertical leg is 12 ft.
Side and angle
A 10 unit hypotenuse at 30 degrees gives an opposite leg of 5 and adjacent leg of about 8.66.
Pythagorean Theorem Calculator FAQ
Answers about right triangles, hypotenuse, missing legs, and angle-based solving.
What does the Pythagorean theorem calculate?
For a right triangle, it relates the two legs and the hypotenuse with a^2 + b^2 = c^2. If two sides are known, the third side can be solved.
Can this calculate a missing leg?
Yes. Choose hypotenuse and leg mode, enter the hypotenuse and one known leg, and the calculator solves the other leg with sqrt(c^2 - a^2).
Can I use an angle instead of two sides?
Yes. The side and angle mode solves a right triangle from one side and one acute angle using sine, cosine, and tangent relationships.
Does this work for non-right triangles?
No. This page is specifically for right triangles. Non-right triangles need law of sines, law of cosines, or other triangle formulas.
Why must the hypotenuse be the longest side?
The hypotenuse is opposite the 90 degree angle and is always longer than either leg. If it is not longer, the side lengths cannot form a right triangle.