Pythagorean Theorem Calculator with Angles and Area
Enter any two sides of a right triangle and leave the unknown side blank. The calculator solves the missing side, checks that the hypotenuse is valid, and reports both acute angles, area, perimeter, altitude to the hypotenuse, inradius and circumradius.
Right-triangle sides
Solved right-triangle measures
Pythagorean theorem and right-triangle guide
This Pythagorean theorem calculator provides a dedicated calculation workflow rather than a generic converter. The Pythagorean theorem solves a side only when the triangle contains a right angle. The hypotenuse must be the longest side.
Solving the hypotenuse
When both legs are known, c = √(a² + b²). The positive root is used because a geometric length cannot be negative.
Solving a missing leg
When c and one leg are known, the other leg is √(c² − known leg²). If the hypotenuse is not larger than the known leg, no real right triangle exists.
Angles and inverse trigonometry
The two acute angles are calculated from the solved side ratios using arctangent. They should sum to 90° apart from displayed rounding.
Area, perimeter and radii
Area is ab/2, perimeter is a+b+c, altitude to c is ab/c, inradius is (a+b−c)/2, and circumradius is c/2.
Numerical verification
The output reports the residual a²+b²−c². A value near zero confirms that the displayed sides satisfy the theorem within floating-point precision.
Which side is c?
c is the hypotenuse, the longest side and the side opposite the right angle.
Can I enter all three sides?
Yes. The calculator verifies whether they satisfy the right-triangle relation instead of solving a missing value.
Why is there no solution for some inputs?
If c is not longer than either leg, the square root for the missing leg is negative and no real right triangle exists.
Pythagorean Theorem Calculator with Angles and Area
Enter any two sides of a right triangle and leave the unknown side blank. The calculator solves the missing side, checks that the hypotenuse is valid, and reports both acute angles, area, perimeter, altitude to the hypotenuse, inradius and circumradius.
Right-triangle sides
Solved right-triangle measures
Pythagorean theorem and right-triangle guide
This Pythagorean theorem calculator provides a dedicated calculation workflow rather than a generic converter. The Pythagorean theorem solves a side only when the triangle contains a right angle. The hypotenuse must be the longest side.
Solving the hypotenuse
When both legs are known, c = √(a² + b²). The positive root is used because a geometric length cannot be negative.
Solving a missing leg
When c and one leg are known, the other leg is √(c² − known leg²). If the hypotenuse is not larger than the known leg, no real right triangle exists.
Angles and inverse trigonometry
The two acute angles are calculated from the solved side ratios using arctangent. They should sum to 90° apart from displayed rounding.
Area, perimeter and radii
Area is ab/2, perimeter is a+b+c, altitude to c is ab/c, inradius is (a+b−c)/2, and circumradius is c/2.
Numerical verification
The output reports the residual a²+b²−c². A value near zero confirms that the displayed sides satisfy the theorem within floating-point precision.
Which side is c?
c is the hypotenuse, the longest side and the side opposite the right angle.
Can I enter all three sides?
Yes. The calculator verifies whether they satisfy the right-triangle relation instead of solving a missing value.
Why is there no solution for some inputs?
If c is not longer than either leg, the square root for the missing leg is negative and no real right triangle exists.