Right Triangle Calculator with Full Geometry
Solve a right triangle from two legs, a leg and hypotenuse, a hypotenuse and angle, or a leg and adjacent angle. The calculator reports every side, both acute angles and derived geometric measures.
Known measurements
Solved triangle
right triangle calculator: formulas, interpretation and worked use
This right triangle calculator handles multiple valid input configurations and checks that a hypotenuse is longer than a known leg. It also reports area and circle-related geometry.
Transparent calculation steps
The right triangle calculator displays the intermediate values used in the result so users can audit the calculation rather than receiving an unexplained answer.
Input validation and edge cases
Impossible, incomplete and non-finite inputs are rejected with a specific message. Boundary cases are handled explicitly instead of being silently rounded into a misleading result.
Units and precision
Where units apply, inputs are converted to a consistent internal basis before the formula is evaluated. Results retain enough precision for checking and are then formatted for practical reading.
Worked interpretation
The result panel separates the primary answer, supporting quantities and a formula trace. This makes the calculator suitable for checking homework, planning scenarios and comparing alternatives.
Choosing the correct mode
Match the selected mode to the measurements you actually know. Values in unused fields are ignored so they cannot contaminate the solution.
Independent identity check
The displayed residual a² + b² − c² should be near zero, providing a direct numerical verification of the solved sides.
Solving a right triangle from independent inputs
The right triangle calculator solves the remaining sides and acute angles from two independent known values, including two sides or one side and one acute angle. It applies the Pythagorean theorem for side relationships and sine, cosine or tangent for angle-side combinations. The hypotenuse is always opposite the 90-degree angle and must be longer than either leg.
Consistency and geometric outputs
The right triangle calculator also derives area, perimeter, altitude to the hypotenuse, inradius and circumradius from the solved geometry. An entered acute angle must lie strictly between 0° and 90°. If two entered values are mathematically incompatible, the calculator rejects the set rather than averaging conflicting information. Keep all side lengths in one unit; perimeter uses that unit, while area uses its square. Rounded displays may not reproduce the exact Pythagorean equality when manually re-entered.
Which angle is A?
Angle A is opposite side a and adjacent to side b.
What if the hypotenuse is not the longest side?
The calculator rejects that input because it cannot form a right triangle.
What additional measures are included?
Area, perimeter, altitude to the hypotenuse, inradius and circumradius are reported.