Quick guide
How to use this calculator
- Choose the data pattern or theorem mode when the calculator offers one.
- Enter only the side lengths, angles, ratios, or coordinates labelled by the active mode.
- Read the main result first, then inspect the validated companion measurements and theorem check.
Calculation method
Apply the selected triangle relationship
r=K/s; tangent segments adjacent to a vertex equal s minus its opposite side.
The engine rejects degenerate triangles, impossible angle sums, failed strict inequalities, undefined ratios, and inconsistent theorem data before returning a result.
Worked example
Worked example
A 3-4-5 triangle has inradius 1.
r=K/s; tangent segments adjacent to a vertex equal s minus its opposite side.
Supported inputs
Precision and limits
Units
Use one consistent length unit. Areas are reported in the square of that unit; angles are in degrees; coordinate tools use the entered Cartesian coordinate system.
Numeric range
Nonzero entered magnitudes must lie from 1e-50 through 1e50. Integer generators and exploratory modes also disclose tighter per-field limits.
Geometry
Ordinary triangle pages require a non-degenerate Euclidean triangle. The strict triangle inequalities and an interior-angle sum of 180° govern accepted data. Coordinate pages also reject vertex triples whose cross product is indistinguishable from zero at double-precision scale.
Precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Coordinate-center tools also report offsets from vertex A; use those offsets when a very large coordinate translation rounds distinct absolute centers to the same displayed coordinate. The Pythagorean page retains a simple exact integer radical when the squared data make that representation available.