CALCULATE WITH CONFIDENCE

Triangle Geometry

Triangle Angle Calculator

Recover all three interior angles from three valid side lengths.

Triangle Geometry

Enter triangle data

Private calculation in your browser

Angles use degrees. Keep all lengths in one consistent unit and coordinates in one Cartesian system. Enter finite decimal or scientific-notation values; supported nonzero magnitudes are 1e-50 through 1e50. Inputs stay on this device.

Result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Choose the data pattern or theorem mode when the calculator offers one.
  2. Enter only the side lengths, angles, ratios, or coordinates labelled by the active mode.
  3. Read the main result first, then inspect the validated companion measurements and theorem check.

Calculation method

Apply the selected triangle relationship

A=acos((b²+c²−a²)/(2bc)), with cyclic forms for B and C.

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

Sides 3, 4, and 5 give a right angle opposite side 5.

A=acos((b²+c²−a²)/(2bc)), with cyclic forms for B and C.

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.