CALCULATE WITH CONFIDENCE

Triangle Geometry

Right Triangle Calculator

Solve every side, acute angle, area, perimeter, and hypotenuse altitude from two independent measures.

Triangle Geometry

Enter triangle data

Private calculation in your browser
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

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.

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Understand the subject

What is Right Triangle?

Triangle geometry connects side lengths, angles, centers, and special lines inside one three-sided figure.

Use it to identify which side, angle, center, or theorem relationship the entered measurements support.

The relationship

Write the rule before calculating

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

Legs 3 and 4 give hypotenuse 5, area 6, and altitude 2.4.

Interpret with care

Important boundary

A triangle must satisfy its inequality and its known measurements may allow no solution, one solution, or an ambiguous pair of solutions.

Use the Mathematics collection to move between connected concepts without duplicating the calculation.

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

a²+b²=c²; A=asin(a/c); K=ab/2; h_c=ab/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

Legs 3 and 4 give hypotenuse 5, area 6, and altitude 2.4.

a²+b²=c²; A=asin(a/c); K=ab/2; h_c=ab/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.