Triangle Inequality Calculator

Test side lengths with accurate geometry checks. Review sums, gaps, type, perimeter, and area instantly. Make stronger triangle decisions for study, design, and analysis.

Calculator Inputs

Enter three side lengths to test the triangle inequality rule.

Example Data Table

Case Side A Side B Side C Status Type
Example 1345ValidScalene
Example 2666ValidEquilateral
Example 3558ValidIsosceles
Example 4236InvalidNot a triangle

Formula Used

Triangle inequality rule: For sides a, b, and c, each pair sum must be greater than the remaining side.

a + b > c

a + c > b

b + c > a

Difference form: The absolute difference between any two sides must stay below the third side.

|a - b| < c, |a - c| < b, |b - c| < a

Area after validation: Heron's formula estimates the enclosed area.

s = (a + b + c) / 2, Area = sqrt[s(s-a)(s-b)(s-c)]

How to Use This Calculator

  1. Enter the three side lengths in the input fields.
  2. Select either quick checking or detailed analysis mode.
  3. Choose the decimal precision for displayed output values.
  4. Enable step details if you want comparison statements.
  5. Press Calculate to view the result above the form.
  6. Review the inequality table, metrics, and chart.
  7. Use the CSV or PDF buttons to export the output.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.