Math

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Triangle Inequality Calculator.

Check whether three lengths can form a non-degenerate triangle.

On-device calculationNo signup
01

Set your values

Results update as you type.

sideA: 3

sideA

0.000000
sideB: 4

sideB

0.000000
sideC: 5

sideC

0.000000
Valid triangle?: true

Valid triangle?

true
a + b − c: 2

a + b − c

0.000000
a + c − b: 4

a + c − b

0.000000
b + c − a: 6

b + c − a

0.000000

Results update automatically as you type.

Use Cases

Verify triangle feasibility

Before constructing a triangle or solving geometry problems, quickly confirm that given side lengths satisfy the triangle inequality.

Example: Check if sides 3, 4, 5 form a triangle (they do).

Educational practice

Students learning geometry can use this tool to test various side combinations and understand the triangle inequality theorem.

Example: Test sides 1, 2, 3 to see they do not form a triangle.

Frequently Asked Questions

What is the triangle inequality theorem?
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. This must hold for all three combinations of sides.
How does this calculator determine if sides form a triangle?
This calculator checks the strict triangle inequality: it verifies that a + b > c, a + c > b, and b + c > a. If all three conditions are true, the sides can form a triangle; otherwise, they cannot.
What does 'strict' mean in strict triangle inequality?
Strict means the sum of two sides must be strictly greater than the third side, not equal. If the sum equals the third side, the sides are degenerate (collinear) and do not form a proper triangle.

Tips & Common Mistakes

Tips

  • Enter all three side lengths in the same unit (e.g., all in centimeters) for consistent results.
  • Remember that the order of sides does not matter; the calculator checks all three conditions.
  • Use positive numbers only; zero or negative lengths cannot form a triangle.
  • If you're unsure about a set of lengths, this calculator gives an immediate yes/no answer.

Common Mistakes to Avoid

  • Forgetting to check all three conditions: a+b>c, a+c>b, and b+c>a.
  • Using equal sums (e.g., 2, 3, 5) which do not form a strict triangle.
  • Entering side lengths in different units without converting, leading to incorrect comparisons.

Last updated: August 13, 2026