Not every three lengths make a triangle: if one stick is longer than the other two together, they cannot meet. The triangle inequality is the rule, and it also says that a straight line is the shortest path between two points.
How to use the Triangle Inequality Calculator
- Side a
- Side b
- Side c
Results update as you type, and everything is calculated in your browser.
How it works
Enter three lengths. The calculator tests the three inequalities, reports any that fail and gives the allowed range for side c. Equality means a degenerate (flat) triangle.
Inputs explained
| Field | What to enter |
|---|---|
| Side a | Units: cm, m, mm, in, ft, yd … |
| Side b | Units: cm, m, mm, in, ft, yd … |
| Side c | Units: cm, m, mm, in, ft, yd … |
What each result means
- Side c must be greater than = abs([Side a] – [Side b])
- Side c must be less than = [Side a] + [Side b]
Formula
a + b > c, a + c > b, b + c > a ⇔ |a − b| < c < a + b
Worked example
Inputs — Side a: 4 cm; Side b: 6 cm; Side c: 9 cm.
Results — Can these sides form a triangle? = Yes; a + b > c = Holds; a + c > b = Holds; b + c > a = Holds; Side c must be greater than = 2 cm; Side c must be less than = 10 cm.
Key terms
- Degenerate triangle
- Three collinear points – a triangle with zero area.
Frequently asked questions
Can 2, 3 and 6 form a triangle?
No – 2 + 3 < 6.
What if a + b = c exactly?
The "triangle" is flat (degenerate) with zero area.
Why is it called an inequality?
It is a "greater than" condition, not an equation.
Does it hold in higher dimensions?
Yes – for any distance: |x + y| ≤ |x| + |y|.