Triangle Inequality Calculator — Can These Sides Form a Triangle?
Enter three side lengths and instantly find out whether they can form a triangle. The calculator checks all three conditions of the triangle inequality theorem and shows the margin of validity.
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Longest side
max(5, 7, 9) = 9 - 2
Sum of two shorter sides
5 + 7 = 12 - 3
Margin (sum − longest)
12 − 9 = 3A positive margin confirms the triangle inequality: the two shorter sides together exceed the longest.
How does this calculator work?
Three sides form a valid triangle if and only if a + b > c, a + c > b, and b + c > a. In practice, just verify that the sum of the two shorter sides exceeds the longest. Enter the three lengths to get an instant pass/fail and the margin of validity.
Formula
How this is calculated
The Triangle Inequality Theorem states that a valid (non-degenerate) triangle exists if and only if the sum of any two sides is strictly greater than the third side. There are three conditions to check — a + b > c, a + c > b, and b + c > a — and all three must hold simultaneously.
In practice, only the most demanding condition matters: if the sum of the two shorter sides exceeds the longest side, the other two inequalities are automatically satisfied. The "margin" (sum of the two shorter sides minus the longest side) tells you by how much the constraint is met or missed. A margin of zero corresponds to a degenerate triangle with zero area (three points on a straight line), and a negative margin means no triangle can exist.
This theorem applies to all triangles regardless of type — scalene, isosceles, equilateral, right, obtuse or acute. Knowing whether a set of lengths forms a valid triangle is the first sanity-check before any further computation such as area, angles, or altitudes.
Frequently asked questions
In principle yes, but in practice only one check is decisive: the sum of the two smaller sides must exceed the largest side. If that holds, the other two inequalities hold automatically. The calculator shows all three for completeness.
A margin of exactly zero means the three points are collinear — they form a degenerate "triangle" with zero area. Real applications require a strictly positive margin, so this case is treated as invalid.
Yes — the inequality is dimensionless; the same rule applies whether the sides are in millimetres, metres or light-years. Just ensure all three values use the same unit.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Inequality Calculator — Can These Sides Form a Triangle? [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-inequality-calculator
TG we-Calculate Editorial Team. "Triangle Inequality Calculator — Can These Sides Form a Triangle?." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-inequality-calculator.
TG we-Calculate Editorial Team, "Triangle Inequality Calculator — Can These Sides Form a Triangle?," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-inequality-calculator
@misc{wecalculate_triangle_inequality_calculator, title = {Triangle Inequality Calculator — Can These Sides Form a Triangle?}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-inequality-calculator}}, year = {2026}, note = {TG we-Calculate} }
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