Triangle Inequality Calculator
Check whether three given side lengths can form a valid triangle using the triangle inequality theorem. Enter three lengths to verify all three conditions (a+b>c, a+c>b, b+c>a) and determine if a valid triangle exists, essential for geometry validation.
This free online triangle inequality calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Minimum: 0.01
Length of the first side
Minimum: 0.01
Length of the second side
Minimum: 0.01
Length of the third side
Results
Valid Triangle (1 = Yes, 0 = No)
1
Perimeter (if valid)
22
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Triangle Inequality Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Triangle Inequality Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Triangle Inequality Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
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About Triangle Inequality Calculator
The Triangle Inequality Calculator checks whether three given side lengths can form a valid triangle. The triangle inequality theorem states that the sum of any two sides must be greater than the third side. All three conditions (a+b>c, a+c>b, and b+c>a) must hold simultaneously. This is a fundamental result in Euclidean geometry with applications in distance verification, network routing (triangle inequality in metric spaces), computer graphics (mesh validation), and structural engineering (ensuring valid triangular bracing). The calculator returns 1 for valid triangles and 0 for invalid combinations, along with the perimeter when valid.
The Math Behind It
Formula Reference
Triangle Inequality Theorem
a + b > c, a + c > b, b + c > a (all three must hold)
Variables: a, b, c = side lengths of the triangle
Worked Examples
Example 1: Valid Triangle: 5, 7, 10
Check if sides 5, 7, and 10 can form a triangle.
Yes, sides 5, 7, 10 form a valid triangle with perimeter 22.
Example 2: Invalid Triangle: 1, 2, 5
Check if sides 1, 2, and 5 can form a triangle.
No, sides 1, 2, 5 cannot form a triangle.
Common Mistakes & Tips
- !Checking only one condition instead of all three. All three inequalities must hold: a+b>c AND a+c>b AND b+c>a.
- !Using >= instead of >. The strict inequality > is needed for a proper (non-degenerate) triangle. When a+b=c, the three points are collinear.
- !Confusing the triangle inequality with conditions for specific triangle types. This theorem applies to ALL triangles, not just specific types.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
What happens when a + b = c exactly?
This is the degenerate case: the three points are collinear (lie on a straight line) and form a 'triangle' with zero area. Mathematically, this is not considered a proper triangle.
Do I need to check all three conditions?
Technically, you only need to check that the sum of the two shortest sides exceeds the longest side. If a <= b <= c, then a + b > c is sufficient because the other two conditions automatically hold. But checking all three is safer and avoids sorting errors.
Does the triangle inequality apply to non-Euclidean geometry?
Yes, with modifications. In spherical geometry, a reversed triangle inequality can hold for large triangles. In hyperbolic geometry, the inequality is always strict. The triangle inequality axiom is part of the general definition of a metric space.
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