Can Three Sides Make a Triangle Calculator

Enter side lengths and verify triangle validity instantly. Review perimeter, area, and triangle classifications clearly. Download results, view charts, and learn each rule confidently.

Calculator Input

Side A

Side B

Side C

Unit Label

Decimal Places

Quick Example

Example Data Table

Side A	Side B	Side C	Valid Triangle	Side Type	Angle Type	Area
3	4	5	Yes	Scalene	Right	6.00
5	5	5	Yes	Equilateral	Acute	10.83
5	5	8	Yes	Isosceles	Obtuse	12.00
2	3	6	No	Not applicable	Not applicable	Not available
7	10	12	Yes	Scalene	Acute	34.98

Each row uses the same unit for all three sides.

Formula Used

1. Triangle inequality rule: Three sides form a triangle only when every pair sum is greater than the remaining side.

2. Compact validity test: Sort the sides. If smallest + middle > largest, the triangle is valid.

3. Perimeter: P = a + b + c

4. Semiperimeter: s = (a + b + c) / 2

5. Area using Heron’s formula: Area = √[s(s - a)(s - b)(s - c)]

6. Angle classification: After sorting x ≤ y ≤ z, compare x² + y² with z². Equal means right, greater means acute, and smaller means obtuse.

How to Use This Calculator

Enter the three side lengths in the input fields.
Optionally enter a unit label, such as cm or ft.
Select how many decimal places you want displayed.
Click Check Triangle to run the test.
Read the result shown above the form.
Review the inequality checks, classifications, perimeter, area, and chart.
Use the CSV or PDF buttons to export the result.

Frequently Asked Questions

1. How do I know if three sides make a triangle?

Check the triangle inequality. The sum of any two sides must be greater than the third side. If even one rule fails, the sides cannot form a triangle.

2. Why does the calculator sort the sides?

Sorting makes the main validity test faster. Once sides are ordered, only the shortest two need comparison against the longest side for the compact check.

3. Can a triangle have one side equal to the sum of two sides?

No. That creates a straight line, not a real triangle. The sum must be strictly greater, not equal, for a valid triangle.

4. What if my side lengths use decimals?

Decimal values work fine. The calculator accepts whole numbers and decimals, then applies the same triangle rules and formulas to the entered measurements.

5. When is the area shown?

Area appears only for valid triangles. Invalid side sets do not enclose a region, so Heron’s formula would not represent a real triangle area.

6. What is the difference between side type and angle type?

Side type compares lengths, such as equilateral or scalene. Angle type compares squared side relationships to determine whether the triangle is acute, right, or obtuse.

7. Do all sides need the same unit?

Yes. Use one consistent unit for all three sides. Mixing units without conversion gives incorrect validity checks, perimeter, and area values.

8. What do the CSV and PDF exports include?

They include the input sides, triangle status, core measurements, classifications, and validity margin. This makes sharing or saving the result much easier.