Calculator Inputs
Plotly Triangle Graph
The chart below draws the triangle from your side lengths. It helps you visually inspect shape, scale, and triangle validity.
Example Data Table
| Example | Side A | Side B | Side C | Semi-perimeter | Area | Triangle Type |
|---|---|---|---|---|---|---|
| Classic right triangle | 3 | 4 | 5 | 6 | 6 | Scalene / Right |
| Scaled 3-4-5 triangle | 6 | 8 | 10 | 12 | 24 | Scalene / Right |
| General valid triangle | 7 | 8 | 9 | 12 | 26.8328 | Scalene / Acute |
Formula Used
Heron’s Formula:
s = (a + b + c) / 2
Area = √[ s(s - a)(s - b)(s - c) ]
Perimeter = a + b + c
Inradius = Area / s
Circumradius = abc / (4 × Area)
This method finds triangle area using only side lengths. It avoids direct height input and is especially useful when all three sides are known.
How to Use This Calculator
- Enter the three side lengths of your triangle.
- Add a preferred unit label, such as cm, m, or ft.
- Choose the number of decimal places you want.
- Click the calculate button to generate results.
- Review area, perimeter, radii, altitudes, angles, and triangle type.
- Use the CSV or PDF buttons to export the output.
- Inspect the Plotly graph to visually confirm the triangle shape.
Frequently Asked Questions
1. What does Heron’s formula calculate?
Heron’s formula calculates the area of a triangle when you know all three side lengths. It first finds the semi-perimeter and then uses it to compute area without needing height.
2. Do the three sides need special units?
No. All three sides only need the same unit. You can use centimeters, meters, feet, inches, or any consistent unit, and the area will appear in squared units.
3. Why does triangle inequality matter?
Triangle inequality confirms that the three sides can actually form a triangle. If one side is too long compared with the other two, the shape is impossible, so the formula cannot be applied.
4. Can this calculator classify the triangle?
Yes. It identifies side-based classification such as scalene, isosceles, or equilateral, and angle-based classification such as acute, right, or obtuse using side relationships and computed angles.
5. What is the semi-perimeter?
The semi-perimeter is half of the triangle’s perimeter. It is written as s = (a + b + c) / 2 and is the first value needed in Heron’s area formula.
6. Does the calculator show only area?
No. It also shows perimeter, semi-perimeter, inradius, circumradius, altitudes, internal angles, and triangle classification. This makes it useful for geometry checks and report-ready outputs.
7. When should I use Heron’s formula?
Use it when you know all three sides but do not know the height. It is ideal for surveying, geometry exercises, construction layouts, and triangle verification tasks.
8. Can I export the result?
Yes. After a valid calculation, you can export the results as CSV for spreadsheets or PDF for reports, records, coursework, or client-facing documentation.