Calculator Input
Example Data Table
| Given Side | Perimeter | Height | Area | Inradius | Circumradius |
|---|---|---|---|---|---|
| 3.00 u | 9.00 u | 2.60 u | 3.90 u² | 0.87 u | 1.73 u |
| 5.00 u | 15.00 u | 4.33 u | 10.83 u² | 1.44 u | 2.89 u |
| 8.00 u | 24.00 u | 6.93 u | 27.71 u² | 2.31 u | 4.62 u |
| 12.00 u | 36.00 u | 10.39 u | 62.35 u² | 3.46 u | 6.93 u |
These sample rows show how one side value determines every other equilateral triangle measurement.
Formula Used
Perimeter = 3a
Semiperimeter = 3a / 2
Height = (√3 / 2)a
Area = (√3 / 4)a²
Inradius = (√3 / 6)a
Circumradius = a / √3
From perimeter: a = P / 3
From height: a = 2h / √3
From area: a = √(4A / √3)
From inradius: a = 2√3r
From circumradius: a = √3R
Because all sides are equal and all internal angles are 60°, solving one valid measure is enough to reconstruct the entire equilateral triangle.
How to Use This Calculator
- Choose the known quantity, such as side, area, height, or radius.
- Enter a positive numeric value.
- Select the desired unit or choose unitless for pure geometry problems.
- Set the number of decimal places for the output.
- Press Calculate Triangle to show the results above the form.
- Review the solved measures, graph, and formula path.
- Use the CSV or PDF buttons to export the result summary.
FAQs
1) What value should I enter first?
Enter any one known equilateral triangle measure that you trust most. Side, perimeter, height, area, inradius, and circumradius all work.
2) Can I calculate everything from the area alone?
Yes. The solver converts the area back into side length using the equilateral area formula, then derives every remaining measurement.
3) What is the difference between inradius and circumradius?
The inradius reaches from the center to a side. The circumradius reaches from the center to a vertex. In an equilateral triangle, the circumradius is twice the inradius.
4) Are the three angles always 60 degrees?
Yes. An equilateral triangle always has three equal sides and three equal internal angles, so each angle must be 60 degrees.
5) Why are the height and median equal here?
In an equilateral triangle, symmetry makes the altitude, median, angle bisector, and perpendicular bisector from the same vertex overlap on one line.
6) Does changing the unit affect the geometry?
No. The underlying ratios stay the same. The selected unit only changes how the outputs are labeled and interpreted.
7) Can I use decimal values?
Yes. Decimal inputs are fully supported, and you can choose the number of decimal places displayed in the final answers.
8) Is this calculator suitable for technical work?
It is useful for quick checking, planning, and learning. For fabrication, construction, or regulated design, verify dimensions with your project standards.