Answer first
What this calculator tells you
Calculate the area, height, perimeter and inscribed circle radius of an equilateral triangle from its side. Find every measurement of a triangle whose three sides match from one length. Formula: Area = √3 ÷ 4 × s²; height = √3 ÷ 2 × s; perimeter = 3s; inradius = s ÷ (2√3). At the worked-example inputs, the area is 15.6. Holding every other input steady, moving side length (s) from 4.8 to 7.2 moves the result from 10 to 22.4.
Transparent method
The formula
Find every measurement of a triangle whose three sides match from one length.
Worked example
Example inputs
How to interpret the result
An equilateral triangle has three equal sides and three 60 degree angles, so a single length fixes every other measurement. A side of 6 gives an area of about 15.59, a height of about 5.2, a perimeter of 18 and an inscribed circle radius of about 1.73. The height is not the side. It is about 87 percent of it, because the peak sits above the middle of the base.
At the worked-example inputs the area is 15.6. It rises with side length (s).
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Verify that all three sides match. If two match and the third differs, the triangle is isosceles and the height comes out different.
The common error
Where people go wrong with equilateral triangle calculator
Using the side as the height in the area formula. That overstates the area, since the true height is shorter than the slanted side.
Sensitivity evidence
How side length (s) changes the area
Holding every other input at the worked-example value, moving side length (s) from 4.8 to 7.2 moves the area from 10 to 22.4: a spread of 12.5, or 80% of the worked-example result.
| Side length (s) | Area | Height | Perimeter | Inscribed circle radius |
|---|---|---|---|---|
| 4.8 | 10 | 4.2 | 14.4 | 1.4 |
| 5.4 | 12.6 | 4.7 | 16.2 | 1.6 |
| 6worked example | 15.6 | 5.2 | 18 | 1.7 |
| 6.6 | 18.9 | 5.7 | 19.8 | 1.9 |
| 7.2 | 22.4 | 6.2 | 21.6 | 2.1 |
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Side length (s) | 6 | Enter the side length (s) used in this calculation. |
| Area | 15.6 | |
| Height | 5.2 | |
| Perimeter | 18 | |
| Inscribed circle radius | 1.7 | |
Inputs, definitions and assumptions
Side length (s)
Enter the side length (s) used in this calculation. The prefilled worked-example value is 6.
How to use this calculator
- 1Verify the inputs. Gather side length (s) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the area at 15.6. Store your own version of it as Scenario A.
- 3Test one change. Start with side length (s), the input with the biggest effect here: moving side length (s) from 5.4 to 6.6 takes the area from 12.6 to 18.9, a swing of 40% of the worked-example figure.
- 4Check the extremes. At half the example side length (s) (3) the area is 3.9; at double (12) it is 62.4.
People also ask
Frequently asked questions
How do you calculate equilateral triangle?
Area = √3 ÷ 4 × s²; height = √3 ÷ 2 × s; perimeter = 3s; inradius = s ÷ (2√3). At the worked-example inputs the area is 15.6.
What does the equilateral triangle result mean?
Find every measurement of a triangle whose three sides match from one length. At the worked-example inputs the area is 15.6. It rises with side length (s).
How much does side length (s) change the area?
Holding every other input at the worked-example value, moving side length (s) from 4.8 to 7.2 moves the area from 10 to 22.4, a spread of 12.5.
What are the limits of this equilateral triangle calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test side length (s) only from 4.8 to 7.2; a value outside that range is not tabulated here.
If I double side length (s) in the equilateral triangle calculator, does the area double?
Doubling it from 6 to 12 takes the area from 15.6 to 62.4, which is 4.00 times the worked-example figure. So the result grows faster than the input does. Halving it to 3 gives 3.9.
Which inputs change the height in the equilateral triangle calculator?
At the worked-example inputs it is 5.2. Side length (s) takes it from 4.7 to 5.7.
Which inputs change the perimeter in the equilateral triangle calculator?
At the worked-example inputs it is 18. Side length (s) takes it from 16.2 to 19.8.
Which inputs change the inscribed circle radius in the equilateral triangle calculator?
At the worked-example inputs it is 1.7. Side length (s) takes it from 1.6 to 1.9.
Does Heron's formula work for any triangle?
Yes, for any triangle where the three side lengths actually form a valid triangle: meaning any two sides together are longer than the third. If that condition fails, the formula produces a negative number under the square root, which is the calculator's signal that the three lengths cannot form a real triangle.
Sources and evidence
Free Calculators Online is independent and is not affiliated with or endorsed by the source organizations. Educational estimates only.