Math
Equilateral Triangle Calculator
Every equilateral triangle is the same shape, so one measurement fixes everything.
Enter the side, height, area, perimeter, inradius, or circumradius and this calculator returns all the others — in exact form with √3 where it belongs and as decimals — with the formulas written out.
Lengths in one unit; area in that unit squared.
Try an example
Result
Side
—
- Height
- —
- Area
- —
- Perimeter
- —
- Inradius
- —
- Circumradius
- —
Student quick launch
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Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the equilateral triangle calculator solves
An equilateral triangle has three equal sides and three 60° angles. Its height splits it into two 30-60-90 triangles, which is where the √3 in every formula comes from. The centroid, incenter, circumcenter, and orthocenter all sit at the same point, two-thirds of the way down each height.
| Side | Height | Area | Inradius | Circumradius |
|---|---|---|---|---|
| 2 | √3 ≈ 1.732 | √3 ≈ 1.732 | √3/3 ≈ 0.577 | 2√3/3 ≈ 1.155 |
| 6 | 3√3 ≈ 5.196 | 9√3 ≈ 15.59 | √3 ≈ 1.732 | 2√3 ≈ 3.464 |
| 10 | 5√3 ≈ 8.660 | 25√3 ≈ 43.30 | 5√3/3 ≈ 2.887 | 10√3/3 ≈ 5.774 |
How to use it
- Choose the measurement you know: side, height, area, perimeter, inradius, or circumradius.
- Enter its value.
- Read the side first, then height, area, perimeter, and both radii in exact and decimal form.
- Copy the formula steps if you need to show the derivation.
How to read the answer
Because √3 is A number that cannot be written as a fraction of two whole numbers, like π or √2., only one of side, height, or area can usually be a 'nice' number at a time. A whole-number side gives a height with √3 in it and an area with √3 in it. The circumradius is always exactly twice the inradius.
Common mistakes and edge cases
- Using ½·s·s for the area — the height is not s, it is s√3/2. Area = s²√3/4 ≈ 0.433·s².
- Forgetting to rationalize: 2h/√3 should be written 2h√3/3.
- Confusing inradius and circumradius. The inscribed circle is the smaller one; R = 2r.
- Negative or zero inputs are rejected — every measurement of a real triangle is positive.
Worked examples
Side 6
Height 3√3, area 9√3
Side
6
Height 3√3 ≈ 5.196
Side comes back as 6
Side
6
Area 25√3 ≈ 43.3
Side 10
Side
10
Perimeter 15
Side 5
Side
5
Inradius 2
Side 4√3
Side
4√3 (6.9282)
Circumradius 4
Side 4√3
Side
4√3 (6.9282)
Zero side
Side
—
Frequently asked questions
What is the area of an equilateral triangle?+
Area = s²√3/4, where s is the side. For s = 4 the area is 16√3/4 = 4√3 ≈ 6.93.
How do I find the height of an equilateral triangle?+
Height = s√3/2. It comes from the 30-60-90 triangle formed by the height, half the base, and one side.
How do I find the side from the area?+
Rearrange A = s²√3/4 to s = √(4A/√3). For A = 10 that gives s ≈ 4.806.
What are the inradius and circumradius?+
The inradius r = s√3/6 is the radius of the circle inside the triangle; the circumradius R = s√3/3 passes through the three corners. R is always twice r.
Are all equilateral triangles similar?+
Yes. They all have angles of 60°, so any one measurement scales the whole triangle.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026