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Equilateral Triangle Calculator

MathTriangles and Trigonometry
I know the

A length for side, height or perimeter; square units for area. Results use the same unit.

Side length a —
Area
—
Height (altitude)
—
Perimeter
—
Inradius (inscribed circle)
—
Circumradius
—
Each interior angle (degrees)
—

In an equilateral triangle all three sides are equal and every angle is 60°. From side a: height = (√3/2)a, area = (√3/4)a², perimeter = 3a. A triangle with 10 cm sides has a height of 8.6603 cm, an area of 43.3013 cm² and a perimeter of 30 cm.

About this tool

Equilateral triangles turn up in truss design, tiling, quilting patterns, signage and geometry homework, and usually you know only one number: the side, the height, the floor area or the length of trim around the edge. Pick which one you have and the calculator recovers the side length, then derives the area, altitude, perimeter, inscribed-circle radius and circumscribed-circle radius. The working lists each formula with your numbers in it. All outputs share the unit you typed in, with area in that unit squared. It assumes a perfect flat triangle; a shape whose sides differ by even a few millimetres needs a general triangle solver instead.

How to use it

  1. Choose what you know

    Select side length, height, area or perimeter.

  2. Type the value

    Enter it in any unit; results update immediately in that same unit.

  3. Read the full set

    Check the side, area, height, perimeter and both circle radii, and open the working to see each formula.

Examples

Side of 10 cm

I know the
Side length
Known value
10

Result Side length a: 10
Area: 43.3013
Height (altitude): 8.6603
Perimeter: 30
Inradius (inscribed circle): 2.8868
Circumradius: 5.7735
Each interior angle (degrees): 60

  1. Side a = 10
  2. Height h = (√3 ÷ 2) × a = 0.8660254 × 10 = 8.660254
  3. Area A = (√3 ÷ 4) × a² = 0.4330127 × 100 = 43.30127
  4. Perimeter P = 3a = 30
  5. Inradius r = a ÷ (2√3) = 2.886751; circumradius R = a ÷ √3 = 5.773503

A 10 cm side gives an area of about 43.30 cm² and a height of 8.66 cm; the circumradius is exactly twice the inradius.

Area of 100 m²

I know the
Area
Known value
100

Result Side length a: 15.1967
Area: 100
Height (altitude): 13.1607
Perimeter: 45.5901
Inradius (inscribed circle): 4.3869
Circumradius: 8.7738
Each interior angle (degrees): 60

  1. a = √(4A ÷ √3) = √(4 × 100 ÷ 1.7320508) = 15.196714
  2. Height h = (√3 ÷ 2) × a = 0.8660254 × 15.196714 = 13.16074
  3. Area A = (√3 ÷ 4) × a² = 0.4330127 × 230.940108 = 100
  4. Perimeter P = 3a = 45.590141
  5. Inradius r = a ÷ (2√3) = 4.386913; circumradius R = a ÷ √3 = 8.773827

Working backwards, a triangle covering 100 m² needs sides of about 15.20 m, so roughly 45.59 m of edging.

Height of 10 in

I know the
Height
Known value
10

Result Side length a: 11.547
Area: 57.735
Height (altitude): 10
Perimeter: 34.641
Inradius (inscribed circle): 3.3333
Circumradius: 6.6667
Each interior angle (degrees): 60

  1. a = 2h ÷ √3 = 2 × 10 ÷ 1.7320508 = 11.547005
  2. Height h = (√3 ÷ 2) × a = 0.8660254 × 11.547005 = 10
  3. Area A = (√3 ÷ 4) × a² = 0.4330127 × 133.333333 = 57.735027
  4. Perimeter P = 3a = 34.641016
  5. Inradius r = a ÷ (2√3) = 3.333333; circumradius R = a ÷ √3 = 6.666667

A 10 in altitude means each side is 20 ÷ √3, about 11.55 in.

How it is calculated

h = (√3 ÷ 2)·a; A = (√3 ÷ 4)·a²; P = 3a; r = a ÷ (2√3); R = a ÷ √3

a
length of each side
h
height, from a vertex perpendicular to the opposite side
A
area
P
perimeter
r, R
radii of the inscribed and circumscribed circles

The height splits the triangle into two 30-60-90 right triangles, so by Pythagoras h² = a² − (a/2)², giving h = (√3/2)a. Area is half base times height. If you start from the height, area or perimeter, the tool first inverts the matching formula to get a, then computes the rest. The centroid sits two thirds down the altitude, which is why R = 2r.

When not to use it

  • If the three sides are not all equal, use a general or isosceles triangle calculator.
  • For triangles drawn on a sphere or a curved surface, flat-plane formulas do not hold.

Common mistakes

  • Entering a slanted side as the height; the height is the perpendicular drop, about 86.6% of the side.
  • Mixing units, such as a side in centimetres read as an area in square metres.

Frequently asked questions

Why is every angle 60 degrees?

The angles of any flat triangle add to 180°. Equal sides force equal opposite angles, so each one is 180 ÷ 3 = 60°.

How do I get the side from the area?

Rearrange A = (√3/4)a² to a = √(4A ÷ √3). For an area of 100 m², that is √(400 ÷ 1.7320508), about 15.1967 m.

What is the relationship between the inradius and circumradius?

In an equilateral triangle the centres of both circles coincide at the centroid, which lies one third of the way up the height. The inradius is h/3 and the circumradius is 2h/3, so the circumradius is always exactly twice the inradius.

Can I use feet, inches or metres?

Yes. The formulas do not depend on the unit. Whatever length unit you enter comes back for the side, height, perimeter and radii, and the area is in that unit squared.

How does the height compare with the side?

The height is √3/2 of the side, about 0.866. A triangle with 1 m sides is about 86.6 cm tall, which is useful when checking whether a triangular panel fits a given space.

Is an equilateral triangle also isosceles?

Under the usual definition, an isosceles triangle has at least two equal sides, so an equilateral triangle qualifies as a special case. Its formulas are simpler because all three sides and angles match.

Cite this tool

Using this tool in an assignment, article or report? Copy a citation, or a link for your website.

APA

Tools Directory Editorial Team. (2026, October 13). Equilateral Triangle Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/triangles-and-trigonometry/equilateral-triangle-calculator/

MLA

Tools Directory Editorial Team. “Equilateral Triangle Calculator.” Tools Directory, 13 Oct. 2026, https://tools.milunir.com/math/triangles-and-trigonometry/equilateral-triangle-calculator/. Accessed 26 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Equilateral Triangle Calculator.” Tools Directory. Last modified October 13, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/triangles-and-trigonometry/equilateral-triangle-calculator/.

Link<a href="https://tools.milunir.com/math/triangles-and-trigonometry/equilateral-triangle-calculator/">Equilateral Triangle Calculator – Tools Directory</a>