Equilateral Triangle Area - Side, Height, and Both Radii

The equilateral triangle area is the two-dimensional space enclosed by a triangle whose three sides are the same length and whose three interior angles each measure 60 degrees. Use this equilateral triangle area calculator when you know one side length and need the area, altitude, perimeter, or the radii of the inscribed and circumscribed circles without rederiving the formula.

• • Geometry homework and classwork: Plug in a side length from a textbook problem to verify a hand calculation, then check the height and both radii against an answer key.
• • Roofing, decking, and fabric estimates: Estimate the surface area of an equilateral triangular panel, sail, gusset, or tent face when the supplier quotes by the square unit.
• • Tile, glass, and sheet material cuts: Compare two equilateral triangle dimensions to find the area each will cover, including the leftover scrap along each side.
• • Design and craft layouts: Plan quilts, signs, lighting diffusers, and stained-glass pieces where an equilateral triangle is the chosen base shape.

An equilateral triangle is the only triangle that is also a regular polygon, so the same side length determines every other measurement: area, altitude, perimeter, circumradius, and inradius. The three angles are always 60 degrees, so there is no second side or angle to measure.

In practical work, the area gives the surface to cover, the height gives the rise, the perimeter gives the trim length, and the two radii give the centers and sizes of the inscribed and circumscribed circles.

If you need a more general triangle tool that accepts base and height, or three side lengths, the triangle calculator covers scalene and isosceles triangles with the same unit system.

The calculator uses the closed-form formula A = (sqrt(3) / 4) * a^2, where a is the side length you enter. It also reports the height, perimeter, and the two radii derived from the same a so you do not have to compute them by hand.

• a: Side length. The three sides of an equilateral triangle are equal, so one value drives every result on this page.

Every other value on the page comes from a. The height is h = (sqrt(3) / 2) * a, the perimeter is P = 3a, the circumradius is R = a / sqrt(3), and the inradius is r = a / (2 * sqrt(3)). The result panel updates each time you change the side or the unit selector, and the area unit always matches the length unit.

The page computes sqrt(3) at full floating point precision and rounds only for display, so the last digit of the area reflects the formula rather than a truncated estimate.

According to Wolfram MathWorld, the area of an equilateral triangle with side a is (sqrt(3) / 4) * a^2 and its altitude is (sqrt(3) / 2) * a

According to Cuemath, an equilateral triangle with side 4 units has an area of 4 * sqrt(3) square units, and the area formula is (sqrt(3) / 4) * a^2

For users who need the area of a general triangle from base and height, the area calculator in the same math category handles rectangles, circles, triangles, and other common shapes with the same unit system.

Four ideas show up every time you work with this shape, and understanding each one makes the formula and the output panel easier to read.

These four ideas give you everything you need to interpret the result panel. The area, height, perimeter, and two radii all come from the same a, which is why the page reports them together.

To compare a 1 m equilateral triangle to a 1 ft one, the area converter handles the unit math without you squaring the conversion factor by hand.

Run the calculator in five short steps, then read the result panel for the value you actually need.

1. 1 Measure or look up one side length: Find a on the triangle. It is the same as the other two sides by definition, so any side measurement is enough to start the calculation.
2. 2 Pick the unit you measured in: Choose centimeters, meters, inches, or feet. The result panel will switch to the matching square unit so you do not have to convert later.
3. 3 Enter the side length: Type the value into the side length box. The page recomputes the area, height, perimeter, and both radii as you type, so the result is always in sync with the form.
4. 4 Read the area result first: The large area tile shows the enclosed space. It is the value you need for coverage, materials, paint, fabric, or a tile quote.
5. 5 Use the supporting outputs as needed: Take the height for layouts or stand-off distance, the perimeter for trim or edge length, and the two radii for the inscribed and circumscribed circles.

A workshop cuts an equilateral triangular gusset with 8 inch sides for a prototype jig. The operator enters side 8, unit inches, and reads area 27.7128 in^2, height 6.9282 in, perimeter 24 in, circumradius 4.6188 in, and inradius 2.3094 in.

The same shape can be checked against a regular n-sided panel by switching to a polygon area workflow with the polygon area calculator.

The page is built for the way people actually use an equilateral triangle measurement in real work, with each benefit tied to a concrete decision or workflow.

• • One side is enough: Enter a single side length and the page returns the area, altitude, perimeter, circumradius, and inradius in the same unit, so there is no second side or angle to measure to get a complete answer.
• • Works in four common length units: Centimeters, meters, inches, and feet cover most craft, school, construction, and engineering tasks without manual unit conversion, and the area output is labeled with the matching square unit.
• • No setup or sign-in: Type the side, read the answer. There are no account walls, ads in the result, or required form fields, and the reset button restores the default 6 m example when you want to start over.
• • Shows the supporting values, not only the area: Height, perimeter, and both radii are on the same screen, so you can plan a layout, a circle template, or a frame in one pass without bouncing between tools.
• • Cites the formula source: The page links to a Wolfram MathWorld reference and a Cuemath worked-example reference, so the result is traceable for classwork or technical documentation.

Because every equilateral triangle is similar to every other, the same one-input workflow handles a 1 cm paper cut-out, a 50 m surveying marker, and a 1,000 ft plot boundary, and the result panel lets you copy values straight into a cut list or a report.

When the design moves to six equal sides for tiling or honeycomb layouts, the same n-sided regular polygon idea extends with the hexagon calculator.

The closed-form formula does not have hidden variables, but the inputs and the unit choice still affect what the number means in practice.

• • The calculator is not a CAD replacement: it does not draw the triangle, accept decimal degrees for an angle, or compute the centroid, and it cannot verify that the shape you measured is truly equilateral in the field.
• • Floating point rounding means the last digit of the area can differ from a hand calculation that uses a truncated value of sqrt(3). The page uses the full-precision constant internally and rounds only for display.

If the result is used for code, cut lists, or classwork, keep the unrounded value until the final step. If it is used in casual conversation, the rounded area on the panel is the right number to share.

According to OpenStax Elementary Geometry, the area of a regular polygon with apothem a and perimeter P is A = (1/2) * a * P, and the equilateral triangle is the n = 3 case of a regular polygon

If the shape is even slightly scalene or isosceles, the formula no longer applies, and the right triangle calculator or a general triangle calculator is the right tool.