Equilateral Triangle Calculator - Area, Height, and Angles in One Step

An equilateral triangle is a triangle in which all three sides have the same length and all three interior angles measure 60 degrees. Use this calculator when you know one side length and need the area, altitude, perimeter, circumradius, inradius, centroid, and the fixed 60 degree angle without rederiving the formulas.

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

This shape is the only triangle that is also a regular polygon, so the same side length determines every other measurement: area, altitude, perimeter, circumradius, inradius, centroid, and the 60 degree interior angle. 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, the two radii give the centers and sizes of the inscribed and circumscribed circles, and the centroid gives the balance point for hanging the shape.

If you need a more general triangle tool that accepts base and height, three side lengths, or an angle, 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 altitude, perimeter, circumradius, inradius, centroid, and the 60 degree angle derived from the same a.

• a: Side length. All three sides 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), the inradius is r = a / (2 * sqrt(3)), and the centroid distance from the base is g = h / 3. 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. The interior angle is always exactly 60 degrees and the three angles always sum to 180 degrees, so those two values do not depend on the side at all.

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

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 shape 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.

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

These five ideas give you everything you need to interpret the result panel. The area, height, perimeter, both radii, and centroid all come from the same a, which is why the page reports them together, and the 60 degree interior angle is listed as a constant reference value.

To compare a 1 m version 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.
3. 3 Enter the side length: Type the value into the side length box. The page recomputes every output 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, paint, fabric, or a tile quote.
5. 5 Use the supporting outputs as needed: Take the height for stand-off distance, the perimeter for trim length, the two radii for circles, the centroid for balance, and the 60 degree angle for joint cuts.

A workshop cuts an equal-sided 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, inradius 2.3094 in, and a 60 degree interior angle.

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 one of these measurements in real work, with each benefit tied to a concrete decision.

• • One side is enough: Enter a single side length and the page returns the area, altitude, perimeter, circumradius, inradius, centroid, and the 60 degree angle in the same unit, so there is no second side 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, 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, 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, both radii, centroid, and the 60 degree angle are on the same screen, so you can plan a layout or circle template in one pass.
• • Cites the formula source: The page links to Wolfram MathWorld and Cuemath, so the result is traceable for classwork or technical documentation.

Because every equal-side 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.

If the only output you need is the area from a single side, the focused equilateral triangle area calculator returns the same area from a tighter interface.

The closed-form formulas do not hide any extra variables, but the inputs and the unit choice still affect what the numbers mean in practice.

• • The calculator is not a CAD replacement: it does not draw the triangle, accept an angle other than 60, or compute the centroid coordinates on a plane.
• • Floating point rounding means the last digit of the area can differ from a hand calculation that uses a truncated sqrt(3). The page uses the full-precision constant internally and rounds only for display.

If the result is used for code or cut lists, 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 regular triangle is the n = 3 case of a regular polygon

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