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Enter the side length or height to instantly calculate the area of an equilateral triangle. Highly accurate results, perfect for students, teachers, and designers.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
This calculator is for an equilateral triangle, whose three sides have equal length. Enter one side length, a, to get area, perpendicular height, and perimeter. It does not take height as an input or solve a general triangle from unrelated measurements.
Area measures the two-dimensional region inside the outline. Height is the perpendicular distance from a vertex to the opposite side. Perimeter is the total length around all three sides. The formulas are A = (√3/4)a², h = (√3/2)a, and P = 3a. The height formula follows by splitting the triangle into two right triangles and applying the Pythagorean theorem; area is then one-half base times height.
The calculator accepts a number and does not ask you to choose a unit. If your side is 6 inches, interpret the output as square inches for area, inches for height, and inches for perimeter. Area uses the square of the length unit because it covers a two-dimensional surface. Keep measurements in one unit before entering them.
For a = 6, area is 15.5885, height is 5.1962, and perimeter is 18.0000, each rounded to four decimal places. The screen provides a separate copy control for area, height, and perimeter.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Use the unit already attached to your measurement, such as inches, feet, centimeters, or meters. Convert first if your measurements use mixed units.
Type the length of any one side. A blank, zero, negative, or nonnumeric value does not produce a result. The starting value is 10, and the clear control restores 10.
Read area as square units and height and perimeter as length units. Copy the particular result you need using its adjacent copy control.
Use the scale relationship as a quick reasonableness check: doubling the side doubles height and perimeter, while area becomes four times as large because the side is squared.
Use cases
See how the tool fits into real work and everyday tasks.
Enter a known side after working through the radical formula by hand. Compare the displayed decimals with your own result while keeping exact expressions such as 9√3 until the final rounding step.
When a plan labels an equilateral panel by one edge, use the height to estimate its vertical span and the area to compare its footprint. Carry the original unit into your notes.
For a triangular cutout or repeated decoration, find one piece's area and perimeter. Multiply by the number of pieces separately and account for trim or waste outside this geometric calculation.
Q&A
Find concise answers to common questions and confusing cases.
No. This page takes side length as its input. If height is all you know, first convert it to the corresponding side length using a = 2h/√3, then enter that side.
No. The area, height, and perimeter relationships here assume all three sides are equal. A scalene or isosceles triangle needs different known measurements and a different calculation.
The triangle occupies only part of the square with the same side length. Its area is (√3/4)a², so a side of 6 gives approximately 15.5885 square units rather than 36.
Notes
Review scope, result limitations, and important precautions before use.
This is an ideal-geometry calculation from one positive side value. It does not measure a physical object or convert units.
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