Equilateral Triangle Calculator
This equilateral triangle calculator needs just one known quantity. Example: for the side a = 6 the height is 5.19615 and the area is 15.5885.
Source: Wikipedia – Equilateral triangle. Updated: .
How it is calculated
An equilateral triangle has three equal sides and three angles of 60° each. That is why a single value is enough to find all the others.
Formulas and steps
From the side a you get the height h = a · √3 / 2, the area A = a² · √3 / 4, the perimeter P = 3a, the inradius r = a · √3 / 6 and the circumradius R = a · √3 / 3. If the height, area or perimeter is given instead, the side is found first: a = 2h / √3, a = √(4A / √3) or a = P / 3.
Worked example
For a = 6 we get h = 6 · √3 / 2 ≈ 5.19615. The area is 36 · √3 / 4 ≈ 15.5885 and the perimeter 18. The incircle has radius r ≈ 1.73205 and the circumcircle R ≈ 3.4641. Check with Pythagoras: the height halves the base, so h² + 3² = 6², and 5.19615² + 9 comes to 36.
- The circumradius is exactly twice the inradius.
- Doubling the side makes the area four times as large.
Frequently asked questions
How do you find the height of an equilateral triangle?
Use h = a · √3 / 2. For a = 6 that is about 5.19615. The height bisects the base and coincides with the median and the angle bisector.
What is the area of an equilateral triangle?
A = a² · √3 / 4. For a side of 6 this is about 15.5885 square units.
Can I get the side from the area?
Yes, with a = √(4A / √3). Choose “Area A” above and enter the value; the calculator returns side, height and perimeter.
Sources and legal basis
As of: · Editorial policy
Related tools
- Triangle CalculatorTriangle calculator from any three values (SSS, SAS, ASA, AAS, SSA): missing sides and angles, area, perimeter, heights, inradius and circumradius.
- Isosceles Triangle CalculatorIsosceles triangle calculator: from base and leg, base and height, or leg and apex angle, find height, area, perimeter and angles with steps.
- 30-60-90 Triangle Calculator30-60-90 triangle calculator: from the short leg, long leg or hypotenuse find all sides, area and perimeter, with the 1 : √3 : 2 ratio and a worked example.
- Pythagorean Theorem CalculatorPythagorean theorem calculator: enter two sides to get the third side, both angles, area and height – with exact square roots, working and a right-angle check.
- Centroid of a Triangle CalculatorCentroid of a triangle calculator: enter the coordinates of the three vertices to get the centroid, the area and the median lengths, with steps and example.
- Regular polygon calculatorRegular polygon calculator for 3 to 1000 sides from side length, circumradius, inradius or area: area, perimeter, radii, angles and diagonals with formulas.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Percentage calculator for marksPercentage calculator for marks: enter the marks of each subject and get total, percentage and best-of-5 result. For 10th, 12th and semester marksheets.
- Arrhenius equation calculatorArrhenius equation calculator: find activation energy from two rate constants at two temperatures, or the new k – with the formula and a worked example.