🔺 Equilateral Triangle Calculator
Calculate all properties of an equilateral triangle
How to Use This Calculator
Select What You Know
Choose whether you know the side length, height, area, or perimeter.
Enter the Value
Input the measurement you know. Make sure to enter a positive number.
Calculate
Click "Calculate" to find all properties of the equilateral triangle.
Review Results
See side length, height, area, perimeter, circumradius, inradius, and angles (all 60°).
Formula
All sides equal: a = b = c
All angles equal: 60°, 60°, 60°
Given Side Length (a):
- Height = (a × √3) / 2
- Area = (a² × √3) / 4
- Perimeter = 3a
- Circumradius = (a × √3) / 3
- Inradius = (a × √3) / 6
Given Height (h):
- Side = (2h) / √3
- Then use side formulas above
Given Area (A):
- Side = √[(4A) / √3]
- Then use side formulas above
Given Perimeter (P):
- Side = P / 3
- Then use side formulas above
Key Relationships:
- Height = Circumradius + Inradius
- Circumradius = 2 × Inradius
- All angles = 60°
About Equilateral Triangle Calculator
The Equilateral Triangle Calculator finds all properties of an equilateral triangle. An equilateral triangle is a special triangle where all three sides are equal in length and all three angles are equal to 60°.
When to Use This Calculator
- Geometry: Calculate equilateral triangle properties
- Construction: Design triangular structures with equal sides
- Education: Learn about equilateral triangles
- Engineering: Design calculations for equilateral components
- Trigonometry: Solve problems involving equilateral triangles
Why Use Our Calculator?
- ✅ Complete Calculations: Finds all triangle properties from one known value
- ✅ Multiple Inputs: Works with side, height, area, or perimeter
- ✅ Accurate Results: Uses exact mathematical formulas
- ✅ Educational: Helps understand equilateral triangle properties
- ✅ Free: No registration required
Key Properties
- Equal Sides: All three sides are equal (a = b = c)
- Equal Angles: All three angles equal 60°
- Symmetry: Equilateral triangles have rotational symmetry of 120°
- Regular Polygon: An equilateral triangle is a regular polygon
- Special Relationships: Height, circumradius, and inradius have fixed relationships to side length
Example
If side length = 10 units:
- Height = (10 × √3) / 2 ≈ 8.660
- Area = (100 × √3) / 4 ≈ 43.301
- Perimeter = 3 × 10 = 30
- Circumradius = (10 × √3) / 3 ≈ 5.774
- Inradius = (10 × √3) / 6 ≈ 2.887
Frequently Asked Questions
What is an equilateral triangle?
An equilateral triangle is a triangle with all three sides equal in length and all three angles equal to 60°. It's a special case of both isosceles and acute triangles.
Are all equilateral triangles similar?
Yes! All equilateral triangles are similar because they all have the same angles (60°, 60°, 60°). They differ only in size.
What's the formula for equilateral triangle area?
Area = (a² × √3) / 4, where a is the side length. This comes from the general formula Area = ½ × base × height, using height = (a√3)/2.
Is an equilateral triangle also isosceles?
Yes, technically an equilateral triangle is also isosceles (has at least two equal sides). However, we typically call it "equilateral" when all three sides are equal.
Can an equilateral triangle be right?
No. An equilateral triangle always has all angles equal to 60°, so it cannot have a 90° angle. An equilateral triangle is always acute.
What's the relationship between side and height?
Height = (Side × √3) / 2. The height is approximately 0.866 times the side length.
How do I find the side from the area?
Rearrange the area formula: Side = √[(4 × Area) / √3]. For example, if Area = 25√3, then Side = √[(4 × 25√3) / √3] = √(100) = 10.