🔺 Isosceles Triangle Calculator
Calculate all properties of an isosceles triangle
How to Use This Calculator
Select Input Type
Choose which measurements you know: equal side and base, base and height, or base and equal side.
Enter Values
Input the known measurements. Make sure all values are positive numbers.
Calculate
Click "Calculate" to find all properties of the isosceles triangle.
Review Results
See all side lengths, height, area, perimeter, and angles displayed clearly.
Formula
Two sides equal: a = b ≠c
Base angles equal, vertex angle different
Given Equal Side (a) and Base (c):
- Height = √[a² - (c/2)²]
- Area = (Base × Height) / 2
- Perimeter = 2a + c
- Base Angle = arccos[(c/2) / a]
- Vertex Angle = 180° - 2 × Base Angle
Given Base (c) and Height (h):
- Equal Side = √[h² + (c/2)²]
- Area = (Base × Height) / 2
- Perimeter = 2 × Equal Side + Base
Key Properties:
- Two sides are equal (legs)
- Base angles are equal
- Height bisects the base
- Height creates two congruent right triangles
About Isosceles Triangle Calculator
The Isosceles Triangle Calculator finds all properties of an isosceles triangle. An isosceles triangle has two sides of equal length (legs) and two equal angles at the base. The third side (base) may be different.
When to Use This Calculator
- Geometry: Calculate isosceles triangle properties
- Construction: Design triangular structures with equal sides
- Education: Learn about isosceles triangles
- Engineering: Design calculations for isosceles components
- Architecture: Calculate dimensions for isosceles structures
Why Use Our Calculator?
- ✅ Multiple Inputs: Works with different combinations of known values
- ✅ Complete Calculations: Finds all triangle properties
- ✅ Accurate Results: Uses precise mathematical formulas
- ✅ Educational: Helps understand isosceles triangle properties
- ✅ Free: No registration required
Key Properties
- Equal Sides: Two sides (legs) are equal in length
- Equal Base Angles: The angles opposite the equal sides are equal
- Symmetry: Height from vertex to base bisects both the base and the vertex angle
- Two Congruent Right Triangles: The height divides the triangle into two congruent right triangles
- Flexible Base: The base can be longer, shorter, or equal to the equal sides
Special Cases
- Equilateral: If base = equal sides, it becomes an equilateral triangle
- Right Isosceles: If base angles = 45°, it's a right isosceles triangle (45-45-90)
- Acute: If vertex angle < 90°, the triangle is acute
- Obtuse: If vertex angle > 90°, the triangle is obtuse
Frequently Asked Questions
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two sides of equal length. The angles opposite the equal sides are also equal.
Are all isosceles triangles also equilateral?
No. An equilateral triangle is a special case of an isosceles triangle where all three sides are equal. But not all isosceles triangles are equilateral.
How do you find the height of an isosceles triangle?
If you know the equal side (a) and base (c), height = √[a² - (c/2)²]. The height forms a right triangle with half the base and one equal side.
Are the base angles always equal?
Yes! In an isosceles triangle, the base angles (angles opposite the equal sides) are always equal. This is a fundamental property.
Can an isosceles triangle be right?
Yes! A right isosceles triangle has a right angle (90°) and two equal legs. Its angles are 45°, 45°, and 90°.
What's the relationship between vertex angle and base angles?
The vertex angle + 2 × base angle = 180°. So if vertex angle = V and base angle = B, then V + 2B = 180°, or V = 180° - 2B.