Triangle Calculator
Calculate various properties of a triangle including area, perimeter, angles, and more.
Triangle Visualization
Enter any 3 values below to calculate the remaining properties
Input Values
Triangle Information
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
Key Properties:
- The sum of interior angles is always 180°
- The sum of any two sides must be greater than the third side
- Area = ½ × base × height
- Perimeter = sum of all three sides
Types of Triangles:
- Equilateral: All sides equal, all angles 60°
- Isosceles: Two sides equal, two angles equal
- Scalene: All sides and angles different
- Right: One 90° angle
- Acute: All angles less than 90°
- Obtuse: One angle greater than 90°
🔺 Isosceles Triangle Calculator – Solve Area, Height, Angles & More Instantly
An isosceles triangle calculator is a powerful online tool that helps you calculate unknown sides, angles, height, and area of an isosceles triangle within seconds. Whether you’re solving a geometry problem, doing architectural planning, or working on a DIY project, this calculator simplifies complex triangle calculations using advanced geometry formulas. Isosceles Triangle Calculator – Calculate Area, Angles, Sides & Height Easily
📘 What Is an Isosceles Triangle?
An isosceles triangle is a triangle with two sides of equal length and two angles of equal measure. This symmetry makes it one of the most useful and widely studied triangle types in geometry.
Properties of an Isosceles Triangle:
Axis of symmetry: Perpendicular from the vertex to the midpoint of the base.essential in academics and professional fields.
Two equal sides: Often called the “legs” of the triangle.
One base: The third side, not equal to the legs.
Two equal base angles: Located opposite the equal sides.
One vertex angle: Located opposite the base.
For a deeper understanding of triangle geometry, you can explore Khan Academy’s Geometry Course or use the comprehensive Triangle Calculator from Omni.
🧰 🧠 What Does the Isosceles Triangle Calculator Do?
The isosceles triangle calculator can compute any of the following parameters, given two known values:
| Input Options | Output You Can Calculate |
|---|---|
| Base + Height | Side lengths, Area, Angles |
| Side + Angle | Base, Height, Area |
| Base + Side | Height, Angles, Area |
What Can the Isosceles Triangle Calculator Do?
Our Isosceles Triangle Calculator is an all-in-one solution that quickly computes the following:
| Calculation | Output |
|---|---|
| Area | Using base and height or sides and angles |
| Perimeter | Sum of all three sides |
| Equal Side Lengths | When base and height are known |
| Base or Height | When other dimensions are known |
| Angles | Base angles and vertex angle |
| Altitude | Perpendicular height from the vertex |
Whether you know the base and height, two sides and an angle, or even just one side and an angle, the tool intelligently applies the correct formulas.
📐 Formulas Used in the Calculator
The calculator uses precise mathematical formulas based on your input:
- Area of an isosceles triangle Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21×base×height
- Perimeter Perimeter=2a+b(where a=equal sides, b=base)\text{Perimeter} = 2a + b \quad \text{(where } a = \text{equal sides, } b = \text{base)}Perimeter=2a+b(where a=equal sides, b=base)
- Height (when only sides are known) h=a2−(b2)2h = \sqrt{a^2 – \left(\frac{b}{2}\right)^2}h=a2−(2b)2
- Base angles
Use cosine rule: cos(θ)=b2a\cos(\theta) = \frac{b}{2a}cos(θ)=2ab
These formulas are coded into the calculator to automate the math, reduce error, and save you time.
👨🏫 How to Use the Isosceles Triangle Calculator
Here’s how to use the tool effectively:
- Choose the type of input: (e.g., base and height, or two sides and angle)
- Enter your known values in the fields.
- Click on “Calculate”.
- Instantly see results: area, perimeter, height, and all angles.
You can also clear the input to run new calculations, making it ideal for students and professionals who need to test multiple scenarios.
📊 Example Use Case
Given: Base = 10 cm, Height = 8 cm
Calculation: Area=12×10×8=40 cm2\text{Area} = \frac{1}{2} \times 10 \times 8 = 40 \text{ cm}^2Area=21×10×8=40 cm2
Equal sides: a=(102)2+82=25+64=89≈9.43 cma = \sqrt{\left(\frac{10}{2}\right)^2 + 8^2} = \sqrt{25 + 64} = \sqrt{89} \approx 9.43 \text{ cm}a=(210)2+82=25+64=89≈9.43 cm
Perimeter: P=2×9.43+10≈28.86 cmP = 2 \times 9.43 + 10 \approx 28.86 \text{ cm}P=2×9.43+10≈28.86 cm
This shows how easily complex calculations can be done with the tool in seconds.
🎯 Who Is This Calculator For?
- Students learning geometry or trigonometry
- Teachers preparing math exercises
- Engineers measuring support angles
- Architects designing triangular structures
- Artists & Designers needing precision in symmetry
🔗 Related Tools You Might Like
These tools work great when used together, especially when solving complex geometric problems.
🔒 Why Choose Our Isosceles Triangle Calculator?
- ✅ 100% Free and online
- ✅ Mobile and desktop compatible
- ✅ Ad-free user experience
- ✅ Based on real mathematical logic
- ✅ Lightning-fast performance
📝 Final Thoughts
An Isosceles Triangle Calculator is more than just a tool—it’s a shortcut to understanding geometry in a fast, visual, and reliable way. No more memorizing formulas or using calculators manually. Whether you’re a math student, a builder, or just curious, this tool provides everything you need.
