📐 Geometry Calculator
Calculate areas, perimeters, volumes, and surface areas for geometric shapes with our free, comprehensive Geometry Calculator. Get accurate results with formula explanations for educational and professional use.
How to Use This Geometry Calculator
How to Use the Geometry Calculator:
- Select the geometric shape you want to calculate (circle, rectangle, triangle, etc.)
- Choose the calculation type (area, perimeter, volume, surface area)
- Enter the required dimensions in the input fields that appear
- Results calculate automatically with formula explanations
- Copy results or download calculations for your records
Pro Tips: All calculations show the mathematical formula used, helping you learn and verify results. For triangles, ensure the three sides can form a valid triangle. For 3D shapes, both volume and surface area calculations are available.
How It Works
Geometry Calculation Formulas:
Our calculator uses standard geometric formulas taught in mathematics curricula worldwide:
- Circle: Area = π × r², Circumference = 2 × π × r
- Rectangle: Area = length × width, Perimeter = 2 × (length + width)
- Triangle: Area = ½ × base × height, or Heron's formula for three sides
- Sphere: Volume = (4/3) × π × r³, Surface Area = 4 × π × r²
- Cylinder: Volume = π × r² × height, Surface Area = 2π × r × (r + height)
Example: For a circle with radius 5 units:
- Area = π × 5² = 3.14159 × 25 = 78.54 square units
- Circumference = 2 × π × 5 = 2 × 3.14159 × 5 = 31.42 units
- Educational Value: Understanding these formulas helps in real-world applications
When You Might Need This
- • Student homework and assignment assistance for geometry problems
- • Teacher lesson planning and example problem generation
- • Standardized test preparation for SAT, ACT, GRE mathematics sections
- • Architectural space planning and area calculations
- • Construction material estimation and project planning
Frequently Asked Questions
How accurate are the geometry calculations?
Our calculator uses precise mathematical formulas with high-precision floating-point arithmetic. Results are accurate to multiple decimal places, suitable for academic, professional, and practical applications. All calculations follow standard geometric principles and mathematical conventions.
What shapes and calculations are supported?
We support comprehensive calculations for 2D shapes (circles, rectangles, squares, triangles) and 3D solids (spheres, cylinders, cones, cubes, rectangular prisms). Each shape includes area, perimeter/circumference, and volume calculations where applicable.
Can I use this calculator for homework and tests?
Yes! Our calculator is designed for educational use and provides not just answers but also shows the formulas used. This helps you understand the mathematical principles and verify your manual calculations. Always check with your instructor about calculator policies for specific assignments or exams.
Are the formulas mathematically correct?
Absolutely. All calculations use standard geometric formulas taught in mathematics curricula worldwide. For example, circle area uses π×r², triangle area uses ½×base×height, and sphere volume uses (4/3)×π×r³. Each result can be verified against textbook formulas.