Geometry Calculator
Calculate area, perimeter, volume, and surface area for various geometric shapes. Includes comprehensive formulas, step-by-step solutions, and visual representations.
2DTwo-Dimensional Shapes
🔵 Circle
⬜ Rectangle
🔺 Triangle
🔶 Square
🔷 Parallelogram
🔸 Trapezoid
3DThree-Dimensional Shapes
🔮 Sphere
📦 Cube
📋 Rectangular Prism
🔺 Pyramid
🥤 Cylinder
🍦 Cone
📏Fundamental Geometry Principles
Pythagorean Theorem
In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
Similar Triangles
Triangles with the same shape but different sizes have proportional corresponding sides.
Circle Relationships
Volume Scaling
When linear dimensions scale by factor k:
🏗️Real-World Applications
🏠 Construction
- • Floor area calculations
- • Material quantity estimation
- • Roof pitch and area
- • Foundation volume
🎨 Design & Art
- • Canvas and frame sizing
- • Pattern and tile layouts
- • Sculpture proportions
- • Garden design
🏭 Manufacturing
- • Product packaging
- • Material optimization
- • Quality control
- • Cost estimation
🌍 Science
- • Astronomical calculations
- • Physics experiments
- • Environmental studies
- • Medical imaging
💡Geometry Tips & Problem-Solving Strategies
✅ Always Check Units
Ensure all measurements use the same units before calculating. Convert if necessary.
✅ Draw Diagrams
Visualize the problem with sketches. Label all known measurements and what you need to find.
✅ Break Down Complex Shapes
Divide irregular shapes into simpler geometric forms you can calculate easily.
💡 Use Estimation
Round numbers to check if your answer is reasonable before doing exact calculations.
💡 Remember π ≈ 3.14159
For quick estimates, use π ≈ 3.14. For more precision, use more decimal places.
💡 Double-Check Formulas
Verify you're using the correct formula for the specific shape and measurement needed.