BravoCalc
📐

Geometry Calculator

Calculate area, perimeter, volume, and surface area for various geometric shapes. Includes comprehensive formulas, step-by-step solutions, and visual representations.

Geometry Calculator

2D
Two-Dimensional Shapes

🔵 Circle

Area: A = πr²
Circumference: C = 2πr
Diameter: d = 2r

⬜ Rectangle

Area: A = l × w
Perimeter: P = 2(l + w)
Diagonal: d = √(l² + w²)

🔺 Triangle

Area: A = ½bh
Perimeter: P = a + b + c
Heron's Formula: A = √[s(s-a)(s-b)(s-c)]

🔶 Square

Area: A = s²
Perimeter: P = 4s
Diagonal: d = s√2

🔷 Parallelogram

Area: A = b × h
Perimeter: P = 2(a + b)
Height: h = A/b

🔸 Trapezoid

Area: A = ½(b₁ + b₂)h
Perimeter: P = a + b₁ + c + b₂
Height: h = 2A/(b₁ + b₂)

3D
Three-Dimensional Shapes

🔮 Sphere

Volume: V = (4/3)πr³
Surface Area: SA = 4πr²
Diameter: d = 2r

📦 Cube

Volume: V = s³
Surface Area: SA = 6s²
Space Diagonal: d = s√3

📋 Rectangular Prism

Volume: V = l × w × h
Surface Area: SA = 2(lw + lh + wh)
Diagonal: d = √(l² + w² + h²)

🔺 Pyramid

Volume: V = (1/3)Bh
Surface Area: SA = B + PL
Lateral Area: LA = PL

🥤 Cylinder

Volume: V = πr²h
Surface Area: SA = 2πr² + 2πrh
Lateral Area: LA = 2πrh

🍦 Cone

Volume: V = (1/3)πr²h
Surface Area: SA = πr² + πrl
Slant Height: l = √(r² + h²)

📏
Fundamental Geometry Principles

Pythagorean Theorem

a² + b² = c²

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.

a₁/a₂ = b₁/b₂ = c₁/c₂

Circle Relationships

• Radius = Diameter ÷ 2
• Circumference = π × Diameter
• Area = π × Radius²
• Arc Length = (θ/360°) × 2πr

Volume Scaling

When linear dimensions scale by factor k:

• Area scales by k²
• Volume scales by k³

🏗️
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.