Surface Area Calculator

Understanding Surface Area

Surface area is the total area that covers the outer surface of a 3D object. This guide explains how to calculate the surface area of various geometric shapes using key formulas. For volume-related information, see our Volume Calculator, and for flat shapes, refer to the Area Calculator.

🔵 Sphere

• Formula: SA = 4πr²
• Example: Truffle with radius 0.325 in: SA = 4π(0.325)² = 1.327 in²

🔺 Cone

• Formulas:
  Base = πr²
  Lateral = πr√(r² + h²)
  Total = πr(r + √(r² + h²))
• Example: Cone with r = 1 ft, h = 0.5 ft → Lateral SA = 0.805 ft²

🟫 Cube

• Formula: SA = 6a²
• Example: Cube with edge 4 in → SA = 6 × 4² = 96 in²

🧊 Cylindrical Tank

• Formula: SA = 2πr(r + h)
• Example: r = 3.5 ft, h = 5.5 ft → SA = 197.92 ft²

📦 Rectangular Tank

• Formula: SA = 2(lw + lh + wh)
• Example: Box 3×4×5 ft → SA = 94 ft²

💊 Capsule

• Formula: SA = 4πr² + 2πrh
• Example: r = 0.05 in, h = 0.5 in → SA = 0.188 in²

🟤 Spherical Cap

• Formula: SA = 2πRh + πr²
• Example: R = 0.8 ft, h = 0.53 ft → SA = 2.664 ft²

🔻 Conical Frustum

• Formula:
  End = π(R² + r²)
  Lateral = π(R + r)√((R – r)² + h²)
  Total = Sum of both
• Example: R = 1 ft, r = 0.3 ft, h = 1.5 ft → SA = 10.185 ft²

🥚 Ellipsoid

• Approx. Formula:
  SA ≈ 4π[(a^1.6b^1.6 + a^1.6c^1.6 + b^1.6c^1.6)/3]^1/1.6
• Example: a = 0.1, b = 0.2, c = 0.35 in → SA ≈ 0.562 in²

⛩ Square Pyramid

• Formula:
  Base = a²
  Lateral = 2a√((a/2)² + h²)
  Total = a² + 2a√((a/2)² + h²)
• Example: a = 3 ft, h = 5 ft → SA = 40.321 ft²

📐 Common Area Units

Related Calculator:
Circle Calculator, Distance Calculator

External Resources:
Surface Area Calculator on Calculator.net