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[(a1.6b1.6 + a1.6c1.6 + b1.6c1.6)/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
Unit | In Square Meters (m2) |
---|---|
Kilometer² | 1,000,000 |
Meter² | 1 |
Centimeter² | 0.0001 |
Millimeter² | 0.000001 |
Micrometer² | 0.000000000001 |
Hectare | 10,000 |
Mile² | 2,589,990 |
Yard² | 0.83613 |
Foot² | 0.092903 |
Inch² | 0.00064516 |
Acre | 4,046.86 |
Related Calculator:
Circle Calculator, Distance CalculatorExternal Resources:
Surface Area Calculator on Calculator.net