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

UnitIn Square Meters (m2)
Kilometer²1,000,000
Meter²1
Centimeter²0.0001
Millimeter²0.000001
Micrometer²0.000000000001
Hectare10,000
Mile²2,589,990
Yard²0.83613
Foot²0.092903
Inch²0.00064516
Acre

4,046.86

Related Calculator:
Circle Calculator, Distance Calculator

External Resources:
Surface Area Calculator on Calculator.net

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