Surface Area Calculator

Solid Geometry & 3D Surface Area Formulas

Surface Area measures the total two-dimensional area occupied by the external surface boundaries of a three-dimensional object.

Primary 3D Solid Surface Area Equations

• Rectangular Prism (Box):

A_total = 2, V = lwh

• Cylinder:

A_total = 2π r^2 + 2π rh = 2π r, V = π r^2 h

• Sphere:

A = 4π r^2, V = (4) / (3)π r^3

• Cone:

Slant Height s = √(r^2 + h^2), A_total = π r^2 + π r s, V = (1) / (3)π r^2 h

• Cube:

A = 6s^2, V = s^3

• Square Pyramid:

Slant Height s = √(^2 + h^2), A_total = b^2 + 2bs, V = (1) / (3)b^2 h

• Surface-to-Volume Ratio:

Ratio = A_totalVolume

How to Use This Calculator

Enter your 3D Geometric Solid — choose from Rectangular Prism / Box (Length × Width × Height), Cylinder (Radius & Height), Sphere (Radius), Primary Dimension — Length / Radius / Side (e.g. 10), Secondary Dimension — Width / Height (e.g. 5), Tertiary Dimension — Height (for Box) (e.g. 4), and Measurement Unit — choose from Centimeters (cm), Meters (m), Inches (in). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Rectangular Prism (a = length, b = width, c = height)

Worked Example

A cardboard shipping box measuring 10cm x 5cm x 4cm requires 220.0 cm² of sheet cardboard to construct and holds 200.0 cm³ of volume.

Understanding Your Result

Geometric calculations assume ideal shapes — real-world measurements should include a 5–15% tolerance for irregular shapes, cutting waste, and installation overlap. For construction applications: always verify calculated areas match your physical measurements before ordering materials. Standard practice is to measure the same dimension twice from different reference points and use the average. Express results in the units required by your supplier or building permit — conversions between cubic yards, cubic feet, and cubic meters must be precise for material orders.