3D Surface Area Calculator

Surface area of 3D shapes

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About 3D Surface Area Calculator

A 3D surface area calculator for common geometric solids. Supports sphere, cylinder, cone, frustum, torus, ellipsoid, and rectangular prism. Shows total and lateral surface areas, formulas used, and step-by-step computation. All calculations are client-side. Essential for geometry, engineering, and manufacturing.

3D Surface Area Calculator Features

  • 7 shapes
  • Total & lateral
  • Step formulas
  • Volume too
  • Unit support
Surface area formulas: Sphere = 4πr². Cylinder = 2πr(r+h). Cone = πr(r+l) where l=slant. Torus = 4π²Rr. Rectangular prism = 2(lw+lh+wh). These formulas calculate the total outer area of 3D shapes.

How to Use

Select a shape and enter dimensions:

  • Shape: Choose from 7 solids
  • Dimensions: Radius, height, etc.
  • Output: Total and lateral area

Key Formulas

  • Sphere: 4πr²
  • Cylinder: 2πrh + 2πr²
  • Cone: πrl + πr²
  • Torus: 4π²Rr

Applications

Paint coverage, heat transfer calculations, material cost estimation, packaging design, and architectural planning all require surface area calculations.

Step-by-Step Instructions

  1. 1Select a 3D shape.
  2. 2Enter dimensions.
  3. 3View total surface area.
  4. 4Check lateral area.
  5. 5See formula used.

3D Surface Area Calculator — Frequently Asked Questions

What's the difference between total and lateral surface area?+

Total includes all surfaces (top, bottom, sides). Lateral includes only the side surface, excluding bases. For a cylinder: lateral = 2πrh, total = 2πrh + 2πr².

How do I find the slant height of a cone?+

Use Pythagorean theorem: l = √(r² + h²) where r is the base radius and h is the height. The slant height is the distance along the side from base to apex.

What is the surface area of a torus?+

A torus (donut shape) with major radius R and minor radius r has surface area 4π²Rr. It's the product of the circumferences of the two generating circles.

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