Geometry Tool

Surface Area Calculator

Calculate surface area of 3D shapes.

Σ The Formula

Cube: SA = 6s² | Sphere: SA = 4πr² | Cylinder: SA = 2πr² + 2πrh

Real World Examples

Gift Box
Cube: s=10cm → SA = 600 cm²
Can Label
Cylinder: r=3cm, h=10cm → SA = 245.04 cm²
Basketball
Sphere: r=12cm → SA = 1809.56 cm²
Shipping Box
Prism: l=20cm, w=15cm, h=10cm → SA = 1300 cm²

# About This Calculator

Surface area is the total area of all faces or surfaces of a 3D object. Unlike volume which measures space inside, surface area measures the outside "skin" of the shape. It's crucial for determining how much material is needed to cover or construct an object.

Surface area calculations are essential in manufacturing (material costs), packaging design (box/can production), construction (paint needed, insulation), heat transfer (radiators, cooling fins), and biology (cell surface-to-volume ratios). Knowing surface area helps estimate costs and optimize designs.

Different shapes have different formulas: cubes use 6s² (6 square faces), spheres use 4πr², cylinders use 2πr² + 2πrh (two circles plus the curved side), and rectangular prisms use 2(lw + lh + wh). Each formula accounts for the specific geometry of that shape.

This calculator supports common 3D shapes: cube, sphere, cylinder, cone, and rectangular prism. It automatically applies the correct formula and shows step-by-step calculations, making it perfect for homework, construction planning, packaging design, or any project requiring surface area measurements.

How To Use

  1. Select 3D Shape.
  2. Enter dimensions.
  3. Click Calculate.

Frequently Asked Questions

What's the difference between surface area and volume?+

Surface area measures the outside (like wrapping paper needed), measured in square units (cm², m²). Volume measures the inside space (like water capacity), measured in cubic units (cm³, m³). A box might have SA=600cm² and V=1000cm³ - different concepts!

How much paint do I need to cover a surface?+

Calculate surface area, then check paint coverage (usually on the can, like '10 m² per liter'). Divide surface area by coverage rate. For 50m² surface with 10m²/L coverage: need 5 liters. Add 10-20% extra for multiple coats.

Why does a sphere have less surface area than a cube of same volume?+

Spheres are the most efficient 3D shape - minimum surface area for a given volume. This is why bubbles are spherical and why cells tend toward spherical shapes. For equal volumes, sphere always has less surface area than cube or other shapes.

How do I calculate surface area for irregular shapes?+

Break them into regular shapes and sum the areas. For example, a house might be a rectangular prism (walls) + triangular prism (roof). Calculate each part separately, then add. This calculator handles the basic shapes; combine results for complex objects.

What's the surface area of a cylinder without the top/bottom?+

Just the curved side: 2πrh. For example, a can label (no top/bottom): r=3cm, h=10cm gives 2π(3)(10) = 188.5cm². The full cylinder formula (2πr² + 2πrh) includes both circular ends.

Is Surface Area Calculator free to use?+

Yes, Surface Area Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Surface area is the total area of all faces or surfaces of a 3D object. Unlike volume which measures space inside, surface area measures the outside "skin" of the shape. It's crucial for determining how much material is needed to cover or construct an object.

Surface area calculations are essential in manufacturing (material costs), packaging design (box/can production), construction (paint needed, insulation), heat transfer (radiators, cooling fins), and biology (cell surface-to-volume ratios). Knowing surface area helps estimate costs and optimize designs.

Different shapes have different formulas: cubes use 6s² (6 square faces), spheres use 4πr², cylinders use 2πr² + 2πrh (two circles plus the curved side), and rectangular prisms use 2(lw + lh + wh). Each formula accounts for the specific geometry of that shape.

This calculator supports common 3D shapes: cube, sphere, cylinder, cone, and rectangular prism. It automatically applies the correct formula and shows step-by-step calculations, making it perfect for homework, construction planning, packaging design, or any project requiring surface area measurements.

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