Surface Area Calculator

Quick Answer

Last updated: 3 November 2026 ·How we calculate this: standard surface area formulas

How This Surface Area Calculator Works

Pick a shape and enter its sizes. Only the boxes that shape needs are shown. The calculator uses the right formula, works out each part, such as the ends and the sides, and adds them for the total surface area. For a cone or pyramid, it finds the slant height from the vertical height.

How to Use the Surface Area Calculator

1. Choose the shape.
2. Enter the sizes shown for that shape.
3. Choose the unit.
4. Press Calculate.
5. Read the total, lateral and base areas and the steps.

Core Formulas

• Rectangular box: 2(lw + lh + wh)
• Cube: 6a²
• Sphere: 4πr², and hemisphere with base: 3πr²
• Cylinder: 2πr² + 2πrh
• Cone: πr² + πrs, where s = √(r² + h²)
• Square pyramid: a² + 2as, where s = √(h² + (a/2)²)
• Triangular prism (equilateral): 2 × (√3/4)a² + 3al

Key Terms

• Surface area: the total area of all outside faces of a 3D shape.
• Lateral area: the area of the sides only, not counting the bases.
• Slant height: the distance from the tip of a cone or pyramid to the edge of its base, along its side.
• Prism: a 3D shape with two matching ends and flat sides.
• Net: a flat pattern that folds into a 3D shape.

Worked Example

Find the surface area of a can with radius 3 cm and height 10 cm.

• Two ends: 2 × π × 3² = 18π ≈ 56.55 cm²
• Side: 2 × π × 3 × 10 = 60π ≈ 188.50 cm²
• Total: 78π ≈ 245.04 cm²

Real-Life Examples

• Wrapping a gift: a 12 × 8 × 4 inch box needs at least 352 sq in of paper.
• Painting a tank: a cylinder 2 ft across and 4 ft tall has about 31.4 sq ft of surface.
• A ball: a basketball with a 4.7-inch radius has about 277.6 sq in of surface.
• A tent: a square pyramid tent 8 ft wide and 6 ft tall has about 115.4 sq ft of fabric on its sides.

Surface Area vs Volume

• Surface area: the outside area, in square units, such as for paint or wrapping.
• Volume: the space inside, in cubic units, such as for filling with water.
• Scaling: doubling every size makes the area 4 times larger and the volume 8 times larger.

Surface Areas of Common Sizes

In square units.

Tips

• Use one unit: convert all sizes to the same unit first.
• Open shapes: for a box without a lid, subtract one face (lw).
• Pipes and tubes: use the lateral area of a cylinder, without the ends.
• Painting: add extra for waste and a second coat.

A good way to check any answer is to draw the shape’s net, the flat pattern you get when you unfold it. A box unfolds into six rectangles, a cylinder into two circles and one long rectangle, and a pyramid into a square and four triangles. Adding the areas of those flat pieces always gives the surface area.

Common Mistakes to Avoid

• Using the vertical height for a cone’s side. Use the slant height s = √(r² + h²).
• Using diameter instead of radius. Halve the diameter first.
• Forgetting the ends. A closed cylinder has two circular ends.
• Mixing units. Inches and feet in one formula give a wrong answer.
• Reporting cubic units. Surface area is in square units.

Frequently Asked Questions

References & Sources