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Surface Area Calculator: Cube, Cylinder, Sphere & Cone

Calculate total and lateral surface area for 6 common 3D shapes.

Quick Answer:Select your 3D shape, input required dimensions (radius, height, width, length), and get exact surface area with step-by-step geometric formulas.

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How to Use the Surface Area Calculator: Cube, Cylinder, Sphere & Cone

1Choose the 3D shape from the dropdown (cube, box, cylinder, sphere, cone, pyramid).
2Enter the required dimensions in any consistent unit.
3Review the total surface area and lateral surface area.
4Inspect the step-by-step formula and intermediate math.

Formula & How It Works

3D Surface Area Formulas

Total Area = Sum of all face areas

Cylinder: 2*pi*r*h + 2*pi*r^2 | Sphere: 4*pi*r^2 | Box: 2(lw + lh + wh).

Worked Examples

Cylinder Can

Input: r = 3 cm, h = 10 cm

Explanation: 2*pi*3*10 + 2*pi*3^2 = 60pi + 18pi = 78pi ≈ 245.04.

Result: 245.04 sq cm

Rectangular Box

Input: l = 4, w = 5, h = 6

Explanation: 2*(4*5 + 4*6 + 5*6) = 2*(20 + 24 + 30) = 148.

Result: 148 sq units

Sphere

Input: r = 5 m

Explanation: 4 * pi * 5^2 = 100pi ≈ 314.16.

Result: 314.16 sq m

Frequently Asked Questions

What is the formula for the surface area of a cylinder?▼

Surface Area = 2πrh + 2πr², where r is radius and h is height (lateral area + 2 circular bases).

What is the surface area of a sphere?▼

Surface Area = 4πr², where r is the radius.

How do you find the surface area of a rectangular prism?▼

Calculate 2(lw + lh + wh), summing the areas of the 6 rectangular faces.

What is the surface area of a cube with side 5?▼

6 * 5² = 6 * 25 = 150 square units.

What is the difference between total and lateral surface area?▼

Total surface area includes all faces and bases; lateral surface area excludes the top and bottom bases.

Is this tool free to use?▼

Yes, Toolzy math calculators are completely free and private.

Quick Reference & Conversion Table

Shape	Surface Area Formula	Key Variables
Cube	6 * s²	s = side length
Rectangular Box	2*(lw + lh + wh)	l = length, w = width, h = height
Cylinder	2πrh + 2π*r²	r = radius, h = height
Sphere	4 * π * r²	r = radius
Cone	πrs + π*r²	r = radius, s = slant height

⚠️ Common Pitfalls to Avoid

•Confusing surface area (2D exterior boundary) with volume (3D interior capacity).
•Forgetting the top and bottom circles when computing cylinder surface area.

💡 Practical Real-World Uses

•Estimating paint and primer required to coat spherical tanks and cylindrical silos.
•Calculating sheet metal material requirements for ductwork and fabrication.
•Packaging box cardboard design and wrapping paper calculations.

Last reviewed & updated: 2026-11-10

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