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Math & Statisticsgeometry

Surface Area Calculator

Surface area of the common solids, with paint quantity. Area scales with the square of a dimension while volume scales with the cube, which is why a larger container needs proportionally less material.

Also called: surface area formula, paint quantity calculator.

m² per litre
Surface area
37

37 m² in total, of which 25 m² is the sides. At 10 m² per litre and 2 coats that needs 5 litres. Doubling every dimension quadruples the area and multiplies the volume by eight.

Side area only
25
Base area
6
In square feet
398.27
Paint needed
5
Enclosed volume
15
On the shape
Doubling every dimension quadruples the area and multiplies the volume by eight.
How this is calculated
Method and background

How this is calculated

Each shape has its own formula, and the side area is separated from the base because painting or cladding usually excludes the base. The square-cube relationship is the useful insight: doubling a tank's dimensions gives eight times the capacity for only four times the material, which is why storage gets cheaper per litre at scale and why small animals lose heat faster than large ones.

surface area scales with the square of a linear dimension where volume scales with the cube
r
Radius

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a rectangular room

Shape
Rectangular box
Length or diameter
3
Width
2
Height
2.5
Paint coverage
10 m² per litre
Coats
2

Surface area37

2(6 + 7.5 + 5); walls 2 x 2.5 x 5

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a sphere has no base

Shape
Sphere
Length or diameter
2
Width
2
Height
2
Paint coverage
10 m² per litre
Coats
2

Surface area12.57

boundary: 4 pi r squared with r = 1

Open this example

Method and limits

What it assumes

  • Smooth surfaces with no openings deducted.

What it deliberately does not model

  • Paint coverage varies with surface porosity and application method, often by a third.
  • Windows and doors need deducting separately for a real room.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does a bigger tank cost less per litre?
Because material scales with area and capacity with volume. Doubling the dimensions gives eight times the capacity for four times the material.