Enter the side length of the cube. You get the surface area (6 × side × side), the area of one face, and conversions between cm² and m².
Enter 0 or a positive number for the side length, without units (for 10 cm, enter "10").
Result and figure
Enter the side length in the field on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the side length, and you get the surface area of the cube (surface area = 6 × side × side) right away
- The area of one face (a square) and unit conversions (ft² for input in inches, in² for input in feet) are shown at the same time. Switch "Units" to Metric for cm² and m²
- The result is also shown as a 3D figure (drag it with the mouse to turn it around)
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the side length as a number only, without units. The answer is in your input unit squared (in² for inches, ft² for feet). The volume of a cube (the space inside) and the surface area of other solids, such as rectangular boxes and spheres, have their own pages.
What is this calculation used for?
Estimating wrapping paper for a gift box (everyday life and gift wrapping)
To wrap a cube-shaped box, you need at least as much paper as its surface area. For a box 8 in on each side, the surface area is \(6 \times 8 \times 8 = 384\,\mathrm{in^2}\) (about 2.67 ft²).
Real wrapping needs extra for folds and overlaps, so add some margin to this number when choosing the paper size. The formula tells you the minimum you need.
Estimating paint for a cube storage box or stool (DIY)
Paint cans list how many square feet they cover. To paint every side of a wooden cube box 16 in on each side, the surface area is \(6 \times 16 \times 16 = 1536\,\mathrm{in^2}\), and dividing by 144 gives about 10.7 ft².
Add up the boxes you want to paint and convert to ft², and you can compare directly with the coverage on the can, so you are less likely to buy the wrong amount.
Finding the glass area of a cube aquarium for cleaning or film (fish tanks)
A cube aquarium 12 in on each side has faces of \(12 \times 12 = 144\,\mathrm{in^2}\), and all 6 faces add up to \(6 \times 144 = 864\,\mathrm{in^2}\).
A real tank is open at the top, so the glass is one face less: \(864 - 144 = 720\,\mathrm{in^2}\) (5 ft²). Taking "6 faces minus the faces you do not need" like this gives you a good idea of how much to clean, or how much background or insulation film to buy.
Estimating the cardboard for a cube-shaped box (online selling and moving)
The amount of cardboard it takes to make one box also starts from the surface area. A cube-shaped box 12 in on each side needs \(6 \times 12 \times 12 = 864\,\mathrm{in^2}\) (6 ft²).
Real boxes need a little more for the overlapping flaps and glue tabs, but this formula tells you roughly how many boxes you can get from a sheet.
Explaining why ice or sugar cubes melt faster when small (science and cooking)
Ice and sugar cubes melt or dissolve from the surface that touches the water or air around them, so the more surface area, the faster they tend to melt. One ice cube 2 in on each side has a surface area of \(6 \times 2 \times 2 = 24\,\mathrm{in^2}\). Split the same amount (8 in³ of volume) into eight 1-inch cubes, and the total surface area doubles to \(8 \times 6 \times 1 \times 1 = 48\,\mathrm{in^2}\).
The everyday experience that crushed ice melts and chills faster can be put into numbers with surface area.
Formulas and figures
Surface area of a cube
Figure
Standard notation
(the usual math form)
\(S\)
\(=\)
\(6\)
\(\times\)
\(a\)
\(2\)
In words
(symbols replaced with words)
④
\(S\): surface area of the cube
\(=\)
③
\(6\): number of faces
\(\times\)
①
\(a\): side length
②
squared (the length times itself)
The formula in words
①
Take the
\(a\): side length
②
and
square it (the length times itself)
to get the area of one face (a square)
③
Multiply that by the
\(6\): number of faces
④
and you get the
\(S\): surface area of the cube
Quick example
The surface area of a cube-shaped box 10 in on each side is
\(S\): surface area of the cube
\(=\)
number of faces (6)
\(\times\)
side length (10 in)
squared
\(10 \times 10 = 100\,\mathrm{in^2}\)
\(6 \times 100 = 600\,\mathrm{in^2}\)
Key idea
Why multiply by 6? A cube is a solid made of 6 square faces of the same size. Picture cutting a box along its edges and laying it flat (a net): you see 6 identical squares. Surface area is the total area of all the outside faces, so it is the area of one face (\(a \times a = a^2\)) times 6.
Do not mix it up with volume (\(a^3\)). Surface area is how much outside surface there is, so it uses the length twice and its unit is in²; volume is the space inside, so it uses the length three times and its unit is in³. Even for the same cube, the formula and the unit change with what you want to find.
Converting area units (in² → ft²)
Figure
Standard notation
(the usual math form)
\(S_{\mathrm{ft^2}}\)
\(=\)
\(S_{\mathrm{in^2}}\)
\(\div\)
\(144\)
In words
(symbols replaced with words)
③
\(S_{\mathrm{ft^2}}\): surface area in ft²
\(=\)
①
\(S_{\mathrm{in^2}}\): surface area in in²
\(\div\)
②
\(144\): in² in 1 ft²
The formula in words
①
Take the
\(S_{\mathrm{in^2}}\): surface area in in²
②
divide it by
\(144\): in² in 1 ft²
③
and you get the
\(S_{\mathrm{ft^2}}\): surface area in ft²
Quick example
The surface area of a cube 12 in (= 1 ft) on each side, 864 in², in ft² is
surface area in ft²
\(=\)
surface area in in² (864)
\(\div\)
in² in 1 ft² (144)
\(864 \div 144 = 6\,\mathrm{ft^2}\)
Key idea
An area conversion factor is the length conversion factor squared. Since \(1\,\mathrm{ft} = 12\,\mathrm{in}\), \(1\,\mathrm{ft^2} = 12\,\mathrm{in} \times 12\,\mathrm{in} = 144\,\mathrm{in^2}\). It is easy to mistakenly divide by 12, so be careful.
To go the other way, from ft² to in², multiply by 144. Likewise \(1\,\mathrm{yd^2} = 3 \times 3 = 9\,\mathrm{ft^2}\). For volume, the factor is the length factor cubed (\(1\,\mathrm{ft^3} = 1728\,\mathrm{in^3}\)), which is different again.
The surface area of a cube is "6 × side × side" (6 times the side squared). Squaring the side gives the area of one face (a square), and there are 6 faces, so you multiply by 6. The answer is in your input unit squared (in² for inches), and to convert in² to ft², just divide by 144.
Symbols and terms
Symbols
| \(S\) | ess | A symbol often used for area. On this page it is the surface area of the cube. Many US textbooks write it as \(SA\). |
| \(a\) | a | The side length of the cube. All 12 edges of a cube are the same length, so one letter is enough. |
| \(a^2\) | a squared | The number \(a\) multiplied by itself (\(a \times a\)). The small 2 at the upper right is an exponent that tells you to multiply the number by itself. A square with side \(a\) has an area of exactly \(a^2\). |
| \(\mathrm{in^2}\) | square inches | A unit of area. A square with 1-inch sides has an area of 1 in². It is also written "sq in". |
| \(\mathrm{ft^2}\) | square feet | A unit of area. A square with 1-foot sides has an area of 1 ft². \(1\,\mathrm{ft^2} = 144\,\mathrm{in^2}\). It is also written "sq ft". |
Terms
| cube | A solid whose faces are all squares of the same size. It has 6 faces, 12 edges and 8 vertices, and every edge is the same length. Dice and a Rubik's Cube are everyday examples. |
| surface area | The total area of the whole outside of a solid. For a cube, it is the sum of the areas of its 6 square faces. It is what you need for wrapping, painting or covering the outside. |
| net | The flat shape you get by cutting a solid along its edges and unfolding it. A net of a cube is 6 identical squares joined together (there are 11 different ones, such as the cross shape). The surface area equals the area of the whole net. |
| squared | Multiplying a number by itself, also called "to the second power". The name comes from the formula for the area of a square. |
| unit conversion | Writing the same amount in a different unit. For area, the key point is that the length factor squared is the area factor (1 ft = 12 in, so 1 ft² = 144 in²). |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Multiplication (Grades 3–4) |
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| Area of squares and rectangles (Grade 3) |
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| Cubes, rectangular prisms and nets (Grade 6) |
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| Multiplying decimals (Grades 5–6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the surface area of a cube
| Side length | 10 |
| Surface area of the cube | =6*B1^2 |
Table to convert in² to ft²
| Surface area in in² | 864 |
| Surface area in ft² | =B1/144 |
After pasting, column A has the item names and column B the numbers. The upper row is your input, and the formula in the last row calculates from it automatically.
"B1" in a formula stands for "the number in that cell". "^" is a power (how many times to multiply), "*" is multiplication and "/" is division. "=6*B1^2" is 6 times the side squared, that is, 6 × side × side (Excel does powers before multiplication, so the squaring comes first as it should).
In the first table, for example, B2 shows 6 × 10 × 10 = 600 (in² if you entered inches). The second table shows 6 (ft²) in B2. Just replace the input with your own length.
"B1" in a formula stands for "the number in that cell". "^" is a power (how many times to multiply), "*" is multiplication and "/" is division. "=6*B1^2" is 6 times the side squared, that is, 6 × side × side (Excel does powers before multiplication, so the squaring comes first as it should).
In the first table, for example, B2 shows 6 × 10 × 10 = 600 (in² if you entered inches). The second table shows 6 (ft²) in B2. Just replace the input with your own length.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the surface area of a cube
| Side length | 10 |
| Surface area of the cube | =6*B1^2 |
Table to convert in² to ft²
| Surface area in in² | 864 |
| Surface area in ft² | =B1/144 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the input with your own length.
How to calculate it in Python
a = 10 # side length (inches in this example)
face_area = a ** 2 # area of one face (a square; in2 in this example)
surface_area = 6 * face_area # surface area of the cube (area of one face x 6 faces)
surface_area_ft2 = surface_area / 144 # for input in inches, the surface area in ft2
print(f"Area of one face: {face_area} in2")
print(f"Surface area of the cube: {surface_area} in2")
print(f"In ft2: {surface_area_ft2} ft2")
Runs with the standard library only. "**" is a power (a ** 2 multiplies a by itself), "*" is multiplication and "/" is division. Change the side length at the top and run it (this example is for input in inches; for input in feet, multiply by 144 to get in²).
How to write it in LaTeX and other math languages (copy and paste)
Surface area of a cube
S = 6a²
S = 6a^{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi>
<mo>=</mo>
<mn>6</mn>
<msup><mi>a</mi><mn>2</mn></msup>
</mrow>
</math>
S = 6a^2
6 a^2
S := 6*a^2;
S = 6*a^2;
S = 6a^2
Converting area units (in² → ft²)
S[ft²] = S[in²] ÷ 144
S_{\mathrm{ft^2}} = S_{\mathrm{in^2}} \div 144
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>S</mi><mrow><msup><mi>ft</mi><mn>2</mn></msup></mrow></msub>
<mo>=</mo>
<msub><mi>S</mi><mrow><msup><mi>in</mi><mn>2</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>144</mn>
</mrow>
</math>
S_(ft^2) = S_(in^2) -: 144
sIn2/144
sFt2 := sIn2/144;
s_ft2 = s_in2/144;
S(ft²) = S(in²)/144
How to have ChatGPT do the calculation
You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). A cube-shaped box is 10 in on each side. Find each of the following: 1. The area of one face (a square) of this cube in in² 2. The surface area of this cube in in² 3. That surface area in ft² Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
Volume of a Cube Calculator (Side × Side × Side)
Calculates the volume of the same cube, the space inside. Surface area goes with squaring, volume with cubing
Area of a Rectangle Calculator (Length × Width)
Calculates the area of a square or rectangle (side × side), the same as one face of a cube
Nth Root Calculator (Square Root, Cube Root, nth Root)
Calculates the square root (√) you use to work back from the surface area to the side length of a cube
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