Total surface area
SA = 6a²
A cube has six identical square faces. Each face has an area of a², so the total surface area is six times the area of one face.
Cube geometry calculator
Cube Surface Area Calculator
Calculate the total surface area, lateral surface area, and volume of a cube using its edge length. Enter a measurement in metric or imperial units and instantly see the formulas, calculation steps, and converted results.
Calculate the surface area of a cube
A cube has six equal square faces. Enter the length of one edge to calculate its surface area and volume.
Enter any positive edge length.
The edge length is converted to metres before calculations are performed. The displayed area and volume are then converted into your selected units.
Cube surface area formula
Lateral surface area
LSA = 4a²
Lateral surface area includes the four side faces only. It excludes the top and bottom faces.
Area of one face
A = a²
Every face of a cube is a square with side length a. Multiply the edge length by itself to find the area of one face.
Volume of a cube
V = a³
Volume measures the space inside the cube. Multiply the edge length by itself three times.
How to calculate cube surface area
- Measure one edge of the cube. All six edges have the same length.
- Square the edge length: multiply it by itself.
- Multiply the square by six to calculate total surface area.
- For lateral surface area, multiply the square by four.
- For volume, cube the edge length by calculating a × a × a.
- Express area in square units and volume in cubic units.
For example, if the edge length is 5 cm, each face has an area of 5 × 5 = 25 cm². The total surface area is 6 × 25 = 150 cm².
Cube surface area examples
One face: 2² = 4 cm²
Total area: 6 × 4 = 24 cm²
Lateral area: 4 × 4 = 16 cm²
Volume: 2³ = 8 cm³
One face: 5² = 25 m²
Total area: 6 × 25 = 150 m²
Lateral area: 4 × 25 = 100 m²
Volume: 5³ = 125 m³
One face: 10² = 100 ft²
Total area: 6 × 100 = 600 ft²
Lateral area: 4 × 100 = 400 ft²
Volume: 10³ = 1,000 ft³
Find the edge length from surface area or volume
Given total surface area
a = √(SA / 6)
Divide the total surface area by six, then take the square root to determine the edge length.
Given volume
a = ∛V
The edge length is the cube root of the volume. Once you find the edge length, calculate the surface area using 6a².
Cube surface area unit conversions
| Area unit | Equivalent |
|---|---|
| 1 cm² | 100 mm² |
| 1 m² | 10,000 cm² |
| 1 m² | 10.7639 ft² |
| 1 ft² | 144 in² |
| 1 yd² | 9 ft² |
| 1 km² | 1,000,000 m² |
Remember that area units are squared. For example, converting centimetres to metres uses a factor of 100 for lengths, but a factor of 10,000 for areas.
Cube vs. rectangular cuboid
| Property | Cube | Rectangular cuboid |
|---|---|---|
| Edge lengths | All equal | May differ |
| Face shapes | Six equal squares | Rectangles |
| Total surface area | 6a² | 2(lw + lh + wh) |
| Volume | a³ | lwh |
Frequently asked questions
What is the formula for the surface area of a cube?
The formula is SA = 6a², where a is the edge length. Since the cube has six equal square faces, multiply the area of one face by six.
How do you calculate lateral surface area?
Use LSA = 4a². This counts the four side faces but excludes the top and bottom faces.
How do you calculate the volume of a cube?
Use V = a³. For a cube with an edge of 4 cm, the volume is 4 × 4 × 4 = 64 cm³.
Can surface area be calculated from volume?
Yes. Find the edge length using a = ∛V, then calculate surface area using SA = 6a².
Why is surface area measured in square units?
Surface area measures a two-dimensional quantity. Multiplying two lengths, such as centimetres by centimetres, produces square centimetres.
Does a cube have six faces?
Yes. A cube has six square faces, twelve edges, and eight vertices.
What happens to surface area if the edge doubles?
Surface area becomes four times larger because it depends on the square of the edge length. Volume becomes eight times larger because it depends on the cube of the edge length.
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