The Surface Area to Volume Calculator converts a known surface area into volume, or a known volume into surface area, for a sphere, cube or cylinder.
Surface Area to Volume Calculator
Convert between surface area and volume for a sphere, cube or cylinder — and find the radius, side or height.
It works backward to the shape’s size first — for example r = √(A ÷ 4π) for a sphere or a = √(A ÷ 6) for a cube — then applies the other formula. A cylinder needs one extra measurement (height or radius), because one area or volume alone does not fix its shape.
Formula
| Conversion | Step 1: size | Step 2: result |
|---|---|---|
| Sphere: volume → area | r = ∛(3V ÷ 4π) | A = 4πr² |
| Sphere: area → volume | r = √(A ÷ 4π) | V = (4/3)πr³ |
| Cube: volume → area | a = ∛V | A = 6a² |
| Cube: area → volume | a = √(A ÷ 6) | V = a³ |
| Cylinder: volume + height | r = √(V ÷ πh) | A = 2πr(r + h) |
| Cylinder: volume + radius | h = V ÷ πr² | A = 2πr(r + h) |
Where: A = surface area, V = volume, r = radius, a = cube side, h = height.
How the Calculation Works
Step 1: Reverse the known formula to find the missing dimension (radius, side or height).
Step 2: Use that dimension in the other formula.
Step 3: Display the result with the dimension found, so you can check it.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| A | Surface area | cm², m², in², ft² |
| V | Volume | cm³, m³, L, in³, ft³, gal |
| r, a, h | Radius, side, height | cm, m, in, ft |
Example Calculation
Sphere: volume to surface area
Given: V = 523.6 cm³
Radius: r = ∛(3 × 523.6 ÷ (4 × 3.14159)) = ∛125 = 5 cm
Result: A = 4 × 3.14159 × 25 ≈ 314.16 cm²
Cube: surface area to volume
Given: A = 150 cm²
Side: a = √(150 ÷ 6) = √25 = 5 cm
Result: V = 5³ = 125 cm³
Cylinder: volume and height
Given: V = 282.74 cm³, h = 10 cm
Radius: r = √(282.74 ÷ (3.14159 × 10)) = 3 cm
Result: A = 2 × 3.14159 × 3 × 13 ≈ 245.04 cm²
Area and Volume Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 L | 1,000 cm³ |
| 1 m³ | 1,000 L |
| 1 US gal | 3.785 L = 231 in³ |
Shape Properties
Why some shapes need more information
A sphere and a cube have only one size measurement, so one area or volume determines everything. A cylinder has two (radius and height): a tall thin can and a short wide one can hold the same volume but have different surface areas.
Dimensions Explained
This calculator converts between the two quantities. If you want to divide surface area by volume (the SA:V ratio used in biology), use the Surface Area to Volume Ratio Calculator instead.
Frequently Asked Questions
Can you convert surface area to volume?
Only if you know the shape. For a sphere or cube, one value is enough; for other shapes you need an extra dimension.
How do you find the volume of a sphere from its surface area?
Find r = √(A ÷ 4π), then V = (4/3)πr³.
How do you find the surface area of a cube from its volume?
Take the cube root of the volume to get the side, then A = 6 × side².
How do you find the surface area of a cylinder from its volume?
You also need the height or radius. With the height, r = √(V ÷ πh), then A = 2πr² + 2πrh.
Is this the same as the surface area to volume ratio?
No. This page converts one quantity into the other; the SA:V ratio divides them.