Surface area to volume ratio calculator helps you determine the amount of surface an object has relative to its size. The concept of surface area to volume ratio, also denoted as SA/VOL or SA:V, is given considerable importance in the sciences (such as aerodynamics for instance), and this article will explore why.

If you want to learn how to find volume and surface area of an object, you can use the volume calculator or the surface area calculator to learn how to find the volume and surface area of geometry shapes like cylinder, cube, cone, rectangular prism, or triangular prism, etc. Also, check out the body surface area calculator to find the surface area of a human body!

Keep reading to learn answers to the following questions:

  • What is the ratio of surface area to volume of different shapes?
  • How to find surface to volume ratio using the surface area to volume calculator?

What is the surface area to volume ratio?

The surface area of an object or a body is the total area of all its exposed surfaces, i.e., SA is simply the outside area of an object. On the other hand, Volume refers to the amount of space occupied by the object; it can also be the amount of space inside of the object.

For instance, let's say we have a cloth box. The box's surface area is a measure of the amount of wrapping paper required to cover the entire box precisely, while the volume of the box is a measure of the space inside the box which determines the number of clothes the box can carry.

How to calculate surface area to volume ratio?

Surface area to volume ratio is simply an object’s surface area divided by its volume. It gives the proportion of surface area per unit volume of the object (e.g., sphere, cylinder, etc.). Therefore, the formula to calculate surface area to volume ratio is:

SA/VOL = surface area (x2) / volume (x3)
SA/VOL = x-1,

where x is the unit of measurement.

Below is a table showing how to calculate the surface area to volume ratio of some common three-dimensional objects.

Shape
Surface area
Volume
Surface area to volume ratio
Cube
6L2
L3
6/L
Cylinder
2πR(R+H)
πR2H
2(R+H)/(RH)
Sphere
4πR2
4πR3/3
3/R
Cone
πRL+πR2
πR2H/3
3(R+L)/(RH)
Hemisphere
3πR2
2πR3/3
4.5R
Capsule
2πR(2R+H)
πR2(4R/3 + H)
(6/R)(2R+H)/(4R + 3H)

How to use the surface area to volume ratio calculate?

Since you've learned how to calculate the surface area to volume ratio, let's find out how to use the surface to volume ratio calculator:

  1. The most important decision is selecting the object's shape from the dropdown list of shape categories.

  2. Once you've done that, you will need to choose the exact shape of the object you want to calculate the SA:V (there is a diagram representing each selection).

  3. Input the values of parameters that determine the object's size, such as the side length, radius, or height.

  4. Once you've entered the values for the object's size, the surface to volume ratio calculator automatically calculates the surface area, volume, and surface area to volume ratio. You can change these values to see how the SA:V changes with different sizes of objects. Simple and straightforward 🙂

Why is the ratio of surface area to volume important?

The ratio of surface area to volume of an object is important in the sciences because it determines how fast matter and energy can be transferred within an object and between an object and its environment.

Looking at the formulas given in the table above, you will find that when the length L of the cube or the radius R of the cylinder is doubled (or reduced by half), it does not lead to a proportionate increase (or decrease) in the value of the surface area and volume. This is because an increase or decrease in these parameters (length or radius) results in a greater increase (or decrease) in volume than the increase in surface area since the value of surface area is squared (x2) while that of volume is cubed (x3).

As a result, the surface area to volume ratio is inversely proportional to the size of an object, given that length and radius determine the size. In other words, as the size of an object increases, its ratio of surface area to volume decreases; conversely, as the size of an object decreases, its ratio of surface area to volume increases.

The implication of the surface area to volume ratio is that energy or matter can move faster in objects or organisms with a higher surface area to volume ratio than those with a lower surface area to volume ratio.

The SA:V has significant implications in cell theory since cell surface area to volume ratio controls the success of its metabolic processes.

Cells are small to allow substances like glucose and oxygen to move through diffusion and get rid of their waste. As the cell grows and the SA:V decreases, it may not be able to get these substances from one end of a cell to the next by diffusion as fast as it should, which slows down cell processes and growth.

Thus, the cell surface area to volume ratio is improved through:

  • Cell division;
  • Slowed down metabolism; or
  • Change its shape to increase the surface area and therefore SA:V ratio.

The principle also explains why sprinkled water evaporates faster than the same amount of water in a bucket or why granulated sugar dissolves faster than a sugar cube. Put simply: a higher surface area improves the reactivity of a process.

FAQ

What is surface area to volume ratio?

Surface area to volume ratio is the amount of surface area or total exposed area of a body relative to its volume or size. It is denoted as SA/VOL or SA:V.

How to calculate surface area to volume ratio?

  1. Calculate the surface area of the object concerned in unit squared (x2);

  2. Calculate its volume in unit cubed (x3);

  3. Divide the object's surface area by its volume to get its surface area to volume ratio.

The formula to calculate surface area to volume ratio is:

SA/VOL = surface area (x2) / volume (x3)

SA/VOL = x-1

What is the ratio of surface area to volume?

The ratio of surface area to volume, or the surface area to volume ratio, is the amount of surface area or total exposed area of a body relative to its volume or size.

Why is the surface area to volume ratio important?

The surface area to volume ratio is important because it determines the rate of movement of materials or energy within a body and between a body and its environment. A high surface area to volume ratio means the body can swiftly transfer materials or energy because there is less space.

In contrast, a low surface area to volume ratio means that the volume or size of the object is larger than the surface medium of transfer. Hence, it'll take a longer time for the materials or energy to reach their destination.

How can I calculate my body surface area to volume ratio?

You can calculate your body surface area to volume ratio using the surface area to volume ratio formula or the simple-to-use body surface area calculator.

Rahul Dhari and Oghenekaro Elem
Shapes
Basic shapes
Basic shapes
Cube
Cube with side L








Side length (L)
in
Surface area (A)
in²
Volume (V)
cu in
Surface area to volume ratio
1/
in
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