Size and surface area to volume ratio

The surface of an organism or structure is its outer boundary, where substances can be exchanged with the surroundings. Its volume is the space contained within that boundary. The surface area to volume ratio compares the amount of surface available with the volume it encloses:

A smaller ratio means there is less surface available for exchange per unit volume.

How size changes the ratio

When similarly shaped structures increase in size, their surface area and volume do not increase at the same rate. Surface area increases with the square of a linear dimension, such as length, while volume increases with its cube.

For example, if every dimension of a structure doubles, its surface area becomes $$2^2 = 4$$ times as large, but its volume becomes $$2^3 = 8$$ times as large. Volume has grown faster than surface area, so the surface area to volume ratio decreases.

Consider two cubes:

• A cube with sides of $$1\ \text{cm}$$ has a surface area of $$6\ \text{cm}^2$$ and a volume of $$1\ \text{cm}^3$$. Its surface area to volume ratio is $$6\ \text{cm}^{-1}$$.
• A cube with sides of $$2\ \text{cm}$$ has a surface area of $$24\ \text{cm}^2$$ and a volume of $$8\ \text{cm}^3$$. Its surface area to volume ratio is $$3\ \text{cm}^{-1}$$.

The larger cube has more surface area in total, but less surface area for each unit of volume.

Exchange adaptations in larger organisms

Cells need substances such as oxygen and nutrients, and they must remove waste substances. These substances must cross a surface to enter or leave the organism. As an organism becomes larger, its volume increases faster than its external surface area. Its surface area-to-volume ratio therefore decreases: there is less external surface available for exchange relative to the volume of living tissue it supplies.

In a larger body, many cells are also farther from the external surface. Substances take longer to diffuse to and from these cells, so exchange across the body surface alone may not meet their needs.

Body shape and exchange

A thin or flattened body has a larger surface area relative to its volume than a more compact body of the same volume. It also keeps cells closer to the body surface, shortening the distance over which substances must diffuse. These features make exchange across the body surface more effective.

Specialised exchange surfaces and transport

Larger organisms can have specialised exchange surfaces that provide a large area for substances to enter or leave the body. They can also have transport systems that carry substances between these surfaces and cells throughout the body.

For example, a transport system can carry oxygen from an exchange surface to internal cells and carry waste substances from cells towards an exchange surface. This reduces the distance substances must travel by diffusion alone.

Surface area to volume ratio and metabolic rate

An organism’s cells carry out chemical reactions that keep it alive. The metabolic rate is the rate at which an organism carries out these reactions. Metabolism creates a demand for substances such as oxygen and nutrients, produces waste substances that need to be removed, and can produce heat.

An organism’s surface area to volume ratio compares its external surface area with its volume. Surface area provides an area across which substances and heat can be exchanged with the surroundings. Volume gives an indication of the amount of living tissue with metabolic demands.

Size, exchange and heat loss

As an organism’s volume increases, its total metabolic demand generally increases. For organisms of similar shape, volume increases faster than external surface area, so a larger organism has less external surface area per unit of volume.

A lower surface area to volume ratio means that, relative to the amount of tissue, there is less external surface available for exchange and heat loss. A higher ratio means there is more surface available relative to the amount of tissue. The ratio therefore affects how readily an organism can exchange substances and lose heat relative to its size.

Surface area to volume ratio in endotherms

Endotherms produce metabolic heat to help maintain their body temperature. When their bodies are warmer than their surroundings, heat is lost across the body surface. Among endotherms maintaining a similar body temperature, a higher surface area to volume ratio promotes greater heat loss per unit volume.

Smaller animals generally have a higher surface area to volume ratio, so they tend to lose heat more readily relative to their size. They therefore generally need a higher metabolic rate per unit body mass to produce enough heat to maintain their temperature. This does not mean that a smaller animal necessarily has a higher total metabolic rate than a larger one.

Surface area to volume ratio is not the only factor determining metabolic rate. For example, insulation and the temperature of the surroundings also affect how quickly an animal loses heat.