Site author Richard Steane
The BioTopics website gives access to interactive resource material, developed to support the
learning and teaching of Biology at a variety of levels.
Surface area to volume ratio
Single-celled organisms vs multicellular organisms
Many micro-organisms are just single cells. Bacteria and protoctista live in watery environments, and they take in the chemicals they require from the liquid surrounding them.
Larger organisms consist of many cells, each surrounded by a thin film of moisture. But they need special systems to provide them with the chemicals they require.
Science fiction and science facts
A couple of themes that sci-fi writers have enjoyed are turning small organisms into large ones, and the transformation of larger ones into microscopic ones.
But each of these are fraught with problems . . .
Surface area to volume ratio
The outside surface of a cell is the cell membrane, and substances diffusing into or out of the cell can pass through at any point in this surface area. If the surface area is increased, more substances can enter or leave in a given time.
After entering the cell, these substances can move into the cytoplasm, again by diffusion, where they can be used in the cell's processes such as respiration. This space has a certain volume. If its volume were increased, it would take longer for substances to get to the centre of the cell.
So the processing of a cell's requirements depends on a balance between the external area and the internal volume.
If we consider the size of a cell - by measuring its length or diameter - we are using a linear measurement, denoted here by L.
The surface area of the cell is proportional to the square of its size : L2, and the volume will be proportional to its size cubed : L3.
The surface area:volume ratio can be used to express the ease of entry or exit of substances.
Since this is L2/L3, it is 1/L, so it is inversely proportional to the linear measurement.
The surface area:volume ratio reduces as the size of an organism increases, and this means that for larger organisms simple diffusion may not provide an adequate supply of dissolved substances such as oxygen.
If only cells were cubes
I have deliberately not used actual units in this section.
For a cube of size 1:
The surface area is 6 (6 sides, each 1x1).
The volume is 1 (1x1x1).
So the surface area:volume ratio is 6
For a cube of size 2:
The surface area is 24 (6 sides, each 2x2).
The volume is 8 (2x2x2).
So the surface area:volume ratio is 3
For a cube of size 3:
The surface area is 54 (6 sides, each 3x3).
The volume is 27 (3x3x3).
So the surface area:volume ratio is 2.
What about a cube of size 4?
The surface area is > 96 (6 sides, each 4x4).
The volume is > 64 (4x4x4).
So the surface area:volume ratio is > 1.5.
How does this relate to cubes of size 2?
> Half and 1?
A value for surface area:volume ratio is not a simple number; because area and volume have different numbers of dimensions, the ratio has units, which are the reciprocal of the distance L used in these measurements. If different units are used, this will result in a different surface area:volume ratio.
So, measuring in millimetres will give a SA:vol value 1000 times larger than measurements in µmetres
Sometimes instead of the surface area:volume ratio, the surface area of an organism is expressed in relation to body mass (perhaps as mm2 mg-1).
For example in comparisons between different stages in the life cycle of an organism, its volume may not be directly proportional to its mass over the entire range, because the amounts of various tissues may change.
Spherical objects, real units
Surface area of a sphere A=4 π r2
Volume of a sphere V=4/3 π r3
π = 3.14
The human egg cell is in fact the largest cell in the human body.
|Organism + cell
||Cell diameter /mm
||Surface area /mm2
||SA:Vol ratio /mm-1
(Southern leopard frog)
You can work out the missing SA:Vol ratios, then mouseover to check your figures.
What trend does this show?
> As size increases, surface area:volume ratio decreases
Cells getting together
Most organisms consist of many cells. But joining cells presents problems, because each cell acts as a barrier to the next.
Some cyanobacteria stay attached to one another after division, forming strands of cells, like a string of beads. Some bacteria (Streptococci) are similar, but the strands are not very long. Filamentous algae such as Spirogyra are made of cylindrical cells that remain attached at the ends. In these cases there is not much reduction in surface area.
Flatworms have developed to extend their bodies sideways. Staying flat means that dissolved substances can pass in (or out) on the exposed upper and lower layers, and they will not need to diffuse far to reach (or leave) the cells beneath.
Larger organisms have within their bodies systems that maximise exchange.
Annelids such as the earthworm have a blood system to take oxygen from their skin and deliver it to cells within their body, as well as having a fairly specialised tubular gut. They have a rather slimy skin to enable oxygen from the air to dissolve and they stay in moist areas under ground. Their respiration is limited by the amount of oxygen that passes over their outer body surface.
It is no wonder that flatworms and earthworms are not very active.
All systems go
Specialised respiratory surfaces such as lungs and gills, together with their associated pipework, muscles and bones, make up respiratory systems which allow more oxygen to be taken from the environment and into the body more efficiently, as well as getting rid of carbon dioxide. This means that more specialised organisms can power their movements more efficiently.
This is integrated with the circulatory system which also delivers oxygen, together with the products of the digestive system to all parts of the body
Kidneys are specialised to remove waste substances from the body and they form the main organs of the excretory system.
Filaments of Nostoc commune
Three cells of Spirogyra
(OK: one in the middle and two part cells
The planarian flatworm
There are in fact three layers of cells: the outer ectoderm, the middle mesoderm and the endoderm, forming the small gut. This arrangement is called triploblastic, and is found in most larger animals.
The first 17 segments of the earthworm
This stylised diagram shows some of the blood circulatory system of the Earthworm. Earthworm blood contains haemoglobin, but it is not enclosed in blood cells.
Metabolism is the name given to all the chemical processes that occur within a living organism in order to maintain life.
Metabolism includes building-up processes (anabolism) as well as breaking-down processes (catabolism).
These processes need energy in order to proceed.
An organism's metabolic rate is the amount of energy expended in a given time period - usually 24 hours.
As this energy is provided by respiration, it can be measured by reference to oxygen consumption, carbon dioxide production or heat production.
The basal metabolic rate (BMR) is the metabolic rate when an organism is at rest, when the body only uses energy to keep vital organs such as the heart, lungs and brain functioning properly.
The BMR is increased when the body is undergoing activities like exercise.
Organisms with a greater mass have a higher overall metabolic rate, and they require a more efficient delivery of oxygen to, and removal of carbon dioxide from, their body cells.
However organisms with a lower mass have a higher surface area:volume ratio so they lose more heat, and in order to stay at the same body temperature they must respire more. Their basal metabolic rate per unit body mass must be higher than larger animals.
This is an ecogeographical observation.
Human body mass in relation to temperature
The sample comprised (males of) 263 groups of long-established human populations at various sites around the world
Within a broadly distributed group of animals, the mean individual size is larger in species and populations which inhabit colder environments, and individuals of consistently smaller size are found in warmer environments.
For instance, polar bears are the largest bears, and the mean size of bears of various species in tropical environments is smaller.
This can be explained in terms of larger animals having a lower surface area to volume ratio than smaller animals, so they radiate less body heat per unit of mass, and therefore stay warmer in cold climates.
Smaller animals have a higher surface area-to-volume ratio which enables them to lose heat more efficiently in hotter and drier climates.
Other related topics on this site
(also accessible from the drop-down menu above)
A Reassessment of Bergmann's Rule in Modern Humans
Experiment to determine the effect of surface area to volume ratio on the diffusion of an acid or alkali:
Effect of size on uptake by diffusion © 2019, Royal Society of Biology