The surface area to volume ratio (SA:V) compares how much surface an object has with how much volume it contains. For an organism, surface area limits how fast substances can be exchanged, while volume sets how much is needed.To calculate it, work out the surface area and the volume, then divide the surface area by the volume. For a cube of side length L:surface area = 6 × L2 volume = L3 Worked examples:
• 1 cm cube: surface area = 6 × 1 = 6 cm2; volume = 1 cm3; SA:V = 6:1
• 2 cm cube: surface area = 6 × 4 = 24 cm2; volume = 8 cm3; SA:V = 3:1
• 4 cm cube: surface area = 6 × 16 = 96 cm2; volume = 64 cm3; SA:V = 1.5:1Each time the side length doubles, the surface area increases 4 times but the volume increases 8 times, so the ratio halves. As an organism gets larger, its surface area to volume ratio decreases.Shape matters too. A long, thin or flat shape has a much larger ratio than a compact one of the same volume. A 1 cm × 1 cm × 4 cm cuboid has surface area = (2 × 1) + (4 × 4) = 18 cm2 and volume = 4 cm3, so SA:V = 4.5:1, while a cube of about the same volume has a ratio close to 3.8:1.Ratios are usually written as n:1, using the same length unit for area and volume.
• 1 cm cube: surface area = 6 × 1 = 6 cm2; volume = 1 cm3; SA:V = 6:1
• 2 cm cube: surface area = 6 × 4 = 24 cm2; volume = 8 cm3; SA:V = 3:1
• 4 cm cube: surface area = 6 × 16 = 96 cm2; volume = 64 cm3; SA:V = 1.5:1Each time the side length doubles, the surface area increases 4 times but the volume increases 8 times, so the ratio halves. As an organism gets larger, its surface area to volume ratio decreases.Shape matters too. A long, thin or flat shape has a much larger ratio than a compact one of the same volume. A 1 cm × 1 cm × 4 cm cuboid has surface area = (2 × 1) + (4 × 4) = 18 cm2 and volume = 4 cm3, so SA:V = 4.5:1, while a cube of about the same volume has a ratio close to 3.8:1.Ratios are usually written as n:1, using the same length unit for area and volume.