Maths Skill: Calculating Percentage Yield
- Farmers use various strategies to increase the yield of their crops or livestock. These strategies include:
- Reducing energy losses from crops to other organisms by removing pests
- Reducing energy losses from livestock through respiration by restricting their movement and keeping them warm (i.e. indoors)
- Increasing yield refers to:
- Increasing the net primary production of crops
- Increasing the net production of livestock
Percentage Yield
- There are two types of yield:
- Theoretical yield is the amount (of crop or livestock biomass) that is theoretically possible to produce, given the ideal conditions
- Actual yield is the amount (of crop or livestock biomass) that is actually produced, given the actual conditions the crops or livestock are kept under
- The percentage yield is the actual yield achieved, given as a percentage of the theoretical yield possible
- Percentage yield can be calculated using the following equation:
% yield = (actual yield ÷ theoretical yield) × 100
Worked example
The maximum theoretical net primary production of wheat crops is approximately 200 kg m⁻² yr⁻¹. A wheat farmer finds that her crops have a net primary production of only 50 kg m⁻² yr⁻¹. Calculate the percentage yield of her wheat crops and explain why the percentage yield is not 100%.
Step 1: Write out the equation and substitute in the known values
% yield = (actual yield ÷ theoretical yield) × 100
% yield = (50 ÷ 200) × 100
Step 2: Calculate the % yield
% yield = 0.25 × 100
% yield = 25%
Step 3: Explain why the percentage yield is not 100%
- The maximum theoretical yield (or maximum theoretical net primary production) can only be obtained if the conditions are perfect
- This includes abiotic factors, such as temperature, water availability and light availability
- This may also include biotic factors, such as a lack of pest species competing with the crop
- The perfect conditions are very difficult to achieve for crops (especially those grown outdoors) and so the percentage yield is often well below 100%
- The maximum theoretical yield (or maximum theoretical net primary production) can only be obtained if the conditions are perfect
Worked example
A cattle farmer estimates that over a five year period, the final biomass of his herd of cattle should be 15,000 kg. At the end of the five years, when the cattle are ready for human consumption, the farmer calculates that the percentage yield is an impressive 90%. Calculate the actual biomass of the herd of cattle at the end of the five years.
Step 1: Rearrange the equation
% yield = (actual yield ÷ theoretical yield) × 100
Actual yield = (% yield × theoretical yield) ÷ 100
Step 2: Substitute in the known values and calculate the actual yield
Actual yield = (90 × 15,000) ÷ 100
Actual yield = 1,350,000 ÷ 100
Actual yield = 13,500
Step 3: Give the appropriate units
The actual yield of the herd of cattle is 13,500 kg
