Enter the carrying capacity of the environment and the intrinsic rate of increase into the calculator to determine the Maximum Sustainable Yield.

## Maximum Sustainable Yield Formula

The following formula is used to calculate the Maximum Sustainable Yield (MSY).

MSY = 0.5 * K * r

Variables:

- MSY is the Maximum Sustainable Yield (units of the species per time period)
- K is the carrying capacity of the environment (units of the species)
- r is the intrinsic rate of increase (per time period)

To calculate the Maximum Sustainable Yield, multiply the carrying capacity of the environment by the intrinsic rate of increase. Then, divide the result by 2. This will give the maximum number of species that can be harvested sustainably without causing a decline in the population over time.

## What is a Maximum Sustainable Yield?

Maximum Sustainable Yield (MSY) is a concept used in environmental science and fisheries management that refers to the largest yield or catch that can be taken from a species’ stock over an indefinite period. The goal of MSY is to achieve a balance between maximum harvest and the capacity of the species to regenerate, ensuring that the population remains sustainable and does not decline over time due to overfishing or overharvesting.

## How to Calculate Maximum Sustainable Yield?

The following steps outline how to calculate the Maximum Sustainable Yield (MSY).

- First, determine the carrying capacity of the environment (K) in units of the species.
- Next, determine the intrinsic rate of increase (r) per time period.
- Next, gather the formula from above: MSY = 0.5 * K * r.
- Finally, calculate the Maximum Sustainable Yield (MSY).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Carrying capacity of the environment (K) = 100 units of the species

Intrinsic rate of increase (r) = 0.2 per time period