S.4 Stocks and flows
Helpful prior learning and learning objectives
Helpful prior learning:
Section 1.1.1 The economy and you which explains what an economy is and how it is relevant to students’ lives
Section 1.1.2 The embedded economy, which explains the relationship between the economy and society and Earth’s systems.
Section S.1 What are systems?, which explains what a system is, the importance of systems boundaries, the difference between open and closed systems and the importance of systems thinking
Section S.2 Systems thinking patterns, which outlines the core components of systems thinking: distinctions (thing/other), systems (part/whole), relationships (action/reaction), and perspectives (point/view)
Section S.3 Systems diagrams and models, which explains the systems thinking in some familiar information tools as well as the symbols used to represent parts/wholes, relationships and perspectives.
Learning objectives:
Distinguish between system stocks and flows
Describe how changes in inflows and outflows change stocks over time
Explain the importance of delays and buffers in the stability of stocks
Diagram stocks and flows in different ecological and social systems
Imagine an empty bathtub. If you plug the drain and turn on the tap (faucet), the tub fills with water. Removing the plug allows water to flow out of the tub. Whether the water level rises or falls depends on how quickly water flows in and out.
What are stocks and flows?
The water in the tub represents a stock (Figure 1). Stocks are things that can accumulate, like the number of trees in a forest, money in a bank account, people in a city, or carbon dioxide (CO2) in the atmosphere. The water entering through the tap or leaving through the drain are flows. Flows describe movement—what adds to or reduces the stock.
Figure 1. Stocks and flows of water in a bathtub.
(Credit: Kaboompics, Pexels license)
Figure 2. A city has a stock of people, its population. Immigration and births are inflows, increasing population. Emigration and deaths are outflows, decreasing population.
(Credit: Jason Hu, Pexels licence)
For example, in a city’s population, births and immigration are inflows, while deaths and emigration are outflows (Figure 2). In a forest, tree growth and tree planting increases the stock, while logging and natural deaths reduce it. Understanding how stocks and flows interact helps us see how the stocks in systems grow, decline, or stay balanced.
Understanding how stocks and flows interact helps us see how stocks in a system increase, decrease, or stay balanced. The size of a stock always depends on its inflows and outflows. Sometimes, however, inflows and outflows also depend on the stock itself.
Take population as an example. A city’s population grows when people move there. But another inflow is births, which usually increase as the population grows because there are more people that could have children. When stocks influence flows, which then affect the stocks again, this is called feedback. Section S.5 explains feedback in more detail.
How do stocks change over time?
A stock’s size and rate of change depends on the relative rate of change in its inflows and outflows. When inflows are greater than outflows, the stock increases. When outflows exceed inflows, the stock decreases. A stock increases in size when inflows exceed outflows and decreases in size when outflows surpass inflows. We can visualise these changes using behavior-over-time graphs, which track whether a stock is increasing, decreasing, or stable. For instance:
decreasing stocks (Figure 3): Coal stocks in a mine decrease over time because there are no inflows—coal doesn’t replenish naturally on a human timescale;
increasing stocks (Figure 4): Carbon dioxide CO2 stocks in the atmosphere rise when CO2 emissions are greater than natural CO2 absorption in forests, oceans and soils;
stable stocks (Figure 5): A healthy forest can achieve a stable stock over time if tree growth and tree planting matches natural deaths and logging.
Figure 3. Declining stock
Inflows less than outflows
Example: coal stocks that deplete over time as coal is mined
Figure 4. Increasing stock
Inflows greater than outflows
Example: carbon dioxide (CO2) in the atmosphere, where CO2 emissions exceed CO2 absorbed by the oceans and biosphere.
Figure 5. Stable stock
Inflows and outflows are equal
Example: A healthy forest where tree death and logging are the same as tree growth and tree planting.
When inflows and outflows are balanced the stock and the system reaches a dynamic equilibrium. This doesn’t mean nothing changes—flows still occur, and stocks may change, but the stock remains stable over time. The healthy forest mentioned above is one example. Dynamic equilibrium is a key feature of healthy systems. When disrupted—like when outflows exceed inflows, or inflows exceed outflows—it can lead to stock depletion or growth, both of which can harm long-term stability of a system.
Why are delays and buffers important?
In many systems, changes in flows take time to affect stocks due to delays—the gap between action and outcome. For example, working extra hours today increases your paycheck, but only later. Delays can make it harder to connect actions with outcomes, as you’ll explore further in Section S.5.
Stocks can act as buffers, absorbing shocks and maintaining stability. For example:
reservoirs collect water during rainy seasons, ensuring a steady supply of water for agriculture, households and industry during dry periods (Figure 6);
forests store carbon, helping to regulate CO2 in the atmosphere.
Buffers make systems more resilient, able to recover stability after a disruption. But large stocks of harmful things, like CO2 in the atmosphere that warms the planet, can delay recovery. Even if CO2 emissions stopped today, it would take decades for CO2 levels to decrease due to slow absorption by forests and oceans (Figure 7).
Recognising delays and buffers helps us plan better. Buffers stabilise systems, while delays highlight the need to act early, especially for long-term challenges like climate change.
Figure 6. A reservoir, like this huge lake, is a buffer that stores water during rainy periods and releases it for use during dry periods.
(Credit: Nick, CC BY-SA 4.0)
Figure 7. Global CO2 levels are still rising. Even if we stop emissions (flows), the stock of CO2 in the atmosphere would take decades to start declining.
(Credit: CO2levels.org)
How can we diagram stocks and flows?
In addition to behaviour-over-time graphs, we use stock and flow models to visually represent systems. These diagrams simplify complex relationships, making them easier to understand. Here’s how to create one (Figure 8):
identify the stock: stocks, like trees in a forest, are shown as rectangles;
determine the flows: flows, such as tree growth (inflow) or logging (outflow), are shown as arrows with faucet symbols to indicate that the rate of inflow or outflow can change;
connect flows to stocks: arrows pointing into the rectangle show inflows, while arrows leaving show outflows;
Figure 8. The basics of stock and flow diagrams
define boundaries: cloud symbols at the ends of arrows show an area outside the boundary of the system you are examining. For example, a cloud at the end of a tree planting inflow arrow could represent trees being brought in from outside the forest system;
add variables (optional): variables influencing flows, like government policies affecting tree planting, can be added as text or circles connected to arrows.
Note: If you have studied Section S.2 on systems thinking basics, you can see how identifying the stocks and flows requires you to distinguish. The flows also represent the relationships between the stock and other elements in the system, often the stock itself. Showing the system boundary with the clouds is also about distinguishing what is in the system from what is not in the system.
Figure 9. A simple stock and flow diagram for a nonrenewable resource like coal
Figure 9 shows coal, a nonrenewable fossil fuel stock with mining as the only outflow. The rate of mining that stock will depend on demand elsewhere in the economic system.
Since coal cannot replenish naturally, its stock steadily declines as you saw in Figure 3. In this diagram, the cloud symbol shows that the coal goes somewhere outside the boundary of this simple system.
Figure 10. Two inflows and two outflows from the population.
A population stock diagram (Figure 10) is more complex, with inflows like immigration and births, and outflows like emigration and deaths.
Again, the cloud symbols show the boundaries of the system. However, in this case, there is a difference between immigration and births as an inflow, because births are dependent on the size of the population stock. These kinds of feedback loops will be addressed in Section S.5.
Figure 11. A stock and flow diagram with multiple stocks and flows
A more advanced diagram (Figure 11) might include multiple stocks and the flows between them. In this case you have the forest stock, but also a stock of timber from trees that have been cut down.
Like population, the rate of tree growth inflow will depend on the size (and age) of the tree stock, as will the deaths.
Stock and flow diagrams are useful tools for making our understanding of systems visible, but they also have limitations. These limitations were discussed at the end of Section S.3.
Activity S.3
Concept: Systems
Skills: Thinking skills (transfer)
Time: varies, depending on the option
Type: Individual, pairs or group
Option 1: Stocks or flows?
Time: 5 minutes, or longer if you explain your reasoning to a partner or in a group
Which of the following are stocks and which are flows?
Water reservoir
Wealth
Inventory in a warehouse
Exports
Income
Savings in a bank account
Rain
Social cohesion
Interest on savings in a bank account
Unemployed people
Fish in a lake
Social media feed
Click on the arrow to reveal the answers.
Stock 7. Flow
Stock 8. Stock
Stock 9. Flow
Flow 10. Stock
Flow 11. Stock
Stock 12. Flow
Option 2: Bathtub dynamics - Behaviour over time graphing practice
Time: 30 minutes
This worksheet from Massachusetts Institute of Technology (MIT) asks students to use graph data about stock levels, inflows and outflows to create a behaviour-over-time graph for the amount of water in a bathtub.
Option 3: The bathtub game
Time: 35-40 minutes
You can model stocks and flows of CO2 in the atmosphere using a simulation with students in your class, where the students represent CO2. The description for this activity is on pp. 30-35 of The Systems Thinking Playbook for Climate Change. It involves simulating inflows and outflows to see how stocks change and graphing the change over time. It also involves discussion of the changes to inflows and outflows that need to be made to reduce the stocks of CO2 and the impact of delays in feedback and action.
Option 3: Stock and flow diagram practice
Time: 30-40 minutes
Read the four examples below carefully. For each example, identify:
The stock (what accumulates).
The inflows (what adds to the stock).
The outflows (what reduces the stock).
Draw a stock and flow diagram for each example. Use rectangles for stocks, arrows with faucet symbols for inflows and outflows, and cloud symbols for flows entering or leaving the system. Check your work by clicking on the arrow below the example. Note: it is possible that your diagram differs from the example answer and is still correct. In that case, make sure to discuss your diagram with a partner or your teacher.
A city’s water supply
A reservoir stores water for a city. Rainfall adds water to the reservoir, and some water flows out to supply households and businesses. During dry periods, the reservoir’s stock of water declines as there is less rain but continued use by the city residents and businesses.
2. A wildlife sanctuary
A sanctuary has a population of deer. The population grows as deer are born and through occasional migration from nearby areas. The population decreases due to predation (predators eating the deer) and other deaths, or migration out of the sanctuary.
3. A savings account
A savings account holds money deposited by an individual. The account balance increases through deposits from the person’s income and interest earned over time. The balance decreases when the person withdraws money for expenses or to transfer to other accounts, or pays fees charged by the bank.
4. A community food bank
A food bank collects food donated from individuals, businesses, and farmers. It distributes food to families in need who store it at home until it is used. Some food is wasted from the food bank and from households if not used in time.
Checking for understanding
Further exploration
In a world of systems - a 10-minute illustrated video from the Donella Meadows Project about systems thinking. It offers brief insights into how systems shape our world and how understanding feedback loops, leverage points, and interconnectedness can help solve global challenges. There is a section of the video specifically on stocks and flows. Difficulty level: easy
Tools of Systems Thinking Courses - short courses (1-hour each) explaining some key tools of systems thinking, from the Waters Center for Systems Thinking. Relevant courses for Section S.4 include (Difficulty level: medium):
Tools Course #1: Behavior-Over-Time Graphs (BOTGs)
Tools Course #3: Stock-Flow Mapping
The Systems Thinking Playbook – A practical guide by Linda Booth Sweeney and Dennis Meadows, offering hands-on exercises to develop systems thinking skills through understanding feedback loops, delays, and interconnected systems in an engaging way. It is widely used in education, leadership training, and sustainability studies. Difficulty level: medium.
Insight Maker - an online modeling platform where students can create systems models and simulate outcomes. Requires a little time to learn how to use, but is a fun way to introduce digital systems modeling. Difficulty level: medium
The Bathtub Game - a game from The Systems Thinking Playbook for Climate Change that illustrates stocks and flows using student’s active participation. Useful for a teacher who wants to have students physically demonstrate stocks and flows. Difficulty level: medium (due to setting up the activity)
Sources
Cabrera, D., & Cabrera, L. (2018). Systems thinking made simple: New hope for solving wicked problems (2nd ed.). Odyssean Press.
Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ). (2011). The Systems Thinking Playbook for Climate Change: A toolkit for interactive learning. https://klimamediathek.de/wp-content/uploads/giz2011-0588en-playbook-climate-change.pdf
Meadows, D. H. (2008). Thinking in systems: A primer. White River Junction, VT: Chelsea Green Publishing.
Terminology
Coming soon!