S.4 Stocks and flows

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.

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.

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.

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.

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.

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.

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):

• 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.

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.

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?

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.

• 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)

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.

Coming soon!