Imagine I hand you two pieces of equipment: a camera and a video recorder. Some things in the world you can capture with a single photograph — the water in a tub, the balance in your account, the number of people in a stadium. Freeze time, click, done; the photo shows the whole truth. Other things a photograph can’t capture at all, because they only exist over time — the speed of a car, the flow from a faucet, the rate you’re spending money. Point a camera at “10 liters per minute” and you get nothing; you need the video, two frames at least, to see a rate.
That is the entire stock/flow distinction, and it’s the most important reflex this course builds. A stock is photographable. A flow is only filmable. Get fluent at sorting the two and a huge class of confident nonsense stops being able to fool you. Get it wrong and you’ll cheerfully confuse the deficit with the debt for the rest of your life. So let’s drill it until it’s instant.
The two-second test
When any quantity comes at you, ask one question: Could I count this at a single frozen instant?
- Yes → it’s a stock. The water in the tub (40 liters). The money in your account ($3,200). The people in the country (68 million). Pause the universe, and the number is right there to read.
- No — I’d need to watch it for a while → it’s a flow. The faucet (10 L/min). Your salary ($5,000 per month). Births (700,000 per year). Freeze the universe and the number vanishes, because a rate is a thing that only happens across time.
There’s a dead-giveaway shortcut hiding in the units. A flow always smuggles a “per [time]” into its unit — per minute, per month, per year, per second. Liters per minute. Dollars per month. If you cannot say the quantity out loud without sneaking a “per something-time” into it, it’s a flow. If the unit is a plain amount — liters, dollars, people, tons, degrees — it’s a stock.
The two-second test
Ask: “Could I photograph this at a single frozen instant?” If yes — it’s a stock (a plain amount: liters, dollars, people). If you’d need a stretch of time to measure it — an amount per unit of time — it’s a flow. Stocks are nouns you can photograph; flows are verbs you can only film.
The same machine, everywhere
The reason this distinction earns a whole course is that the same stock-and-flow skeleton sits under almost anything that builds up gradually — not just things you can pour into a bucket. Reputation, skill, debt, anger, followers, forest: all stocks, all fed and drained by flows.
| Stock (photograph it) | Inflow (fills it) | Outflow (drains it) |
|---|---|---|
| Water in a reservoir (liters) | Rain, rivers (L/day) | City draw, evaporation (L/day) |
| Money in a bank account ($) | Deposits, interest ($/month) | Spending, fees ($/month) |
| People in a country (persons) | Births, immigration (persons/yr) | Deaths, emigration (persons/yr) |
| CO2 in the atmosphere (gigatons) | Emissions (Gt/yr) | Ocean and plant absorption (Gt/yr) |
| Inventory in a warehouse (units) | Production, deliveries (units/day) | Sales, spoilage (units/day) |
| Skill in a craft (skill) | Deliberate practice (skill/week) | Forgetting, rust (skill/week) |
| Followers on an account (people) | New follows (people/day) | Unfollows (people/day) |
| Trust in a relationship (trust) | Kept promises (trust/week) | Broken promises (trust/week) |
Look down the middle and right columns: every flow carries a “per time.” Look down the left: none of the stocks do. That’s not a coincidence; it’s the test, made into a table. And notice “skill” and “trust” sitting there with a straight face. Anything that accumulates gradually and drains gradually is a stock — which is exactly why the bathtub model travels so far, from a reservoir to a marriage.
Sort the vocabulary by its unit.
Pick the right option for each blank, then check.
A quantity you could photograph at a single instant — like the 50,000 followers on an account — is a . A rate measured in amount-per-time — like the 300 new followers per day — is a . The dead giveaway is the : anything that needs a 'per [time]' is the rate, not the level.
The trap of quantities that masquerade
Most quantities announce themselves honestly, but a few wear disguises, and those are where smart people slip. The fix is always the same: ignore the noun, check the unit.
- “Cases” during an epidemic. New cases per day is a flow; active cases right now is a stock. A country can have falling new cases (flow dropping) while active cases (the stock of currently-sick people) is still rising — because people are getting infected faster than they’re recovering. Same disguise as the deficit and the debt.
- “Speed.” Speed is a flow — it’s distance per hour. The odometer reading (total distance) is the stock. Your speedometer and your odometer are a flow gauge and a stock gauge bolted to the same dashboard.
- “Income” versus “wealth.” Income is a flow (dollars per year); wealth is a stock (dollars, full stop). A surgeon with a $600k income and a $700k mortgage may have less wealth than a frugal teacher — high flow, low stock. Confusing the two is how people mistake a big paycheck for being rich.
- “Growth.” “The company grew 20%.” Grew what — revenue (a flow) or total customers (a stock)? “Growth” is a rate-of-change, so it’s almost always a statement about how fast a stock is moving, not the stock itself.
The pattern: a single word (“cases”, “growth”, “income”) gets used for both the level and the rate, and the listener picks whichever meaning is more comforting. Don’t. Check the unit, every time.
A health ministry proudly reports that the number of NEW infections per day has been falling for two weeks. A reporter asks whether the hospitals will get less crowded soon. What's the sharpest reading?
Dynamic equilibrium: a flat stock with roaring flows
Here’s the idea that most cleanly proves stocks and flows are different animals. A stock can hold perfectly still while enormous flows rush through it — as long as the inflow and outflow exactly cancel. Systems thinkers call this dynamic equilibrium: dynamic because the flows are roaring, equilibrium because the level isn’t budging.
A calm lake fed by a river and drained by a river is not a still lake — it’s a violently busy one that happens to balance. Your body holds about 37°C while a furnace of metabolism pours heat in and sweat and breath carry it out. A mature company can sit at exactly 5,000 employees for years while hiring 50 people a month and losing 50 a month — a flat headcount stock riding on top of constant, busy churn. In every case the level is boring and the flows are anything but.
Go back to the tub and feel it directly. Set the faucet and the drain to the same value — say 8 and 8 — and scrub time all the way across. The level doesn’t twitch. Now set them to 2 and 2: still flat, just a quieter version. The level sits wherever it started, at any height, regardless of how big the matched flows are. That’s the signature of equilibrium: not “no flow,” but “no net flow.”
Fill the tub
Find the equilibrium
Set the faucet and the drain — two independent rates — then drag the time slider. Watch the level integrate the net flow: it ramps up when the faucet wins, drains when the drain wins, and holds perfectly steady when they match (at any level).
Inflow 6 beats outflow 4 L/min: a net of +2 L/min. The stock climbs by 2 L every single minute — a straight ramp — even though neither flow ever changes. By minute 12 the level has reached 74 L. The level is the running total of the net flow, not the flow itself.
Equilibrium means no NET flow — not no flow
A steady stock does not mean nothing is happening. A lake, a body temperature, a company’s headcount can all sit rock-steady while gigantic flows pour in and out, exactly canceling. The level is flat because inflow equals outflow, not because the taps are off. Mistaking “the number isn’t moving” for “the system is idle” misses the entire busy machine underneath.
When to use it
Run the stock-or-flow check the instant a problem involves something that builds up over time — savings, emissions, headcount, backlog, body fat, skill, followers, technical debt. Before you propose a single fix, sort every quantity in the problem into level or rate, because half of all “obvious” solutions are obvious only because someone quietly mixed the two. And whenever you see a number that isn’t moving, don’t assume calm — ask whether you’re looking at a dead system or a dynamic equilibrium with a hurricane of flow underneath.
Each item is either a level you could photograph (a STOCK) or a per-time rate (a FLOW). Sort them — and watch for the disguised ones.
Place each item in the right group.
- The total distance on a car’s odometer
- The water sitting in a reservoir
- The river feeding the reservoir, in liters per day
- The number of people currently sick with a virus
- New infections per day
- Your total wealth (net worth) today
- Your salary in dollars per year
- The car’s speed in km/h
Match each term to its precise meaning.
Pick a term, then click its definition.
It’s a flow — and a great example of how the test cuts through fancy words. Acceleration is change in speed per second, so its unit carries a “per time” (meters per second, per second). It can’t be photographed at an instant; you need to watch speed change over time. In fact you can stack these: position is a stock, speed is its flow (the rate position changes), and acceleration is the flow of speed (the rate speed changes). Each layer adds a “per time” to the unit. The lesson isn’t the physics — it’s that the unit test never fails: count the “per times,” and you know exactly what you’re holding.
Where this goes next
You can now sort any quantity into stock or flow in about two seconds — photograph it (stock) or film it (flow), or just count the “per times” in its unit. You’ve met the net flow (inflow minus outflow) and seen its strangest trick: a stock that sits flat at any level while matched flows roar through it, the dynamic equilibrium.
But we’ve been describing snapshots. The real action is in motion — what happens to the level over time once the net flow isn’t zero. That’s governed by a single rule, the only equation this course needs, and it explains why a stock is the running total of everything that has ever flowed through it — why it smooths, why it lags, why it remembers. In Lesson 2, “Stocks Integrate,” we turn on the taps and watch the level accumulate, with real numbers on a real clock.