What is a Sankey diagram?

Adapted from Electrify, by Saul Griffith,
MIT Press (2021)


What is a Sankey diagram?

Adapted from Electrify, by Saul Griffith, MIT Press (2021)




I am a little obsessed with what is called a “Sankey diagram” (I even once had shower curtains made with Sankeys on them). They’re elegant tools that can communicate complex issues—the big picture and the little details at once—and they are fairly simple to understand. They are particularly good at allowing us to visualize energy flows, so that we know how much our energy needs are in order to understand how and where we can replace fossil fuels with electricity backed by renewables

The first Sankey-style flow diagram that we know of was drawn by a French engineer named Charles Joseph Minard. In 1845, he created a flow chart to depict the traffic on roads between Dijon and Mulhouse, France, to inform the routing of a new railroad. In 1869, he created the chart that he is best known for: a visualization of Napoleon’s foray into Russia, his retreat, and troop losses throughout the campaign.

Figure 21.1The often-cited 1869 “Sankey” diagram of Napoleon’s troop levels as he fought his way into, and back from, Russia


The two-dimensional band chart displays six types of data: the number of Napoleon’s troops, the distance they traveled, temperature, latitude and longitude, direction of travel, and their location on specific dates.

The pink line that starts out thick on the left is proportional to the number of troops that were alive at any point. The thinner the line, the more tragic the story. By the time he arrived in Moscow, he’d lost two-thirds of his troops, and then he was beaten all the way back, losing more men along the way, as represented by the black line. The chart shows that by the time he returned to Kowno, his 422,000 troops had been reduced to just 10,000.

The original Sankey diagram, by Captain Sankey. We can see from Sankey’s diagram the conversion of coal energy into pressurized water and steam in the boiler, and the consequent losses as it is turned into propulsive power at the propeller of his boat.  


The year after Minard created his flow chart of Napoleon’s 1812–13 Russian campaign, Irish Captain Matthew Henry Phineas Riall Sankey created a flow chart to visualize the efficiency of the steam engine (that presumably powered his ship). This is the first known use of the (as it would become known) Sankey diagram to visualize the flow of energy. The width of the arrows is proportional to the flow rate of energy.

At the time, coal had become an important fuel in powering ocean-going vessels, and for very good reason. Wind doesn’t always blow, and only rarely from the direction you want. Coal sits in the bottom of your hull, ready to use at a shovel’s notice. While many sailors were still mainly concerned with the weather and sails, Sankey was diagramming the conversion of coal energy into pressurized water and steam, and understanding the energy losses along the way.

Sankey diagrams are particularly good for visualizing energy because they conserve proportion at every point along the flow. This gels well with the law of conservation of energy and the related first law of thermodynamics, which both state that energy can neither be created nor destroyed, but can only change from one form to another.

This Sankey diagram is more relatable to your everyday life. This takes Census Bureau data for household spending in the average US home and represents it as flow.


If you look where energy is lost in the flows, it is typically to heat. This is as true today as it was for Captain Sankey; the cold hard destiny of all energy is that eventually it becomes low-grade heat from which it is too difficult to extract useful work. The temperature of the universe is 2.73°K, –270°C or –455°F—chilly no matter what unit we express it in. The fate of all of our waste heat here on earth will ultimately be to radiate its way out into space as it cools to the temperature of the universe.

I am mostly concerned with energy budgets. To illustrate them with an analogy, most people have some understanding of their household budget, so in figure 21.3, I present the average US household budget as a Sankey flow diagram. 

The chart is read from left to right. The inputs to the house are things like income and interest on accounts. These flow into a total household budget. The total household budget then flows into four large categories of things: housing, transportation, food, and the catch-all bucket “everything else.” These further break down into the minutiae of how we spend money—on gasoline, eating out, clothes, and other activities of our daily lives. This same data is presented in table form in figure 21.4.

The average US household is known as the “consumer unit.” Consumer units include families, single persons living alone or sharing a household with others who are financially independent, or two or more persons living together who share major expenses. In 2019, the average American consumer unit had a pre-tax income of $78,635.

The average household expenditures totaled $61,224. We can see that it is spent on four large categories of things: transportation, housing, food, and everything else. Housing is the biggest category. $3,477 is spent in the home on utilities, fuels, and public services; we can already see the link between energy and our own personal budget. Transportation is another big segment; of that sector, a third flows into the cost of gasoline. The average household spends a little more than that on health care, and less on savings and retirement. We spend less again, under $1,000, on education. We spend only about $120 a year on reading.

Just as some of you might be interested in chasing down every dollar in your household budget, I’m interested in tracking down every joule of energy in the US and global economy. Sankey diagrams have been instrumental in this analysis. Let’s go for an eye-opening ride (if you can keep your eyes open!).

Sankey diagrams found widespread use during the oil crises of the early 1970s. In 1973, Jack Bridges, working for the Joint Committee on Atomic Energy, reprised the Sankey and improved upon it in a fabulous book, Understanding the National Energy Dilemma. The United States had just experienced oil shortages, and energy was on people’s minds.

The book was quite novel. It not only employed a Sankey to show current energy trends, it provided historic Sankeys and future projections to communicate the challenges of planning and delivering a country’s energy supply. A Sankey of 1950, 1960, 1970, 1980, and 1990 were included in special full-color, fold-out centerfolds. These fold-outs were intended to be assembled into a three-dimensional view of the history and future of US energy consumption. It showed the rapidly increasing total demand, divided into portions of “lost” energy and “used” energy. Lost energy is waste heat.

Table 21.1. Average Income and Expenditures of All Consumer Units, 2016–18


Place yourself in the historical context of this diagram, when the energy world was in upheaval. There was a major oil crisis because America’s appetite for oil had outpaced its production, and for the first time our energy destiny, growth capacity, and entire future as a nation were tied to geopolitics. Everything was being disrupted; our desire for electricity was proving as insatiable as our desire for gasoline, and we were installing hydroelectric plants everywhere we could. Nuclear-powered electricity was just starting to take off, and estimates of its future potential were hyperbolic; it was already controversial.

Nuclear advocates at the time would say that “electricity will be too cheap to be metered.” People had a renewed interest in wind power for generating electricity, and some people at the fringes were just starting to talk about solar architecture and solar thermal. The changing energy landscape, and the urgency of the oil crises, underscored the importance of tools for visualizing and planning the future of the American and global energy supply.

The methodologies behind these visualizations are now used in the EIA Annual Energy Review (AER) and in yearly summaries of the energy economy made public by Lawrence Livermore National Laboratory (LLNL).

Perhaps the most intense Sankey diagram is the one by Wes Hermann, shown in figure 21.4. I was first introduced to this chart in around 2007 by Wes, who interviewed with me for my company Makani Power. Wes didn’t take the job with us, though the interview was great; he took a job with a young electric vehicle company—Tesla—instead. When I asked him about the choice, emphasizing how important wind energy was, he simply replied that burning gasoline to run cars was the dumbest destruction of otherwise useful energy in the whole system and that electric cars were the only way to go. He was right about electric cars, though wind is still key. He made the chart as a student of the Global Climate and Energy Program at Stanford. While the chart itself is nearly impossible to read without more explanation than I can provide here, what it shows are all possible energy sources on planet earth, including fossil fuels—which are only a tiny fraction of our possible energy sources. We have many other sources of energy.

Wes Herman’s Sankey charts for Exergy and Carbon

These visualizations of our energy sources and uses allow us to imagine that if we electrify everything, we will need far less energy to begin with. The Sankey diagrams give us the opportunity to clearly see a carbon-free future.