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Sankey diagram

Sankey diagram is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Sankey diagram rather than just read about it. In short: Sankey diagrams are a data visualisation technique or flow diagram that emphasizes flow/movement/change from one state to another or one time to another, in which the width of the arrows is proportional to the flow rate of the depicted extensive property. The arrows being connected are called nodes and the connections are called links.

Sankey diagram — main illustration
Sankey diagram — illustration

Key takeaways

  • Sankey diagram belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Sankey diagram to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Sankey diagram from memory before moving on to harder problems.

Reference excerpt

Sankey diagrams are a data visualisation technique or flow diagram that emphasizes flow/movement/change from one state to another or one time to another, in which the width of the arrows is proportional to the flow rate of the depicted extensive property. The arrows being connected are called nodes and the connections are called links. Sankey diagrams can also visualize the energy accounts, material flow accounts on a regional or national level, and cost breakdowns. The diagrams are often used in the visualisation of material flow analysis. Sankey diagrams emphasize the major transfers or flows within a system. They help locate the most important contributions to a flow. They often show conserved quantities within defined system boundaries.

History and name Sankey diagrams are named after Irish Captain Matthew Henry Phineas Riall Sankey, who used this type of diagram in 1898 in a classic figure (see diagram) showing the energy efficiency of a steam engine. The original charts in black and white displayed just one type of flow (e.g., steam); using colors for different types of flows lets the diagram express additional variables. Over time, it became a standard model used in science and engineering to represent heat balance, energy flows, material flows, and since the 1990s this visual model has been used in life-cycle assessment of products.

One of the most famous Sankey diagrams is Charles Minard's Map of Napoleon's Russian Campaign of 1812. It is a flow map, overlaying a Sankey diagram onto a geographical map. It was created in 1869, predating Sankey's diagram of 1898. Minard had used this form of diagram for visualising flow of goods and transport of people from at least since 1844.

Use in science

Sankey diagrams are often used in fields of science, especially physics. They are used to represent energy inputs, useful output, and wasted output.

Current examples The US Energy Information Administration (EIA) produces numerous Sankey diagrams annually in its Annual Energy Review which illustrate the production and consumption of various forms of energy. The US Department of Energy's Lawrence Livermore Laboratory maintains a site of Sankey diagrams, including US energy flow and carbon flow. Eurostat, the Statistical Office of the European Union, has developed an interactive Sankey web tool to visualise energy data by means of flow diagrams. The tool allows the building and customisation of diagrams by playing with different options (country, year, fuel, level of detail). The International Energy Agency (IEA) created an interactive Sankey web application that details the flow of energy for the entire planet. Users can select specific countries, points of time back to 1990, and modify the arrangement of various flows within the Sankey diagram.

See also Alluvial diagram – a type of Sankey diagram that uses the same kind of representation to depict how items re-group Material flow management Parallel coordinates Time geography

References

External links Media related to Sankey diagrams at Wikimedia Commons

Illustrations

Sankey diagram: A Sankey diagram of seats held by parties before and after the 2021 West Bengal Legislative Assembly election
A Sankey diagram of seats held by parties before and after the 2021 West Bengal Legislative Assembly election
Sankey diagram: Sankey's original 1898 diagram showing the energy efficiency of a steam engine
Sankey's original 1898 diagram showing the energy efficiency of a steam engine
Sankey diagram: Minard's diagram of Napoleon's invasion of Russia, using the feature now named after Sankey
Minard's diagram of Napoleon's invasion of Russia, using the feature now named after Sankey
Sankey diagram: Earth's energy budget – line thickness is linearly proportional to relative amount of energy
Earth's energy budget – line thickness is linearly proportional to relative amount of energy
Sankey diagram: Balance of trade with the United States (2023)
Balance of trade with the United States (2023)

Worked examples

Example 1 — a first encounter with Sankey diagram

Start with the simplest possible case. Write down what Sankey diagram claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Sankey diagram before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Sankey diagram ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Sankey diagram

In research
Sankey diagram appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Sankey diagram in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Sankey diagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1840s in science, British inventions, Eponymous diagrams, so understanding it makes those chapters shorter.
In everyday life
Look for Sankey diagram outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Sankey diagram in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Sankey diagram means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Sankey diagram out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sankey diagram in simple terms?

Sankey diagrams are a data visualisation technique or flow diagram that emphasizes flow/movement/change from one state to another or one time to another, in which the width of the arrows is proportional to the flow rate of the depicted extensive property. The arrows being connected are called nodes…

Why does Sankey diagram matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Sankey diagram?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Sankey diagram.

Tags

  • 1840s in science
  • British inventions
  • Eponymous diagrams
  • French inventions
  • Irish inventions
  • Material flow
  • Statistical charts and diagrams

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