Size & scale

The Sankey ribbon

A ribbon is a length that has been bent, and two of them are never added by eye.

a.k.a. Sankey diagram · alluvial diagram · flow diagram · the income-statement Sankey · the P&L Sankey · the where-the-money-goes chart · riverplot · d3-sankey

A Sankey encodes each quantity as the vertical distance between a ribbon’s two edges, and the arithmetic is usually impeccable — every ribbon to one scale, every node conserving its total. What it asks of the reader is harder than it looks, in three ways. It ranks by shape, so anything split across two ribbons is judged as two ribbons: salary beside benefits, licence beside support, each labelled, each correct, and no shape on the page for the pair. It gives every ribbon a slope, and a sloped band’s width — measured across it, which is the dimension there is to look at — is its drawn thickness times the cosine of that slope, the ink unchanged and the split between width and length quietly moved. And the slope itself is not a fact about the number: it comes from where the band landed in the stacking order and from how much horizontal run the diagram was given, which is a fact about the panel. Under all three sits the plainest thing of all. A Sankey prints no scale, draws no gridline and offers no baseline, so a ribbon can only be judged against its neighbours.

How to spot it

Ask whether one thing has been drawn as two ribbons. Wages and benefits, hardware and shipping, licence and support: each is labelled, each is right, and nobody adds two shapes by eye — so a category drawn twice reads smaller than its total.
Look for the scale. A Sankey carries none, which means the numbers you are reading came off labels rather than off the chart, and a ribbon you cannot find a label for is unmeasurable.
Check the outermost ribbons, top and bottom, since a fan puts its steepest bands at its edges. On the curved links most libraries draw, the slope halfway across is exactly twice the average, and that waist is the narrowest the ribbon ever gets — so read the pinch as the worst case rather than the whole story.
Measure the diagram’s stack against its horizontal run. Pour the same fan into a narrow column and every slope steepens: it is the aspect-ratio trick riding along, and the shape of the box is the one parameter no chart has ever printed.
Reorder the nodes in your head. Nine categories have 362,880 orderings and the picture looks equally finished in all of them — though not every re-ordering does something, since reversing one changes no slope at all, a fan being symmetric about its centre.
Ask what is flowing. Where a total simply fans out into its parts, nothing moves between the two columns, and the whole apparatus of nodes and crossings is drawn over what is really a list.
On a multi-stage diagram, remember that ink is not conserved the way the quantity is: a flow crossing four stages is drawn four times, and the node that appears in every stage looks the most important by construction.

The fix

Decide which of the two questions a flow diagram gets asked you are actually answering, because it is reliably good at one of them. Where does it go is its question: a quantity that genuinely moves, conserved at every node, the crossings carrying the routing — crude oil into refined product into end use, water through a catchment, a cohort through four stages of a funnel. Which is biggest is not, because ranking wants marks on a shared baseline and a fan has no baseline to share. Asked the second question, reach for a sorted bar chart and let the ribbons go. Before you draw either, add up the things that are one thing: a cost split across two rows is one cost, and the reader should meet it as one mark with its parts inside rather than as two shapes to combine mentally. When a Sankey is right, hand it what it is missing. It has no axis, so the scale goes in the caption the way a unit goes on one, and every ribbon gets its number printed on it. It has an ordering, so choose one deliberately, say what you sorted by, hold it across every version, and put whatever ought to be read together next to itself. It has a shape, so state the proportions or keep them fixed, since the same fan in a narrow column charges its outer ribbons several times what a wide one does. And where both questions are genuinely live, the honest answer is usually both charts — the flow for the routing, a short sorted chart beside it for the ranking, and no confusion about which one the decision came off.

In the gallery

Dark navy briefing slide, masthead “Fleet cost briefing · Class 8 truckload · Marginal cost per mile · Calendar year 2025 · Industry average · US$”, headlined “Every mile costs $2.336. Here is where it goes.” A standfirst says there are nine line items, one flow diagram and every cent of the mile on the page; that the figures are the publisher’s own and close exactly, the nine ribbons summing to $2.336, the total cost of operating a Class 8 truck for one mile in 2025, 3.4% above 2024’s $2.260 and the highest in the report’s history; that every ribbon is drawn to one scale with its thickness set by its own line item; that nothing is indexed, annualised, smoothed, projected or rebased; that no category has been merged into an “other” bucket and none dropped; and that no axis has been truncated, broken or capped. It closes by reading off the diagram: the largest single band is driver wages at 35.0% of the mile, no other band reaches 21%, and the four vehicle-side items — fuel, equipment, maintenance and tires — take $1.151 of every mile between them. The main panel, headed “The cost of a mile, as it flows out · All nine line items · ATRI, calendar year 2025 · ribbon thickness proportional to dollars per mile”, is a one-source Sankey diagram of the kind a charting library draws by default. A single gold bar on the left is labelled “$2.336 · One mile, one truck · Marginal cost, 2025”, and nine steel-blue ribbons fan out of it across the width of the panel to nine labelled nodes on the right, each label carrying its dollars and its share: Driver wages $0.818 per mile, 35.0% of the mile, at the very top and by a clear margin the fattest ribbon in the picture, sweeping upward; Truck & trailer lease or purchase $0.404, 17.3%; Fuel $0.482, 20.6%, the second-fattest, rising gently across the middle; Repair & maintenance $0.215, 9.2%, nearly level; Truck insurance premiums $0.106, 4.5%, dead level at the centre of the fan; Tires $0.050, 2.1%; Tolls $0.043, 1.8%; Permits & licenses $0.008, 0.3%, a hairline; and Driver benefits $0.210, 9.0%, at the very bottom, seven ribbons below driver wages and descending at the same angle by which wages climbs. A caption under the diagram reads “Ribbon thickness ∝ dollars per mile · one scale throughout · all nine line items shown.” Six cards run down the right. “The mile, in one figure” prints $2.336 in large type over a note that this is marginal cost per mile for Class 8 operations in 2025, up 3.4% on 2024, and $1.854 excluding fuel, up 4.2% and ahead of 2.7% consumer inflation. “Read-out for the operations committee” says the mile is diversified, that the largest single band on the diagram is driver wages at 35.0% while nothing else reaches 21% and six of the nine bands are under a tenth of the mile each, and that this shape argues against looking for one big saving and in favour of working the vehicle side where the ribbons cluster — fuel, equipment payments, maintenance and tires being four of the nine bands and $1.151 of every mile, 49.3%, against 35.0% for the largest band on the chart. “Cost-reduction priorities, in the order the diagram gives them” lists six: fuel economy programme $0.482 at 20.6%, equipment cycle and residuals $0.404 at 17.3%, maintenance intervals $0.215 at 9.2%, insurance re-tender $0.106 at 4.5%, tire policy $0.050 at 2.1% and routing and tolls $0.043 at 1.8%, with a note that driver wages sit outside the list because the band is large but pay is set by a market the fleet does not control. “The nine line items, as filed” tabulates all nine — driver wages $0.818, fuel $0.482, truck & trailer $0.404, repair & maintenance $0.215, driver benefits $0.210, truck insurance $0.106, tires $0.050, tolls $0.043, permits & licenses $0.008 — with the total $2.336. “How to read the diagram” tells the reader to follow a ribbon from the bar on the left to its label on the right, says the thicker the ribbon the larger the item, and adds that all nine are drawn to a single scale so two ribbons of the same thickness are the same money. “Why a flow diagram” says a pie would need a legend and a bar chart would need an axis, while a flow diagram carries the whole mile as one shape. A final card gives the basis of measurement: the American Transportation Research Institute’s An Analysis of the Operational Costs of Trucking: 2026 Update, July 2026, calendar-year 2025, industry-average marginal cost per mile across all sectors and fleet sizes. Five ticked boxes run along the foot: “All nine line items shown”, “No ‘other’ bucket”, “One scale for every ribbon”, “Items sum to the published total” and “No axis truncated, broken or capped”. A footnote credits the source, notes the nine line items sum to $2.336, and says the slide is a demonstration drawn by us in the manner of a fleet cost briefing — the committee, the read-out and the priority list are invented, and every figure behind them is real.

The 44% of a truck mile that arrives as two ribbons

The Sankey ribbon