Size & scale

The radial bar chart

The value sets the angle. The ring sets everything else.

a.k.a. circular bar chart · the race track chart · radial column chart · the ring chart · progress rings · coord_polar · the bar chart bent into a circle · concentric arcs · the activity rings · polar bar

Bend a bar chart into a circle and each bar becomes an arc on its own concentric ring. The value still sets the angle, honestly and exactly — but what the reader measures is not the angle, it is the ink, and the length of an arc is its radius times its angle. So every bar on the chart has been multiplied by its ring, and a ring is not data. It is a slot, handed out by whatever order the rows happened to be in: alphabetical, the order they came back from the query, the order the legend lists them, the sort somebody clicked. Two categories with the same number get different bars; a category with a smaller number gets the longer bar whenever it got the outer ring by enough. The exchange rate is the ratio of the two radii — on a thirteen-ring chart the outermost ring is routinely four or five times the innermost — and it appears nowhere on the page, because the chart has no idea it is applying one. Inside a single ring the arcs are perfectly comparable, which is what makes it hard to see: nothing is exaggerated, no axis is bent, every number is drawn to its own correct angle, and only the comparison between rings — the entire reason the categories were put in one picture — is a fact about the seating plan. Two neighbours share the room and are worth telling apart. “The radar chart” puts categories on spokes from a common centre and asks the reader to judge the area of the polygon they enclose; this one gives every category its own ring and asks for a length that has been multiplied by which ring it got. “The gauge” is the one-ring case with a needle on it. And the coxcomb or polar-area rose is the same family again with the knob turned the other way: there the value sets the radius, so the area grows as the square of it, which is “The area illusion” drawn in polar coordinates. The family resemblance that matters most, though, is to “The free-scale small multiple”: both hand the reader a grid of marks that look like one chart and quietly price a unit of ink differently in each cell, and in both the exchange rate between cells is the one number the picture never prints.

How to spot it

Find two rings with the same number on them, or nearly. If one arc is plainly longer than the other, the difference you are looking at is the difference between two radii.
Compute the exchange rate: divide the outermost ring’s radius by the innermost. That is how much more a degree is worth at the edge than at the middle, and no radial chart prints it.
Ask what decided the ring order. Alphabetical, the order of the legend, the order of the source table, a sort somebody clicked — every one of those is a multiplier applied to the data by something that is not the data.
Read the innermost ring. It has the shortest radius on the chart, so its bar is the one most likely to look like nothing, whatever its value; a category can be third-worst and nearly invisible.
Look at the outermost ring with suspicion, not because it is wrong but because it is flattered. It is the ring that turns a middling number into the second-longest bar on the page.
Count the turns. A full circle is the axis maximum, so the frame is choosing the scale — and anything past a full turn either wraps round on top of itself or gets pinned at the top, which is the clipped axis arriving in a second body.
Notice that there is no shared baseline. Every arc starts at twelve o’clock on a different circle, so no two bars begin in the same place and none of them ends against a common ruler.
Ask what a gap between two arcs means. On a bar chart the gap is a difference; here it is a difference in angle drawn at two different radii, which is not a quantity in any unit.
The places they come from: a bar geometry sent through ggplot2’s coord_polar, the “radial bar” and “race track” widgets in ECharts, Highcharts, Flourish and most BI tools, and the activity-ring style of fitness and progress displays.

The fix

Unbend it. A sorted, zero-based horizontal bar chart is the same encoding with the multiplier taken out: one length per number, all of them starting at the same baseline and ending against the same ruler, in the order the values put them rather than the order the rows arrived in. That is the whole of the improvement and it is a large one, because length against a common baseline is the comparison people judge most accurately and a curved length at an undeclared radius is not a comparison at all. It costs the picture its symmetry, which is usually what the radial version was for; it buys a ranking the reader can read, room to print the numbers, and the ability to see a tie as a tie. Where the circle is genuinely wanted, the honest version of it is a dot on each ring rather than an arc, because a dot marks an angular position and position is all a shared angular axis can carry — no length is being multiplied, and the same ring-to-ring comparison becomes an alignment the eye can actually make. Keep the form outright where the quantity really is angular or cyclical — a wind rose, a chart of the hours of the day, a phase — since there the circle is the data rather than a decoration applied to it. And if a radial bar chart has to ship, at minimum draw the angular gridlines so the angles can be read, print every value on its own arc, order the rings by the values so the flattery at least runs the same way as the data, and say in the caption what a full turn is worth. A chart that has multiplied its data by thirteen different constants owes the reader a list of them.

In the gallery

Dark navy dashboard slide, masthead “Structures asset desk · national bridge inventory” on the left and “Share of a fleet rated poor · by owner · 2025” on the right, headlined “Thirteen owners, one ring each.” Beneath the headline sits a bordered chip reading “Demonstration · drawn by us from published figures”. A standfirst says every figure is the Federal Highway Administration’s own 2025 National Bridge Inventory summary — the share of each owner’s bridges whose lowest condition rating puts them in Poor; that all 623,810 bridges in the thirteen named owner classes are on the chart with nothing dropped, smoothed or rescaled; that the angular axis is linear, zero-based, evenly ticked and gridded with every value printed beside its own bar; that the rings are in the order the source lists the owner classes, which is the order of NBI Item 22; and that FHWA publishes these figures as a table while the rings are ours. The main panel, headed “Bridges rated poor, by owner · 2025” and subtitled “One ring per owner class · angle = share rated Poor · linear angular axis, 0–35% over 330°, gridded every 5 points · rings in NBI Item 22 order”, is a radial bar chart: thirteen concentric gold arcs on faint navy tracks, each starting at twelve o’clock and running clockwise, with dashed grey spokes marking every five points from 0% at the top round to 35%. The category labels are stacked at twelve o’clock, innermost at the bottom: State 4.4%, County 9.2%, Town 10.5%, City 6.5%, State Park 10.1%, Local Park 12.3%, Other State Agency 9.2%, Other Local Agency 7.2%, Private 6.5%, Railroad 33.1%, State Toll 2.5%, Local Toll 0.6%, Federal/Tribal 7.6%. The picture is dominated by Railroad, on the tenth ring, running almost all the way round; Federal/Tribal sweeps only a fifth of a turn but, on the outermost ring, draws the second-longest bar on the page. State, on the innermost ring, is a short stub near the middle, and County, on the second, is a little over a quarter-turn. A “How to read” note in the lower-left corner says each ring is one owner class, that the further round its arc travels the larger the share of that owner’s bridges rated Poor, and that every arc starts at the top and runs clockwise on the same angular scale. A caption reads “Published figures as reported · every named owner class · one angular scale throughout”. Two columns of cards run down the right. “The four long arcs” prints “4 of 13 owner classes” in large type and says that after Railroad, four classes draw the longest bars on the chart — Federal/Tribal, Local Park, Other State Agency and Other Local Agency — while State and County, on the two innermost rings, are among the shortest. “Read-out for the desk” says railroad-owned structures are the outlier at 33.1% Poor against a national 6.7%, that below that the weight of the chart sits with those four classes, none of them a state DOT or a county road department, that the two largest owners sit in the quiet centre of the picture, and recommends holding the state and county inspection cycle where it is and moving the supplementary allocation to the four long arcs, where the ink is. “Every value on the chart” tabulates all thirteen rings with their owner class, share Poor, number Poor and total bridges, from State (4.40%, 12,799 of 290,912) to Federal/Tribal (7.56%, 859 of 11,363). “The ring order” explains that the rings run outward in the order the source lists the owner classes — State, County, Town, City, and so on out to Federal/Tribal — that the chart adds nothing to it, and that Item 22 is a codebook field whose federal codes are rolled into the single Federal/Tribal row on the outermost ring, the rings inheriting that order because it is the order the rows arrived in. “How a bridge is rated” explains that inspectors score the deck, superstructure and substructure from 0 to 9 — for a culvert, its culvert rating — and that the lowest of those sets the classification — 7–9 Good, 5–6 Fair, 0–4 Poor — and that Poor does not mean unsafe. “What a full turn is worth” says the angular axis runs from 0% to 35% across 330° of arc, so one percentage point is 9.43° on every ring. “Who owns what” notes that State (290,912 bridges) and County (226,268) hold more than four-fifths of the inventory, while the four classes above hold 14,090 between them, or 2.3% of the structures on the chart. “Why a share and not a count” says the owner classes hold wildly different numbers of structures, from 146 to 290,912, so a count of Poor bridges would rank the large owners first whatever condition they were in — the share answers how likely, not how many. “The national picture” gives 41,685 of 624,193 bridges rated Poor, 6.7% of the inventory, with 309,729 Fair and 272,779 Good. “Basis of measurement” credits the Federal Highway Administration, National Bridge Inventory, “Bridge Condition by Owner 2025”, table dated 15 June 2025 and page updated 23 June, totals for all states, DC, Guam, Puerto Rico and the U.S. Virgin Islands, notes that Guam did not submit data for 2025, and says the thirteen named owner classes are shown while the residual rows — Other (13 bridges), Unknown (370) and Null (0) — are left out and named, being 0.06% of the inventory, retrieved 10 September 2026. A method line runs along the foot: published figures as reported; every named owner class; linear angular axis, zero-based, gridded; every value printed; nothing smoothed, dropped or rescaled. A footnote credits the source, says all thirteen values are as published, and states that FHWA publishes them as a table while this slide is a demonstration drawn by us in the manner of an asset-management dashboard — the desk, the read-out and the recommendation are invented, and every figure behind them is real.

The 9.17% drawn 2.17 times longer than the other 9.17%

The radial bar chart