A proportional symbol map is a type of map where symbols, most commonly circles, change in size to reflect the data values they represent. If one city has twice the population of another, its circle will have twice the area. This direct, visual relationship between symbol size and data value is what makes the map “proportional” and distinguishes it from other thematic mapping techniques.
How Proportional Symbol Maps Work
The core idea is simple: bigger values get bigger symbols. Each location on the map receives a symbol whose size corresponds to a quantity at that location, such as population, revenue, earthquake magnitude, or number of COVID cases. The symbols are placed at specific points, whether those points represent cities, counties, or countries.
Circles are the most popular choice, but proportional symbols can also be squares, bars, or even three-dimensional shapes like spheres and cubes. When applied to polygon data (like states or countries), the symbol typically draws at the center of the polygon rather than filling the entire shape. This keeps the focus on comparing values rather than on the geographic size of each region, which is a common distortion in other map types like choropleths.
Scaling: How Symbol Sizes Are Calculated
The math behind proportional symbols depends on the type of symbol being used. For one-dimensional symbols like bars or columns that only grow taller, the relationship is straightforward: a value twice as large produces a bar twice as tall. A bar’s height is directly proportional to the data value it represents.
For two-dimensional symbols like circles and squares, things get slightly more complex. Because a circle grows in two directions at once, you can’t simply double the radius to represent a doubled value. Doubling the radius would actually quadruple the area, making the symbol look four times as large. Instead, the radius is scaled using a square root function so that the circle’s area stays proportional to the data value. This formula works the same way regardless of whether you’re using circles, squares, or any other flat shape.
Three-dimensional symbols like spheres and cubes use a cube root function for the same reason. Since volume expands in three directions, you need the cube root to keep the perceived size in line with the data.
The Perception Problem
Even when the math is perfectly correct, human eyes don’t always cooperate. Research dating back to the 1950s found that people consistently underestimate the size of larger circles. When shown two circles where one has twice the area of the other, most viewers judge the larger circle as less than twice as big. This means a mathematically accurate proportional symbol map can still be visually misleading.
To fix this, cartographer James Flannery developed an adjustment formula known as Flannery compensation. Instead of using a pure square root (an exponent of 0.5), the formula uses an exponent of approximately 0.5716, which makes larger symbols slightly bigger than strict math would dictate. The result is a map where the perceived differences between symbols more closely match the actual differences in data. Many cartographers apply this correction by default when working with circles, though some prefer the mathematical precision of uncompensated scaling.
Proportional vs. Graduated Symbols
These two terms are often confused, but they represent different approaches. A proportional symbol map uses a continuous scale: every unique data value gets its own unique symbol size. A city of 500,000 people and a city of 502,000 people will have slightly different circles.
A graduated symbol map, by contrast, groups data into classes. You might have one symbol size for cities with 0 to 250,000 people, another for 250,001 to 500,000, and so on. This makes the map easier to read at a glance but sacrifices precision. Two cities with very different populations could end up with the same symbol if they fall in the same class. The choice between the two comes down to whether precision or readability matters more for your purpose.
When Proportional Symbols Work Best
Proportional symbol maps are ideal for data that represents countable or measurable quantities at specific locations: total population, number of hospital beds, tons of carbon emissions, or dollar amounts of economic output. The data needs to be numeric and continuous, not categorical. You wouldn’t use proportional symbols to show which political party won each state, for example.
They’re especially useful when you want to avoid the area bias built into choropleth maps (the colored-region maps you see in election coverage). On a choropleth, geographically large regions with small populations can dominate the visual impression. Proportional symbols sidestep this because the symbol size is tied to data, not geography. A tiny city-state can have a much larger circle than a sprawling but sparsely populated territory.
Common Challenges
The biggest practical problem with proportional symbol maps is overlap. When data points are clustered close together, their symbols stack on top of each other. Research in cartographic perception has shown that when circles are partially hidden behind other circles, viewers have a much harder time judging their size accurately. In dense areas, some symbols can become completely obscured, cluttering the map without conveying any information at all.
Several strategies help manage this. Making symbols semi-transparent lets you see overlapping circles underneath. Sorting the drawing order so smaller symbols sit on top of larger ones prevents small values from disappearing entirely. Some mapmakers offset symbols slightly from their true locations to reduce overlap, though this trades geographic accuracy for readability. In web maps and interactive tools, clustering algorithms can consolidate nearby points at zoomed-out views and reveal individual symbols as you zoom in.
Another limitation is that proportional symbols are harder to read precisely than, say, a bar chart. Viewers can tell that one circle is bigger than another, but estimating that it represents exactly 2.3 times the value is difficult. Legends help, but even well-designed legends only give a few reference points. For this reason, many interactive proportional symbol maps include tooltips that display exact values when you hover over a symbol.
Creating Proportional Symbol Maps in GIS Software
Most major GIS platforms support proportional symbols as a built-in option. In ArcGIS Pro, you apply proportional symbology through the Symbology pane, where you choose a numeric field from your data and set a minimum symbol size. The software then scales all other symbols relative to that minimum. You can use relative sizing (for raw counts or values without a unit) or actual sizing (for measurable quantities like area or volume where the symbol matches a real-world unit of measure).
You can also set a maximum symbol size to cap how large the biggest symbols get, which is useful when your data has extreme outliers that would otherwise dominate the map. All values between the minimum and maximum draw proportionally within that range, and anything beyond the limits gets the smallest or largest symbol. QGIS offers a similar workflow through its layer styling panel, and most web mapping libraries like Leaflet and Mapbox GL support proportional circles through straightforward code.
ArcGIS Pro also lets you layer additional variables onto proportional symbols by varying their color, transparency, or rotation. This lets a single symbol communicate two pieces of information at once: size for population and color for median income, for instance. Be cautious with this approach, though, since adding too many visual variables at once can make the map harder to read rather than more informative.