Minimum dimensions for cartographic symbology – history, rationale and relevance in the digital age

Figures & data

Figure 1. The apparent size of objects, expressed as angle δ, defines the size of their retinal image and depends on their real-world size (S₁, S₂) and distance from the observer (D₁, D₂).

Table 1. Various real-world sizes at 30 and 60 cm viewing distances, and their corresponding angular sizes, logMAR and ppi values. Numbers set in bold indicate anchoring values of special relevance, as explained in the comments column and referred to from various parts of the paper.

Size @ 30 cm mobile, printed maps	Size @ 60 cm desktop screen	Apparent size (minutes of arc)	logMAR	PPI @ 30 cm mobile resolution	PPI @ 60 cm desktop resolution	Comments
1.00 mm	2.00 mm	11.46'	1.06	25	13	Metric units
0.10 mm	0.20 mm	1.15'	0.06	254	127	”
0.50 mm	1.00 mm	5.73'	0.76	51	25	”
0.05 mm	0.10 mm	0.57'	−0.24	508	254	”
0.09 mm	0.17 mm	1.00'	0.00	292	146	20/20 Vision
0.04 mm	0.09 mm	0.50'	−0.30	577	289	Upper limit of visual acuity
0.02 mm	0.03 mm	0.17’	−0.76	1693	847	Vernier acuity
0.16 mm	0.31 mm	1.79'	0.25	163	81	iPhone 1st Gen.
0.08 mm	0.16 mm	0.89'	−0.05	326	163	iPhone 4
0.06 mm	0.11 mm	0.63'	−0.20	460	230	iPhone 13 Pro
0.05 mm	0.10 mm	0.58'	−0.23	500	250	Samsung Galaxy S22 Ultra
0.03 mm	0.06 mm	0.36'	−0.44	801	401	Sony Xperia Z5 Pro
0.15 mm	0.30 mm	1.72'	0.24	169	85	Conventional Pixel
0.11 mm	0.22 mm	1.26'	0.10	231	116	CSS Pixel (1/96th inch @ 28 inch)

Table 2. Minimum dimensions for cartographic point symbols, as specified by various authors. Only values for optimal contrast are listed. Values established in empirical studies are set in bold, values converted from other units for this paper are set in italics.

Symbol type: Point
Value	Symbol type/dimension	Source
0.1 mm	Point diameter (as part of fill pattern)	Imhof (1972)
0.2 mm	Point diameter (in groups)	Imhof (1972)
0.3 mm	Point diameter (circular)	Imhof (1972)
0.6 mm	Point diameter (simple geometric figures, filled)	Imhof (1972)
1.0 mm	Point diameter (simple geometric figures, hollow)	Imhof (1972)
1.5 mm	Point diameter (simple graphical icons)	Imhof (1972)
0.24 mm	Point diameter (dot)	Arnberger and Kretschmer (1975)
0.44 mm	Point diameter (circular)	Arnberger and Kretschmer (1975)
0.40 mm	Side length of square	Arnberger and Kretschmer (1975)
0.3 mm	Point diameter (circle/square)	Schweizerische Gesellschaft für Kartografie (1980)
0.3 mm	Point diameter (hollow circle)	Schweizerische Gesellschaft für Kartografie (1980)
0.15 mm	Point diameter (circular)	Schweizerische Gesellschaft für Kartografie (1980)
1.0 mm	Side length (hollow triangle)	Schweizerische Gesellschaft für Kartografie (1980)
0.48 mm	Side length of square symbol (>95% correct identification)	Chlupac (1982)
0.50 mm	Side length of triangle symbol (>95% correct identification)	Chlupac (1982)
0.21 mm	Short side of 2:1 rectangle symbol (>95% correct identification)	Chlupac (1982)
2 arcmin (≈ 0.3 mm @ 50 cm)	Point diameter	Robinson et al. (1995)
0.25 mm	Point diameter	Hake et al. (2002)
0.5 mm	Point diameter (circle/square)	Hake et al. (2002)
0.6 mm	Point diameter (circle/square, hollow)	Hake et al. (2002)
0.30 mm	Point diameter (circular)	Schweizerische Gesellschaft für Kartografie (2002)
0.70 mm	Side length (hollow square)	Schweizerische Gesellschaft für Kartografie (2002)
0.80 mm	Cross symbol	Schweizerische Gesellschaft für Kartografie (2002)

Table 3. Minimum dimensions for cartographic line symbols, as specified by various authors. Only values for optimal contrast are listed.

Symbol type: Line
Value	Symbol type/dimension	Source
0.05 mm	Line width	Arnberger and Kretschmer (1975)
0.1–0.15 mm	Line width (contour lines)	Arnberger and Kretschmer (1975)
0.15 mm (better: 0.25 mm)	Line separation (for counting contour lines)	Arnberger and Kretschmer (1975)
0.05 mm	Line width	Schweizerische Gesellschaft für Kartografie (1980)
0.1 mm	Line width (dotted line)	Schweizerische Gesellschaft für Kartografie (1980)
0.25 mm	Line separation	Schweizerische Gesellschaft für Kartografie (1980)
0.05 mm	Line width	Hake et al. (2002)
0.25 mm	Line separation (fine lines)	Hake et al. (2002)
0.15 mm	Line separation (thick lines)	Hake et al. (2002)
0.2 mm	Line separation	Töpfer (1974)
0.08 mm	Line width	Schweizerische Gesellschaft für Kartografie (2002)
0.08 mm	Line width (double line)	Schweizerische Gesellschaft für Kartografie (2002)
0.25 mm	Line separation (double line)	Schweizerische Gesellschaft für Kartografie (2002)
0.15 mm	Line width (dotted line)	Schweizerische Gesellschaft für Kartografie (2002)

Figure 2. Graphical representation of current symbology guidelines for printed maps, extracted from Hake et al. (2002) and Schweizerische Gesellschaft für Kartographie (2002).

Figure 3. Applying minimum dimensions in the generalization of building footprints (Spiess, 1990).

Table 4. Minimum dimensions for areas on maps, as specified by various authors. Only values for optimal contrast are listed.

Symbol type: Area
Value	Symbol type/dimension	Source
0.25 mm²	Area size (footprint of lake)	Töpfer (1974)
0.4–0.6 mm	Area diameter (for recognizing form)	Arnberger and Kretschmer (1975)
0.25 mm	Area separation	Schweizerische Gesellschaft für Kartografie (1980)
1 mm²	Area size (for recognizing color)	Hake et al. (2002)
0.3 mm	Area size (side length of rectangle)	Hake et al. (2002)
0.20 mm	Area separation (rectangle, small areas)	Hake et al. (2002)
0.15 mm	Area separation (rectangle, large areas)	Hake et al. (2002)
0.35 mm	Side length of square	Schweizerische Gesellschaft für Kartografie (2002)
0.20 mm	Separation of rectangular shapes	Schweizerische Gesellschaft für Kartografie (2002)
0.80 mm	Minimum diameter of colored area	Schweizerische Gesellschaft für Kartografie (2002)

Table 5. Minimum dimensions for text labels on maps, as specified by various authors.

Symbol type: Text labels
Value	Symbol type / dimension	Source
1.2 mm	Text height	Schweizerische Gesellschaft für Kartografie (1980)
0.6 mm	Text height (optimal contrast)	Hake et al. (2002)
1.0 mm	Text height (reduced contrast)	Hake et al. (2002)
3.2 points (≈ 1.15 mm)	Text height (uppercase, sans serif)	Slocum et al. (2009)

Figure 4. Development of pixel densities of mobile phone screens over the last 20 years. Pixel density of commercially available devices has peaked at about 800 pixels per inch (PPI). Sources: pixensity.com, wikipedia.org.

Table 6. Minimum dimensions for point symbols on screen, as specified by various authors. Values established in empirical studies are set in bold, values converted from other units for this paper are set in italics.

Symbol type: Point
Value in pixels	Metric dimension	Dimension	Source
	1.2 mm @ 60 cm	Side length of triangle^4	Malić (1998)
	1.2 mm @ 60 cm	Side length of square^4	Malić (1998)
	2.1 mm @ 60 cm	Diameter of circle^4	Malić (1998)
	3.0 mm @ 60 cm	Diameter of circle	Brunner (2000)
	2.0 mm @ 60 cm	Side length of square	Brunner (2000)
10 phys. pixel		Diameter of circle	Neudeck (2001)
8 phys. pixel		Diameter of circle (with antialiasing)	Neudeck (2001)
6 phys. pixel		Side length of square	Neudeck (2001)
8 phys. pixel		Side length of square (hollow)	Neudeck (2001)
15 × 15 phys. pixel		Graphical icon	Neudeck (2001)
	2 mm @ 60 cm	Point symbol	Hake et al. (2002)
5 phys. pixel		Diameter of circle	Schweizerische Gesellschaft für Kartografie (2002)
5 phys. pixel		Square (hollow)	Schweizerische Gesellschaft für Kartografie (2002)
5 phys. pixel		Circle (hollow)	Schweizerische Gesellschaft für Kartografie (2002)
6 phys. Pixel		Diameter of Geometric Symbol (square/circle/triangle)	Jenny et al. (2008)
7.3 CSS pixel ^5	0.8 mm @ 30 cm	Point symbol (icon, conventional resolution)	Ledermann (2022)
5.5 CSS pixel ^5	0.6 mm @ 30 cm	Point symbol (icon, high resolution)	Ledermann (2022)

Table 7. Minimum dimensions for line symbols on screen, as specified by various authors. Values established in empirical studies are set in bold, values converted from other units for this paper are set in italics.

Symbol type: Line
Value in pixels	Metric dimension	Dimension	Source
	0.3 mm @ 60 cm	Line width^4	Malić (1998)
	0.3 mm @ 60 cm	Line separation^4	Malić (1998)
	0.4 mm @ 60 cm	Line width	Brunner (2000)
	0.5 mm @ 60 cm	Line separation	Brunner (2000)
1 phys. pixel		Line width	Hake et al. (2002)
1 phys. pixel		Line width	Schweizerische Gesellschaft für Kartografie (2002)
2 phys. pixel		Line separation	Schweizerische Gesellschaft für Kartografie (2002)
2 phys. pixel		Line width (dotted line)	Schweizerische Gesellschaft für Kartografie (2002)
1.5 phys. pixel		Line separation	Jenny et al. (2008)
1.3 CSS pixel ^5	0.15 mm @ 30 cm	Width of line (dashed/dotted, conventional resolution)	Ledermann (2022)
1.1 CSS pixel ^5	0.12 mm @ 30 cm	Width of line (dashed/dotted, high resolution)	Ledermann (2022)
1.7 CSS pixel ^5	0.19 mm @ 30 cm	Line separation (conventional resolution)	Ledermann (2022)
1.2 CSS pixel ^5	0.13 mm @ 30 cm	Line separation (high resolution)	Ledermann (2022)

Table 8. Minimum dimensions for areas depicted on screen, as specified by various authors.

Symbol type: Area
Value in pixels	Metric dimension	Dimension	Source
	0.3 mm @ 60 cm	Area separation^4	Malić (1998)
	3 × 3 mm² @ 60 cm	Area size	Hake et al. (2002)
2 phys. pixel		Area separation	Schweizerische Gesellschaft für Kartografie (2002)
	10 mm² @ 60 cm	Area to distinguish color	Brunner (2000)
1.5 phys. pixel		Area separation	Jenny et al. (2008)

Table 9. Minimum dimensions for text labels on screen, as specified by various authors. Values established in empirical studies are set in bold, values converted from other units for this paper are set in italics.

Symbol type: Text label
Value in pixels	Metric dimension	Dimension	Source
	7 pt (≈1.4 mm)^6 @ 60 cm	Text height^4	Malić (1998)
	10 pt (≈2.0 mm)^6 @ 60 cm	Text height (curved) ^4	Malić (1998)
	14 pt (≈ 3.6 mm) ^6 @ 60 cm	Text height	Brunner (2000)
	12 pt (≈ 4.2 mm) ^6 @ 60 cm	Text height	Hake et al. (2002)
	12 pt @ 60 cm	Font size (rotated)	Schweizerische Gesellschaft für Kartografie (2002)
	12 pt @ 60 cm	Font size	Jenny et al. (2008)
	10 pt @ 60 cm	Font size (for fonts optimized for screen)	Jenny et al. (2008)
11 CSS pixel ^5	1.2 mm @ 30 cm	Text height	Ledermann (2022)

Figure 5. Empirical verification of the legibility of cartographic symbology on various digital displays in a lab-based setting (Ledermann, 2022).

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