Charts & Data Visualization
Bubble Chart Size Formula: Area-Proportional Radius SQRT(Z / Z_max) vs Diameter Distortion
Encode a third quantitative variable Z accurately in Bubble Charts by scaling circle radius as R_i = R_max * SQRT(Z_i / MAX(Z)) so visual disk area PI * R_i^2 stays strictly proportional to magnitude Z_i.
Avoid Tufte’s "Lie Factor" — scale bubble RADIUS by SQRT(Z), never linearly by Z!
Human visual perception judges circular bubble magnitude by 2D disk AREA (A = PI() * R^2), not 1D diameter! As Edward Tufte (The Visual Display of Quantitative Information) and William S. Cleveland proved, if a chart scales circle radius linearly with data value Z_i, a company with 4x larger revenue gets 4^2 = 16x the ink area — creating a 400% perceptual Lie Factor!
To make disk area strictly proportional to magnitude (Area_i / Area_max = Z_i / Z_max), set normalized bubble radius to R_i = R_max * SQRT(Z_i / MAX($C$2:$C$5))! Now a 4x larger Z value produces exactly SQRT(4) = 2.00x the radius and 2^2 = 4.00x the visual area!
| Market Segment | Revenue Z ($M) | Area Share Z / Z_max | True Area-Scaled Radius (R_max = 20 pt) | Distorted Linear Radius Error |
|---|---|---|---|---|
| Enterprise | $160M | 1.0000 (100% of Max) | 20.00 pt | 20.00 pt (1.0x area) |
| Mid-Market | $40M | 0.2500 (1/4 of Max) | 10.00 pt (Area = 1/4!) | 5.00 pt -> 1/16 area (4x too tiny!) |
| SMB Self-Serve | $10M | 0.0625 (1/16 of Max) | 5.00 pt (Area = 1/16!) | 1.25 pt -> 1/256 area (invisible!) |
Area-Proportional Bubble Radius R_i = R_max * SQRT(Z_i / MAX(Z_range))
Scales positive magnitude C3 ($40M) relative to peak C2:C5 against maximum marker radius E2 (20 pt).
=IF(OR(C3 < 0, MAX($C$2:$C$5) <= 0, $E$2 <= 0), "Requires Non-Negative Z, Positive Max Z, and R_max > 0", ROUND($E$2 * SQRT(C3 / MAX($C$2:$C$5)), 2))Visual Area Verification Ratio (R_i / R_max)^2 = Z_i / Z_max
Confirms that squared relative radius equals exact data proportion C3 / MAX($C$2:$C$5).
=IF(OR(C3 < 0, MAX($C$2:$C$5) <= 0), "Invalid Z Values", ROUND(C3 / MAX($C$2:$C$5), 4))Try the example
Use the original values or change them to test your understanding.