The Same Data, Two Stories: What a Truncated Axis Changes

A 0.6-point change drawn two ways

“Every chart axis must start at zero” is a useful warning but an incomplete rule. A bar chart uses length to represent magnitude, and cutting off its baseline changes the visual ratio between bars. A line chart often uses position to show movement over time, and a narrower scale may be necessary to reveal a small but important pattern.

The opposite slogan, “truncated axes are fine if labelled,” is also incomplete. Labels do not prevent a dramatic visual from overpowering the numeric change. Graphical form, purpose, uncertainty, and context determine whether a scale clarifies or distorts.

The goal is not to enforce one axis mechanically. It is to make the visual claim proportional to the underlying evidence. The U.S. Census Bureau visualization guide warns that a truncated scale can exaggerate variability while still leaving room for judgment about the chart’s purpose.

Bars and lines ask different questions

Create five fictional batch pass rates: 98.1%, 98.3%, 98.2%, 98.5%, and 98.7%. These are synthetic values and have no connection to a real factory, product, safety standard, or quality claim.

Plot them first as bars on a 0%-to-100% vertical axis. The bars are almost the same length, correctly reflecting that every batch has a pass rate near 98%. Plot the same values as bars on a 97.5%-to-100% axis. The last bar now appears several times taller than the visible portion of the first, even though their actual values differ by only 0.6 percentage points.

Next display the values as a line chart. The full axis preserves magnitude context but makes the upward pattern difficult to inspect. The narrow axis reveals the sequence. A responsible design can present the focused line chart with conspicuous tick labels, direct value labels, and a small overview showing the full 0%-to-100% scale.

The linked truncated-axis experiment places the same values in a full-context panel and a focused panel. A control moves the focused minimum while the maximum stays at 100%. Another control switches both panels between bars and a line. The metrics report the unchanged numeric range, the focused span, and the resulting visual amplification. The data never change; only their mapping to pixels changes.

A pixel-level audit

Suppose a plot area is 400 pixels tall and maps a value v between axis minimum a and maximum b to vertical position:

position(v) = 400 * (v - a) / (b - a)

On a 0-to-100 scale, the difference between 98.1 and 98.7 occupies 400 * 0.6 / 100 = 2.4 pixels. On a 97.5-to-100 scale, it occupies 400 * 0.6 / 2.5 = 96 pixels. The numerical difference is identical, but its visible displacement is forty times larger.

For bars, viewers compare lengths from a shared baseline. If the bar begins at 97.5 rather than zero, visible length represents value - 97.5, not the full value. The resulting length ratio does not equal the ratio of the rates. A bar at 98.7 is not meaningfully “four times” a bar at 98.1 even if their cropped visible segments suggest it.

For lines, slopes and changes are often the focus. A restricted axis can allocate enough pixels to inspect them. That focused view should still disclose the limits and avoid language that implies a larger absolute change than the values support.

Redesign the focused view

Imagine this graphic is headed for a weekly operations memo. The author wants readers to notice the upward sequence without suggesting that pass rates have changed by a large proportion. Review three candidate designs:

1. A cropped bar chart from 97.5% to 100% makes the final bar’s visible segment much taller than the first. Reject it because bar length no longer represents the full magnitude.
2. A line chart from 97.5% to 100% reveals the 0.6-point range. Keep it only if the limits and exact values are easy to see.
3. A dot plot with direct labels, paired with a small 0%-to-100% overview, shows both the local sequence and its absolute scale. This is the strongest choice when the memo needs both messages.

The answer can change with the task. A safety threshold at 98.5% might make the focused view operationally essential; a promotional graphic with no threshold would need more restraint. The Census reporting standard supports the underlying review questions: are units and definitions clear, are comparisons consistent, and is uncertainty reported when it affects interpretation?

Conditions behind the comparison

The comparison assumes identical chart dimensions and linear scales. Logarithmic scales have different interpretations and should be clearly identified. A log scale can be appropriate for multiplicative changes across orders of magnitude, but equal pixel distances then represent equal ratios rather than equal differences.

Values must share units and definitions. No axis treatment can repair mismatched denominators or inconsistent measurement. Time points should also be spaced according to their actual intervals rather than placed equally when dates are irregular.

If rates are estimated, uncertainty matters. A 0.6-point change can look smooth in a line while confidence intervals overlap substantially. Showing intervals or another honest uncertainty summary may be more important than the baseline choice.

A sign-off before publication

Do not crop a bar chart solely to make a small difference dominate the page. If a zero-based bar makes the comparison hard to inspect, use a dot plot, line plot, table, or paired overview and detail rather than corrupting the length encoding.

Do not hide an axis break in a decorative mark, omit tick labels, or use inconsistent scales across panels meant for comparison. Readers should not need to reverse-engineer the mapping from data to pixels.

Do not insist on zero for every quantity. Temperature on an interval scale, residuals around a reference, and long time series may need context-specific domains. Starting every line at zero can flatten meaningful variation until the chart stops communicating. State the reference and show exact values.

Do not infer importance from visual size alone. A small numeric change may be operationally important, or a large one may be noise. Importance requires thresholds, uncertainty, and subject knowledge that an axis cannot provide.

Before approving a focused axis, ask four concrete questions. Does the encoding use length or position? Are both endpoints printed? Can a reader recover the 0.6-point numeric change without estimating pixels? Is a full-range view, threshold, or uncertainty interval needed to keep the claim in proportion? A chart that fails any one of these checks needs another edit, even when every plotted value is technically correct.

What the guidance does and does not decide

The U.S. Census Bureau visualization guidance says quantitative axes should usually start at zero and warns that truncated scales can exaggerate variability. Its reporting standard emphasizes clear axes, units, consistent scales, and uncertainty. This guide treats “usually” as a design question and uses a new synthetic pass-rate sequence to compare bar and line encodings.

Revision note, August 26, 2026. Added the three-option redesign exercise, a publication sign-off checklist, and paragraph-level links to the Census visualization and reporting guidance. The fictional pass rates did not change.