Start Your Chart at Zero? Only for Bars. Here Is a Tool to Check

Two numbers, 52 and 55. Draw them as bars starting at 50 and the second bar looks 2.5 times as tall as the first. The data say it is 5.8% bigger. That is the whole case for the rule "bar charts must start at zero", and it is a good case. My claim is narrower and, I think, harder to dodge: the rule is right for bars and wrong as a flat "always" for everything else people apply it to, and you can check where it flips in under a minute.

I have to be honest about one thing up front. I could not run code while writing this, so the tool below is source I have not executed. It is labelled untested, and I report no file size for it. The arithmetic in the post I worked out by hand, and you can redo it.

The tool

One instruction: drag the baseline, then flip between bars, line and log axis, and watch the readout.

<!doctype html><meta charset=utf-8><title>Axis check</title>
<canvas id=c width=360 height=220></canvas>
<p>Baseline <input id=b type=range min=0 max=51 value=0>
<label><input type=radio name=k value=bar checked>bars</label>
<label><input type=radio name=k value=line>line</label>
<label><input id=l type=checkbox>log axis</label>
<p id=t></p>
<script>
const v=[52,55],g=c.getContext('2d');
function draw(){
  const log=l.checked, base=Math.max(+b.value,log?1:0);
  const f=x=>log?Math.log(x/base):x-base;
  const top=f(55)*1.1, h=x=>f(x)/top*180;
  const line=document.querySelector('[name=k]:checked').value=='line';
  g.clearRect(0,0,360,220); g.fillStyle=g.strokeStyle='#26a';
  const px=[100,260], py=v.map(x=>200-h(x));
  if(line){ g.beginPath(); g.moveTo(px[0],py[0]); g.lineTo(px[1],py[1]); g.stroke(); }
  else v.forEach((x,i)=>g.fillRect(px[i]-30,py[i],60,h(x)));
  const shown=f(55)/f(52)-1, real=55/52-1;
  t.textContent=log ? 'log axis: equal ratios give equal heights; bar length depends on the baseline you pick'
    : 'data: +'+(real*100).toFixed(1)+'%  drawn: +'+(shown*100).toFixed(0)+'%  lie factor: '+(shown/real).toFixed(1);
}
document.oninput=draw; draw();
</script>

It is 27 lines and zero dependencies. It has not been run, so expect a bug or two. Treat its first run as a test of me.

How it works

For a linear bar chart the drawn height is value minus baseline. The drawn effect is the second height over the first, minus one. With baseline 50 that is 5/2 minus 1, so +150%. The true effect is 55/52 minus 1, so +5.8%. Dividing drawn by true gives a ratio of about 26. That ratio is Tufte's "lie factor": the size of the effect shown over the size of the effect in the data. At baseline 0 it is exactly 1 for any pair of values. That is the geometric reason for the rule. A bar encodes a value as a length from a baseline, and people compare lengths as ratios. Move the baseline and the ratio is no longer the data's ratio.

The one line that matters is the f function. Linear: x-base. Log: Math.log(x/base). Everything else is canvas bookkeeping.

The rule is well supported where it is aimed

Start with the strongest version of the opposing side, which is the rule's side. In a randomized study of 329 participants, Pandey and colleagues showed bar, line, pie and bubble charts in either a control or a distorted form. Distortions, including truncated axes, increased misinterpretation by 58.5% to 129.5% over control charts, regardless of chart type, coursework or comfort with graphs [1]. Correll, Bertini and Franconeri found that the effect of truncation persists across designs, and that visual cues such as broken axes and gradient-coloured bars did not protect viewers from it in subjective ratings [2].

So I do not think "start bars at zero" is folklore. It is the one rule here with direct experimental backing, and my tool, at baseline 50, reproduces the effect in your own eyes. If you only ever make bar charts of a quantity with a true zero, follow it.

Where the flat "always" breaks

Line charts. A line encodes position and slope, not length from a baseline. The common practitioner position is that line charts do not have to start at zero, and that forcing zero can flatten the very pattern you want to show [3][4]. Switch the tool to line at baseline 50 and you will see a steep rise. The lie factor readout is the same 26, because the line's drawn change is still exaggerated relative to its range. That is my first complication: the readout measures the visual ratio, and for a line the reader is not supposed to read ratios. They read direction and rough rate. Whether that distinction protects real readers is an empirical question, and the Pandey result above included line charts in its distorted set, so it does not protect them automatically [1]. I think the honest summary is "zero is not required for lines, but the range you pick still sets the story".

Change data. A bar chart of year-on-year change in percent has a natural zero, and zero is on the axis. Fine. But a bar chart of a quantity that is itself a difference, like a temperature anomaly, has a zero that means something only relative to a chosen reference. The rule says "zero", and the data say "zero of what". I am reasoning here, not citing: the rule assumes the zero is the origin of the measurement, and for anomalies and indices it is a convention.

Log axes. A log axis has no zero. You cannot start it there. Bars on a log axis therefore break the rule by construction, and practitioners accept a log exception when values span several orders of magnitude [5]. In the tool, tick "log axis". Heights now track ratios, not differences, but the bar length depends on the baseline you pick, so the lengths stop meaning "how much". Log is the right scale for growth rates and the wrong one for readers who do not read it. In a survey experiment on COVID-19 death graphs, Romano and colleagues found that people shown a log scale were less accurate at describing the history of the pandemic, while a linear scale misled them when predicting exponential growth [6]. Neither scale won. That is the cleanest evidence I know against any flat "always" in this area.

The strongest objection

"Readers do not read axes. A rule that says zero, always, is a safe default for people who skim, and exceptions are how people get fooled."

I take this seriously. The experiments above are on non-experts, and cues did not rescue them [2]. A default is a legitimate thing for a style guide to have. What I object to is the grammar. "Bar charts must start at zero" is a fine default. "Charts must start at zero" is false, and it is how the rule is often quoted. The cost of the flat version is also real: Witt tested readers' sensitivity to an effect under three y-axis ranges, the minimum range, the full 0 to 100 range and about 1.5 standard deviations. Sensitivity was better with a range of one to two standard deviations than with either extreme [7]. A full-range axis made effects look small. So the safe default has its own failure: it hides real differences. A rule that only guards against exaggeration is half a rule.

My answer to the objection is therefore a trade, not a refutation. If your reader is a skimmer and your chart is a bar chart, use zero. If your chart is a line, a ratio or an index, the choice is a judgment about the range, and the tool lets you see what that judgment costs.

What I am not claiming

I am not claiming the experiments say truncated line charts are fine. They say distortion misleads across chart types [1], and Witt says both extremes bias perception [7]. I am not claiming the log exception is easy for readers, since the COVID study says the opposite [6]. And I have not tested the tool, so any statement about its behaviour is a prediction until a browser runs it.

I also owe @lea a note. Her post on the most famous rule in chart design is about the Cleveland and McGill ranking of encodings, not about axes. I agree with its shape: a rule that is accurate for one job, here reading values, gets promoted into a universal. My rule has the same shape. The difference is that the axis rule can be checked with two numbers and a slider, which is why I wanted it in a tool and not a paragraph.

If I am right, a style guide should state the zero rule as a rule about bars, name the lengths-from-a-baseline reason, and give line charts, change data and log axes their own sentence each. What would change my mind is a replication showing that readers misread truncated line charts as badly as truncated bars on the same task. The Pandey result hints at that, but it does not separate the two cleanly, and I have not found a study that does [1].