Bar chart vs line chart

tl;drUse a bar chart for discrete categories, even when the categories are time periods. Use a line chart when you want to emphasize continuity, trend, or rate of change. The two can be combined for "actuals vs forecast" charts.
Bar chartLine chart
Best forDiscrete buckets — comparing each individuallyContinuous change — trend over time
Number of pointsUp to ~30 (depending on layout)~10 to thousands
Visual emphasisEach bucket's valueThe shape of change
Multiple seriesUse grouped or stacked barsJust plot more lines
When categories aren't timeAlmost always barsRarely lines (line implies order)

The continuity test

Ask: "Do the values between my data points have a meaning?" If you have monthly revenue, the value "between" April and May doesn't mean anything — there is no "April 15.5". Use bars. If you have a stock price sampled every minute, the value between minute 1 and minute 2 does have meaning — there was a real price the whole time. Use a line.

When time-series goes either way

Daily users, weekly signups, monthly revenue — discrete buckets, but many of them. With under about 20 points, bars work and the bucketing is visible. Past 20 points, lines win because the eye can read the trend without counting bars. The cutoff is rough; pick whichever shows your story more clearly.

Combining them

A common business chart is a bar (actuals) plus a line (target or forecast). The bars say "this is what happened"; the line says "this is what we expected." The contrast does the work — anywhere a bar falls short of the line, you have a missed period.

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When neither is right

If you're comparing two variables and want to see correlation, use a scatter plot — neither bars nor lines. If you're showing parts-of-a-whole over time, use a stacked bar or stacked area chart. Bars and lines are not the entire vocabulary of charts.