Linear and Logarithmic ScaleLog
On a linear price scale equal distances mean equal amounts of money; on a logarithmic scale equal distances mean equal percentage changes, which suits long histories.
The same price history can look calm or explosive depending on one chart setting. The vertical scale decides whether a $10 move always looks the same size, or whether a 10% move does.
- Category
- Technical Analysis
- Reading time
- 3 min
- Also called
- Arithmetic scale, Log scale, Semi-log chart
- Updated
The two scales in plain words
A linear (arithmetic) scale shows 10 points as the same vertical distance at any price level.1
A log scale measures moves in percentage terms.1 It is often called semi-log because the time axis stays arithmetic.1
So on a log Trading Chart, $10 to $20 looks as large as $20 to $40.1
How to choose a scale
Check the range
Linear works when price stays in a tight range.1
Check the history
Use log for wide ranges and long-term charts.2
Check the timeframe
Use linear for narrow intraday ranges where dollar moves are easier to read.2
Redraw trendlines
Trend lines differ between the two scales.2
Prefer log for long trendlines
Highs and lows line up better on a semi-log scale.3
Stay consistent
Choose one scale for each analysis and stick with it.2
Worked examples
Example 1 — Equal dollars, different percentages
Log shows the real proportionA hypothetical stock moves from $10 to $20, then from $100 to $110.
| Move 1 | +$10 = +100% |
| Move 2 | +$10 = +10% |
On a semi-log scale the first move looks much larger, because it is a 100% gain versus 10%.3
Example 2 — Doubling twice
Log: equal heightsA stock goes $10 → $20 → $40.
| First leg | +100% |
| Second leg | +100% |
On an arithmetic scale the $10–$20 leg is half as tall as the $20–$40 leg; on a log scale equal percentage advances look the same height.1
Example 3 — Trendlines on a big rally
Use log for long trendsA hypothetical stock rises tenfold over three years.
| Arithmetic | Needs several trendlines |
| Log | One line fits |
On the arithmetic scale, several trend lines were needed to keep pace with a big advance, while highs and lows align better on semi-log.3
Linear vs logarithmic
| Aspect | Linear | Logarithmic |
|---|---|---|
| Equal distance means | Equal dollars | Equal percent |
| Best for | Short-term, tight ranges | Long-term, big moves |
| Trendlines | Can break on big rallies | Fit long trends better |
| Other name | Arithmetic | Semi-log |
When traders switch scales
Long-term trend analysis
Viewing years of a Trend on log.
Intraday trading
Using linear for Day Trading in tight ranges.
Drawing trendlines
Checking a Trendline on both scales.
Comparing drawdowns
Seeing Drawdown percentages fairly on log.
Advantages and disadvantages
Advantages
- Log shows percentage moves fairly.
- Linear shows dollar moves directly.
- Switching is one click in most platforms.
Disadvantages
- Trendlines and patterns differ by scale.
- Linear exaggerates recent moves after big rallies.
- Log compresses large price levels and can look congested.
- Switching mid-analysis creates conflicting levels.
Going deeper
Read as far as you need. Each level builds on the one before it.
Common mistakes
Linear on decades of data
Making recent moves look huge.
Switching scales mid-analysis
Getting levels that disagree.
Ignoring scale on breakouts
A break on one scale may not exist on the other.
Assuming one is always right
Each scale answers a different question.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Linear: equal dollars, equal distance.
- Log: equal percent, equal distance.
- Use log for long, wide histories.
- Use linear for short, tight ranges.
- Trendlines change with the scale.
Frequently asked questions
Which scale do long-term investors use?
Do indicators change with the scale?
Why is it called semi-log?
Further learning
- Trading Chart
Chart basics.
- Trendline
Why scale changes your lines.
- Timeframe
How period affects scale choice.
- Drawdown
Why percentages matter.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- StockCharts ChartSchool. What Are Charts? (opens in a new tab) Checked .
- TradingSim. Log Scale vs Linear Scale: 5 Key Differences (opens in a new tab) Checked .
- StockCharts ChartSchool. Trend Lines (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.