Log Scale vs Linear Scale Charts: Which One to Use
A logarithmic price scale gives equal percentage moves equal vertical distance, while a linear scale gives equal rupee moves equal vertical distance. That single difference decides which to use: log for long multi-year charts and compounding stocks, linear for intraday and short-term charts where price barely moves in percentage terms.
Most traders never touch the setting, and on a 5-minute chart it genuinely does not matter. On a ten-year chart it changes what you conclude, including whether a trendline has broken. Every platform has the toggle, usually marked log or semi-log in the price axis settings.
What the Two Scales Do
On a linear scale the axis is spaced by absolute value, so the gap from Rs 100 to Rs 200 takes the same height as the gap from Rs 1,000 to Rs 1,100. The first is a 100 percent gain and the second is 10 percent, drawn identically.
On a log scale the axis is spaced by the logarithm of price, so equal ratios take equal space. Rs 100 to Rs 200 occupies exactly the same height as Rs 500 to Rs 1,000 and as Rs 2,000 to Rs 4,000, because each is a doubling. The distance between two prices is proportional to log(P2) minus log(P1), which equals log(P2 / P1), a pure ratio. That is the entire mathematical content of the difference.
Worked Example (Illustrative)
Take a stock that compounds from Rs 100 to Rs 1,600 over twelve years, which is four doublings.
| Leg | Rupee gain | Percent gain | Height on linear | Height on log |
|---|---|---|---|---|
| Rs 100 to Rs 200 | Rs 100 | 100 percent | 1 unit | 1 unit |
| Rs 200 to Rs 400 | Rs 200 | 100 percent | 2 units | 1 unit |
| Rs 400 to Rs 800 | Rs 400 | 100 percent | 4 units | 1 unit |
| Rs 800 to Rs 1,600 | Rs 800 | 100 percent | 8 units | 1 unit |
On the linear chart the first eight years compress into a flat squiggle near the bottom while the last two look like a vertical spike. An investor who doubled money in the first two years sees almost nothing. On the log chart all four legs are the same height, which is fair, because each doubled the money. The same applies to the Sensex over its history: a linear chart makes every early move invisible and the recent decade look like a bubble.
Why Log Is the Right Default for Long Charts
- Returns are percentages. You earn a return on capital, not a fixed number of rupees, so a scale that treats a 10 percent move equally at every price level matches how the money works.
- Compounding becomes readable. Steady compounding plots as a straight line on log. A curve bending upward means the growth rate itself is accelerating.
- Old history stops being invisible. Crashes and corrections from twenty years ago keep their true proportion.
- Percentage drawdowns read correctly. A 50 percent fall is the same vertical distance whether it happened at Rs 200 or Rs 2,000.
Linear is fine, often better, for intraday and short-term charts. Within a session Nifty might move 1 percent, and across such a small range the two scales look almost identical. Linear also matches how you think about intraday risk, which is in points and rupees per lot rather than percentages, and it suits measured moves and flag targets on short-term charts.
The Trendline Problem
This is the practical point that changes decisions. A straight line on a linear chart represents a constant rupee gain per unit of time. A straight line on a log chart represents a constant percentage gain per unit of time. They are different objects, so the same two anchor points produce two different lines.
Take an illustrative long-term uptrend. You connect two major lows, Rs 400 four years ago and Rs 800 two years ago, and extend. Price is now around Rs 1,500. On the linear chart the line rises Rs 400 every two years, so it sits near Rs 1,200 and price is comfortably above it. On the log chart the line doubles every two years, so it sits near Rs 1,600 and price is below it.
Same lows, same data, opposite conclusion. On one chart the trend is intact, on the other the trendline has already broken. Neither chart is lying, they are measuring different things.
The practical rule: on multi-year charts draw trendlines and channels on the log scale, because a trend holding a constant percentage rate is the more meaningful structure. Whatever you choose, be consistent. Switching scales after a line breaks, to find a version where it has not, is the same self-deception as scrolling timeframes until one agrees with you. One more caution: log scales cannot display zero or negative values, so they do not suit indicators that oscillate around zero such as MACD or Force Index.
Frequently Asked Questions
Do candlestick patterns change on a log scale?
An individual candle changes shape very slightly, because body and wicks are drawn on a compressed axis, but pattern definitions rest on the relationship between open, high, low and close, which does not change. On daily charts the visual difference is negligible.
Which scale suits Fibonacci retracements?
For a move inside one trend over weeks or months the difference is small and linear is standard. For a retracement measured across a multi-year advance where price multiplied several times, log levels make more sense, because a 61.8 percent retracement is a percentage concept. Most platforms offer a log option in the tool settings.
Is semi-log the same as logarithmic?
In charting terms, yes. A chart with a log price axis and a linear time axis is technically semi-logarithmic, and that is what platforms mean by log scale. A fully logarithmic chart would compress time too, which nobody does for price charts.
Does the scale affect my indicators?
Indicator values are computed from price data and do not change with the display scale. What changes is how they look if they share the price axis, such as moving averages and Bollinger Bands. Separate-pane indicators with their own axis, especially any that go negative, need a linear axis.
Key Takeaways
- Log scale gives equal percentage moves equal height, linear gives equal rupee moves equal height.
- Use log for multi-year charts, compounding stocks and long index history such as the Sensex.
- Linear is fine for intraday and short-term charts where percentage ranges are small.
- A trendline drawn on linear can look completely different on log, which can flip a breakout conclusion.
- Pick a scale for an analysis and stay with it, and remember log axes cannot show zero or negatives.
