A logarithmic (log) price scale is a way of plotting prices on a chart where equal vertical distances represent equal percentage (multiplicative) changes rather than equal absolute (additive) dollar amounts. On a log scale, moving from $10 to $20 (a 100% increase) occupies the same vertical distance as moving from $20 to $40 (also a 100% increase), even though both moves differ by $10 and $20 in absolute terms.
Key takeaways
– Logarithmic scales map prices using a logarithm so that equal percentage changes are plotted with equal vertical distance.
– They compress large nominal price ranges and expand low-price ranges, making long-term and high-growth moves easier to interpret.
– Most charting platforms offer log vs linear settings; use log charts when percentage moves matter (long-term performance, exponential growth, volatile assets).
– Log scales cannot display zero or negative prices.
How a log price scale works (simple math)
– Linear scale: y ∝ p (equal increments in p give equal vertical spacing).
– Log scale: y ∝ log(p). Typically base-10 (log10) or natural log (ln) is used — the base only changes units, not the relative spacing.
– The vertical difference between two prices p1 and p2 on a log chart is proportional to log(p2) − log(p1) = log(p2/p1). Thus the chart visually encodes multiplicative (percent) changes.
Short numerical example
– log10(20) − log10(10) = log10(20/10) = log10(2) ≈ 0.3010
– log10(40) − log10(20) = log10(40/20) = log10(2) ≈ 0.3010
So a 100% rise (×2) shows the same vertical distance whether from 10→20 or 20→40.
When to use a logarithmic price scale
– Long-term charts where prices changed by large multiples (stocks that rose many-fold).
– Assets that display exponential-like growth or compound returns.
– Comparing dollar moves across different price levels is misleading; prefer log to focus on percentage performance.
– Technical analysis where trendlines and channels should reflect percentage-based trends (e.g., consistent compound growth).
When linear scale can be preferable
– Short-term analysis or when absolute dollar moves matter (e.g., fixed pip targets in forex, exact price targets for limit orders).
– Very low-volatility assets where price range is narrow and showing absolute distances is useful.
– When you need to visualize very small absolute price differences at high price levels (though a large screen or zooming can help).
Practical implications for technical analysis
– Trendlines: Draw trendlines on the same scale you analyze: if you want to capture percentage-based trends, draw them on a log-scaled chart. Trendlines drawn on linear and log charts can look different.
– Support/resistance: Price levels remain price levels, but their visual prominence shifts. Percent-based support/resistance (e.g., trend of compound growth) is clearer on log charts.
– Indicators (RSI, MACD): These are computed from price but typically plotted on linear axes; switching the price axis to log affects only the price plot and drawings, not the indicator math unless you explicitly feed log(price) into the indicator.
Limitations and cautions
– Cannot handle zero or negative prices (log undefined). For assets close to zero, log charts are inappropriate.
– For very short-term trading where single-dollar moves matter, log scale may mask meaningful absolute moves.
– Some traders unfamiliar with log scaling may misinterpret distances; always verify whether a chart is log or linear.
Practical steps — how to use log scales in common tools
1) Check chart settings (general)
– Look for a “Scale” or “Y-axis” setting and choose “Logarithmic,” “Log,” or similar. Many platforms default to log on long-term charts.
– Confirm the axis labeling — spacing between labels will compress as price increases.
2) In TradingView (or similar web charting tools)
– Open the chart.
– Right-click the price axis (right side) or click the axis options (gear icon).
– Choose “Log Scale” / toggle “Log” on.
– Draw trendlines and channels while the chart remains in log mode for percent-consistent lines.
3) In Excel
– Prepare two columns: Date and Price.
– Insert a Scatter plot (Date on X, Price on Y).
– Right-click the Y-axis → Format Axis → check “Logarithmic scale.”
– Note: Excel’s log axis requires all positive values (>0).
4) In Python / Matplotlib
– Example snippet:
import matplotlib.pyplot as plt
plt.plot(dates, prices)
plt.yscale(‘log’) # sets log scale on y-axis
plt.ylabel(‘Price (log scale)’)
plt.show()
– Alternatively plot y = np.log(prices) if you want to compute values directly — but using plt.yscale(‘log’) keeps axis labels as real prices.
5) In Excel if you prefer to plot log-transformed values
– Create a new column: LogPrice = LN(Price) or LOG10(Price).
– Plot LogPrice versus Date on a linear axis; vertical spacing will match percent changes, but axis will show log units (not raw prices). To keep raw price labels, prefer the built-in log axis.
Examples to illustrate interpretation
– Example A: Stock went from $5 to $50 (×10) over several years. On a linear scale the early $5→$10 move looks tiny relative to $40→$50; on a log scale the early compounding growth is visible and trendlines show consistent compound rates.
– Example B: An asset falls from $100 to $10. On a linear chart the lower-dollar region becomes compressed and small moves near the bottom look very small; on a log chart a fall from $100→$50 (50% decline) and $50→$25 (50% decline) display equal vertical distances.
How to draw percent-based trendlines and channels
– Keep the chart in log mode and use the platform’s trendline tool. A straight line drawn on a log-y chart represents a constant compound growth rate.
– If drawing trendlines in linear coordinates, convert prices to log(price) first so the line corresponds to consistent percent change.
Quick checklist before analysis
– Decide whether percent or absolute moves are most relevant.
– Ensure no zero/negative prices in your data.
– Toggle log scale on before drawing lines or making visual comparisons.
– If sharing a chart, label whether the Y-axis is log or linear to avoid misinterpretation.
Summary
Logarithmic price scales map prices so equal percentage moves are equally spaced vertically. They are most useful for long-term charts, high-growth assets, and any analysis that is naturally multiplicative (compounding). Use log scales when you want trendlines and visual impressions that reflect percent changes rather than absolute dollar changes. Always verify the axis mode on your charting platform and choose the scale that best fits the question you are asking.
Source
– Investopedia — “Logarithmic Scale.” (background and conceptual reference)
How Logarithmic Scales Are Calculated
– A logarithmic price scale plots the logarithm of price on the vertical axis rather than the price itself. Most charting platforms use either base‑10 (log10) or the natural logarithm (ln); the choice of base only scales the axis differently but preserves the property that equal percentage changes occupy equal vertical distances.
– Formula (conceptual): y = log(price). If you want the vertical distance between two prices p1 and p2 to represent the percentage/ratio change, then the plotted distance is proportional to log(p2) − log(p1) = log(p2 / p1).
– Example calculation (base 10):
• log10(20) − log10(10) = log10(2) ≈ 0.3010
• log10(40) − log10(20) = log10(2) ≈ 0.3010
• log10(120) − log10(100) = log10(1.2) ≈ 0.0792
These show that a doubling (100% increase) is the same vertical distance whether 10→20 or 20→40, while 100→120 (a 20% increase) is much smaller.
Practical Example: Step‑by‑Step Numeric Demonstration
1. Choose prices to compare: 10, 20, 40, 100, 120.
2. Compute base‑10 logs (or natural logs) of each:
• log10(10)=1.0000; log10(20)=1.3010; log10(40)=1.6021; log10(100)=2.0000; log10(120)=2.0792.
3. Vertical distances (differences in log values):
• 10→20: 0.3010
• 20→40: 0.3010 (identical to 10→20)
• 100→120: 0.0792 (much smaller)
4. Interpretation: equal ratios (e.g., ×2) give equal vertical spacing; equal absolute dollar changes do not.
When to Use a Logarithmic Price Scale (Practical Guidance)
– Use log scale when:
• You’re studying long-term charts where price has changed by large multiples (years to decades).
• You want to analyze percentage-based trends (compounding growth, long-term trendlines, exponential moves).
• The asset has experienced large moves (e.g., small‑cap stocks that later became large caps, commodities, cryptocurrencies).
– Use linear scale when:
• You need to focus on absolute-dollar moves over a short horizon (intraday or very short-term targets).
• The asset price has limited range and low volatility, and you care about fixed dollar differences (e.g., bid/ask gaps, fixed strike options).
– Practical rule of thumb: if price has changed by more than a few multiples (e.g., >2–3×) over the analysis window, prefer log scale.
How to Switch to a Log Scale (Common Steps)
Note: Steps differ slightly by platform; these are general instructions and examples.
– TradingView (web/mobile):
1. Open chart.
2. Right‑click the price axis (right side) and select “Log Scale” or click the price axis menu and toggle “Log Scale.”
– Thinkorswim (TD Ameritrade):
1. Open chart settings or right-click the price axis.
2. Select “Log Scale” from the axis options.
– Yahoo Finance:
1. Open interactive chart.
2. Click the settings/gear icon or the price axis menu and choose the log scale option.
– Generic mobile/web apps:
• Look for a “Scale,” “Axis,” or “Settings” option near the chart and toggle between linear/log.
If you can’t find it, consult your platform’s help or search for “log scale” + platform name.
Implications for Technical Analysis and Indicators
– Trendlines: When measuring percentage trends over time (e.g., steady growth), draw trendlines on a log chart for more meaningful, consistent slopes. A straight trendline on a log chart corresponds to exponential growth on a linear chart.
– Moving averages: The numerical calculation of a moving average is done on price values; plotting the moving average on a log chart simply displays those values on the log‑scaled axis. The relative fit vs. price may look different between linear and log scales, but the MA values themselves do not change.
– Fibonacci, support/resistance: Percentage‑based tools (e.g., Fibonacci retracements measured from big swings) often benefit from log scale if the move spans large percentage changes, because retracement percentages are visually consistent on log charts.
– Volume, momentum indicators (RSI, MACD): These are calculated independently of axis scaling, so their values are unaffected; but their visual relationship to price bars may appear different because the price axis is scaled differently.
Examples and Case Studies
– NVIDIA example (from prior section): On a log chart, the vertical gap between $20→$40 equals $40→$80 (both ×2), whereas $100→$120 is much smaller despite the same absolute $20. This makes long-term growth trends easier to see.
– Bitcoin (historical): Bitcoin’s price moved from single digits to thousands. A linear chart would compress early price action into a near-flat line with massive-looking spikes later. A log chart shows consistent percentage-based trends, allowing clearer long-term trendlines and comparisons across cycles.
– Stock with small absolute changes: A blue‑chip stock that trades between $45 and $60 over several months may be simpler to analyze on a linear chart if your targets are fixed-dollar limits or options strikes.
Advantages and Disadvantages
– Advantages:
• Equal representation of equal percentage moves.
• Better visualization of exponential/compound trends.
• More informative for long timeframes and high-multiplication price movements.
– Disadvantages:
• Less intuitive when thinking in absolute dollars (e.g., “how many dollars do I need to make $5 profit?”).
• Short-term, fixed-dollar targets may be harder to visualize.
• Some traders unfamiliar with log charts may misinterpret visual slopes or bar heights.
Practical Steps for Analysts and Traders
1. Establish your analysis horizon and objective:
• Short horizon / dollar targets → consider linear.
• Long horizon / percentage growth → use log.
2. Switch the chart to log scale if price has moved multiple times over the analysis window.
3. Re-draw trendlines and support/resistance on the chosen scale (trendlines drawn on linear vs log are not equivalent).
4. Use the same scale consistently when comparing multiple assets or multiple timeframes to avoid misleading visual comparisons.
5. Re-check indicator signals after changing scale (indicators’ numeric outputs unchanged, but their visual alignment with price may look different).
6. Document which scale you used when saving charts or sharing analysis with others, so interpretations remain consistent.
Common Pitfalls and How to Avoid Them
– Pitfall: Drawing a trendline on a linear chart for a multi‑decade, multiplicative move and assuming it represents a constant percentage trend. Fix: Use a log chart for percentage/compounding interpretation.
– Pitfall: Forgetting to switch scales when comparing assets with very different price ranges. Fix: Apply log scale when comparing percentage behavior across assets.
– Pitfall: Misreading small dollar changes at high prices as insignificant; on a log chart they may appear small—but remember small dollar moves can be small percentage moves when price is high.
Summary and Recommendation
– A logarithmic price scale maps price using a logarithm so that equal percentage changes take equal vertical space. This makes log scales the preferred choice for long-term analysis, assets that have experienced large multiplicative moves, and when you want to analyze percentage trends or exponential growth.
– Use linear scales when your analysis depends on absolute-dollar movements over short timeframes.
– Always choose the scale that matches the nature of your analysis, re-draw annotations after switching scales, and document which scale you used for clarity.
Source: Investopedia — “Logarithmic Scale” (see