Choosing Between Arithmetic and Logarithmic Price Scales

Hello! Last lesson, you set up weekly and daily charts of the same stock, with a consistent price-adjustment choice and volume on both. Before using those charts to judge trends, there is one more display choice to make: what does a given vertical distance represent?

This lesson distinguishes arithmetic from logarithmic price scales and gives you a practical way to choose between them. Allow about 35–40 minutes, including time to compare both settings on your TradingView layout.

Two ways to measure a move

On an arithmetic, or linear, scale, equal vertical distances represent equal changes in price. A move from ₹100 to ₹120 occupies the same height as a move from ₹500 to ₹520: each is a ₹20 change. But the first is a 20% gain and the second is a 4% gain.

On a logarithmic, or log, scale, equal vertical distances represent equal proportional changes. A rise from ₹100 to ₹200 occupies the same height as a rise from ₹200 to ₹400: both are 100% gains. Their price changes—₹100 and ₹200—are not equal.

Watch how these definitions appear on an actual chart. The presenter uses TradingView’s Regular setting for the arithmetic scale and Logarithmic for the log scale.

The two scales do not change a stock’s recorded prices, dates, candles, or volume. They change the spacing of prices on the vertical axis. Time remains on the horizontal axis, so a stock chart with a log price axis is often called semi-logarithmic.

For a short account of the distinction and its usual applications, read the “Price Scaling” section below. Its paired chart images are worth comparing before you read its guidance on when each scale helps.

Why the same history can look different

The illustration below puts the distinction into one picture. On the left, large recent changes in currency units dominate the long chart, and earlier movement is compressed near the bottom. On the right, earlier moves take up more room because the vertical distance reflects their size relative to the price at the time.

Neither view is inherently false. They answer different questions:

• Arithmetic: “How large was the move in rupees?”
• Logarithmic: “How large was the move relative to its starting price?”

For example, a ₹20 rise matters differently when a stock starts at ₹100 than when it starts at ₹500. The percentage change is calculated from the starting price:

This also explains a visual trap in long stock charts. If a stock grows substantially over several years, later swings may be much larger in rupees even when they are no larger in percentage terms. An arithmetic chart gives those later swings more vertical space. A log chart lets you compare their proportional sizes more directly.

A log chart still labels the axis in prices, not percentage returns. Its spacing changes; it is not the same setting as TradingView’s separate Percent view. Also, Auto generally concerns fitting the visible data to the chart area; it is not another name for either arithmetic or log scaling.

Choose the scale for the question and the visible range

For your position-analysis layout, a sound default is to inspect a multi-year weekly chart in log scale, especially if the stock has multiplied in price or suffered large proportional declines. That keeps earlier percentage moves legible beside later ones. On a daily chart covering a relatively narrow price range, arithmetic is often convenient: equal rupee moves look equal, and switching to log may make little visible difference.

Those are defaults, not “weekly means log; daily means arithmetic” rules. A daily chart showing a very large rise or fall can benefit from log scaling. A weekly chart confined to a tight price band may look nearly identical on either scale. Choose according to the history currently visible and whether you are comparing rupee amounts or proportional moves.

Scale choice matters most when you judge the shape or steepness of a move. A long rise can look increasingly steep on an arithmetic chart while appearing steadier on a log chart. Later, when you draw trendlines, keep the selected scale in mind: changing scales can change how well a sloping line visually fits the prices. It does not move the actual swing highs and lows or change a horizontal price level.

One more practical distinction follows from last lesson: price adjustment and price scaling are separate settings. An adjustment can change the historical prices plotted to account for a corporate action; switching between arithmetic and log only changes how the chosen price series is spaced. Hold the adjustment choice constant when you compare scales.

Make the choice on your own layout

Return to the weekly–daily TradingView layout you built previously. Use the same NSE cash-stock listing in both panels, and leave their adjustment settings unchanged.

1. On the weekly panel, display several years of history. Right-click the price axis and look for Regular and Logarithmic (the control may also appear in chart or scale settings). View the same dates with each setting.
2. Look first at an early advance or decline, then at a later one. Does arithmetic compress the earlier move? Does log make a large recent rupee move seem less dominant because its percentage change is smaller? Read the price labels rather than relying only on the curve’s appearance.
3. On the daily panel, display several months. Toggle its scale independently. If the stock stayed in a narrow range, note how little the picture changes. If it moved dramatically, compare the two views more carefully.
4. Leave each panel on the scale that serves its job, and record the choice in your chart notes. A reasonable starting pair is log weekly, arithmetic daily—but change either when its visible price range calls for it.

If you revisit a chart after zooming far out or into a much shorter period, check the scale again. The suitable choice can change with the span of history you are examining.

Where this leaves you

Arithmetic means equal price-unit spacing; logarithmic means equal proportional spacing. Use arithmetic when absolute price changes and a relatively tight range are your focus. Use log when a wide-ranging chart calls for meaningful comparison of percentage moves across time. Above all, check the scale before interpreting a chart’s apparent steepness.

Next, you will use successive peaks and troughs to distinguish primary, intermediate, and minor trends. The scale will affect how those swings look, but their sequence—not the chart’s dramatic appearance—will be your starting evidence.