Log versus linear scale

Buy a stock at ₹10 and watch it reach ₹20, and you have doubled your money - a 100% return. Buy a stock at ₹1000 and watch it reach ₹1010, and you have made 1% - barely a savings account. In one case ₹10 changed your life; in the other ₹10 was a rounding error. They are not remotely the same event.

Yet on a standard chart - a linear one, the default on almost every app - a ₹10 move takes up exactly the same vertical space whether the stock trades at ₹10 or ₹1000. The chart measures rupees, and treats every rupee as equal, no matter how large or small the base it is measured against.

That is fine for a single busy afternoon. It becomes a genuine problem the moment you look at years. If a stock has grown from ₹10 to ₹1000 over a decade, how are you supposed to study it when the early years - where the biggest percentage gains actually happened - are squashed into an invisible smear along the bottom of the screen?

There are two ways to mark the price axis, and they measure different things.

A linear scale treats absolute rupees equally. The gap on screen from ₹10 to ₹20 is the same as the gap from ₹100 to ₹110 - both are ₹10. Simple, and honest about how much money moved.

A logarithmic (log) scale treats percentages equally. The gap from ₹10 to ₹20 (a 100% move) is drawn exactly as tall as the gap from ₹100 to ₹200 (also 100%). On a log scale, a stock compounding at a steady rate plots as a straight line, because equal percentage steps get equal height.

Neither ruler is wrong; they answer different questions. If you are a day trader watching a five-minute chart, price barely moves in percentage terms and linear is perfectly fine. But if you are an investor studying compound growth over a decade, a linear chart will actively mislead you - it will make a healthy, steady compounder look like a runaway bubble simply because the later rupee jumps are numerically larger.

The clearest way to feel the difference is to flip the switch on a real long history and watch the shape change. Below is a multi-bagger drawn first on a linear scale - where it curves upward into an alarming near-vertical rise at the end - and then on a log scale, where that same rise reveals itself as a steady, roughly straight climb.

Press Switch to Log Scale and watch the "bubble" turn into an orderly line. Nothing about the prices changed. Only the ruler did.

Every price in this module is an illustrative composite, not a real quote. illustrative

Here is the same trap in miniature. Below are the last few months of a long-running compounder, drawn on an ordinary linear chart. The stock runs from ₹800 to ₹1200 - and on this scale it looks like a vertical rocket, the kind of chart that makes you shout "bubble" and either chase it or refuse to touch it.

Now do the arithmetic the linear scale hides. ₹800 to ₹1200 is a 50% move. If this stock has been compounding at roughly that pace for years, then on a log scale this "spike" would be an ordinary continuation of the same slope it has followed all along - not an acceleration, just the same growth rate producing a bigger rupee number because the base is now bigger. The linear chart did not lie about the prices; it exaggerated the shape, because it always makes late-stage compounding look violent.

But do not over-correct into the opposite error. The log view would show the move as calm - and that calm is its own kind of flattery, because it makes you forget that ₹400 of gain (or, on the way down, ₹400 of loss) in a few months is a genuinely large amount of real money to be riding.

A log chart is visually forgiving, and that forgiveness can hurt you. A fall from ₹1000 to ₹500 is a devastating 50% crash - but on a log scale it occupies exactly the same height as a drop from ₹10 to ₹5. Because our eyes are trained on linear charts, that 50% crash simply does not look as frightening as it feels to the account behind it. In a bear market, a log chart can lull you into a false calm, drawing catastrophic drawdowns as gentle, unremarkable dips.

And there is a deeper limit that no scale can fix: neither ruler tells you anything about the business underneath the line. A beautifully straight log trend is a description of what the price did, not a promise about what it will do. The scale can make the past look orderly; it cannot make the future safe. A stock can compound in a perfect log line for a decade and then break - the straightness was never a guarantee, only a record.

Finally, respect the size of real moves even when the chart shrinks them. a 50% fall drawn as a small dip is still a 50% fall, and large drops arrive more often than a calm-looking chart suggests. Read the percentage, not the pixels.

A concrete, common mistake: a support trendline drawn on a linear chart over many years is essentially meaningless. Connect the lows of a stock from 2010 to 2020 on a linear scale, then switch to log, and the line floats off into empty space, touching nothing. Multi-year trendlines belong on a log scale, because across long spans you are trying to measure the consistency of percentage growth, not of absolute rupees. Draw the line on the wrong ruler and you are measuring the wrong thing.

The deeper trap is the belief that one scale is simply "the honest one". Take a 10-year chart where price recently jumped from ₹800 to ₹1200 in a few months.

The repair, as always, is to decide your test before the chart flatters you. If you switch to log and the recent spike still stands well above the multi-year slope, the "steady compounder" story weakens - you are looking at something faster and less proven than the smooth line suggested. Let the comparison across both rulers, not the comfort of one, do the deciding.

We have now bent the price axis (linear versus log) just as earlier modules bent the horizontal axis (time, volume, range). Every one of these is a different lens on the identical stream of trades, and each reveals one truth by hiding another.

One axis remains to examine directly: time itself. Before you open any chart, you have already made a hidden choice - how much time each candle contains, and therefore which reality you are about to see. A five-minute chart and a monthly chart of the same stock can tell opposite stories. Choosing between them, honestly, is the final module of this part.