Granthara03.02.01Linear vs logarithmic scale

03.02.01 · Linear vs logarithmic scale

PreviouslyYou chose a chart by naming the question first, then the fields that question needs.

Two rises of ₹100. One of them doubled your money.

A chart has to turn a price into a height. It cannot draw ₹100 without first deciding how far up the screen ₹100 belongs. That decision is the scale, and there are two common ways to make it.

The prices are recorded facts. The distance between them on screen is a setting.

Updated

₹100
The same rupee rise: once a doubling, once a ninth added
Part 03 · Axis, Scale, and Visual Deception
  1. 03.02.01 Linear vs logarithmic scale
  2. 03.02.02 Why log scale is mandatory for long-term charts
  3. 03.02.03 Aspect ratio and the illusion of steepness
  4. 03.02.04 Auto-scaling traps
0 of 4 read
Learn

The axis is a conversion rule

Every chart in chapter 03.01 kept the prices intact. This chapter changes nothing about them either. What changes is the price axis — the rule that converts each rupee value into a position on screen.

A linear axis gives equal space to equal rupee change. One centimetre is worth the same number of rupees everywhere on the axis, so the distance from ₹100 to ₹200 equals the distance from ₹900 to ₹1,000.

A logarithmic axis gives equal space to equal percentage change. One centimetre is worth the same multiple everywhere, so the distance from ₹100 to ₹200 equals the distance from ₹200 to ₹400 — both are a doubling.

See it

Two rises of exactly ₹100

An illustrative share rises ₹100 twice: once from ₹100, once from ₹900. Switch the axis and watch the same two facts change size.

Neither drawing is wrong. They answer different questions: how many rupees, and how many percent.

Learn

How to tell which one you are looking at

You do not need a settings menu. Read two consecutive labels on the price axis and look at the gaps.

If the labels step by a constant rupee amount and sit at equal distances — ₹400, ₹700, ₹1,000 — the axis is linear. If the labels multiply while the distances stay equal — ₹100, ₹200, ₹400, ₹800 — the axis is logarithmic.

There is a second tell. On a logarithmic axis, the gridlines inside each stretch crowd together as you move up it, because each further rupee is a smaller percentage of the price it is added to. A linear axis is evenly ruled from bottom to top.

The two ₹100 rises, in both currencies of measurement
₹100 rising to ₹200
+₹100 · +100%
₹900 rising to ₹1,000
+₹100 · +11.1%
Their height on a linear axis
identical
Their height on a logarithmic axis
the first is about 6.5 times the second
+₹100what a linear axis measures
+100% / +11.1%what a logarithmic axis measures
Try it

A chart's price axis is labelled ₹250, ₹500, ₹1,000, ₹2,000, with the same gap between each label. What does that tell you?

Learn

What the choice does and does not do

Both axes plot the same recorded prices. Every high, low, close and gap is still there, at the same date, with the same value. Changing the scale changes no data and no return.

What it changes is which comparison your eye can make without arithmetic. On a linear axis, two moves that look the same size are the same size in rupees. On a logarithmic axis, two moves that look the same size earned the same percentage.

So the choice follows the question, exactly as the chart type did in 03.01.05. If you are thinking about a fixed rupee amount — a ₹50,000 position, a ₹20 difference between two orders — linear answers you directly. If you are thinking about rate of return across different price levels, linear will mislead your eye and logarithmic will not.

Try it

Which of these changes when you switch a chart from linear to logarithmic?

The apparent steepness of an early rise
The recorded high, low, open and close
Whether two separate rises look equally large
The return the share actually delivered
The spacing of the gridlines on the price axis
The date each price belongs to

Before you read any chart's shape

Name the scale out loud. A screenshot with no visible axis labels is not evidence of a move's size, because the two axes draw the same data into two different shapes. If you cannot see the labels, you cannot tell whether a dramatic early climb is a large percentage or a rounding error — and you cannot tell whether a flat stretch is genuinely quiet.

Over a few weeks the two axes usually draw similar pictures, because a share rarely changes by a large multiple in that time. The difference becomes impossible to ignore once the chart covers years.

Remember

A linear axis gives equal height to equal rupees and a logarithmic axis gives equal height to equal percentages, so the axis you are on decides which of two moves looks bigger — while changing neither the prices nor the returns.

Next
03.02.02 — Why log scale is mandatory for long-term charts

Next: stretch the same choice across years, and one of the two axes stops working.