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Linear scale

Linear scale is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Linear scale rather than just read about it. In short: A linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing. A scale bar is common element of map layouts.

Linear scale — main illustration
Linear scale — illustration

Key takeaways

  • Linear scale belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Linear scale to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Linear scale from memory before moving on to harder problems.

Reference excerpt

A linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing. A scale bar is common element of map layouts. On large scale maps and charts, those covering a small area, and engineering and architectural drawings, the linear scale can be very simple, a line marked at intervals to show the distance on the earth or object which the distance on the scale represents. A person using the map can use a pair of dividers (or, less precisely, two fingers) to measure a distance by comparing it to the linear scale. The length of the line on the linear scale is equal to the distance represented on the earth multiplied by the map or chart's scale. In most projections, scale varies with latitude, so on small scale maps, covering large areas and a wide range of latitudes, the linear scale must show the scale for the range of latitudes covered by the map. One of these is shown below. Since most nautical charts are constructed using the Mercator projection whose scale varies substantially with latitude, linear scales are not used on charts with scales smaller than approximately 1/80,000. Mariners generally use the nautical mile, which, because a nautical mile is approximately equal to a minute of latitude, can be measured against the latitude scale at the sides of the chart. While linear scales are used on architectural and engineering drawings, particularly those that are drawn after the subject has been built, many such drawings do not have a linear scale and are marked "Do Not Scale Drawing" in recognition of the fact that paper size changes with environmental changes and only dimensions that are specifically shown on the drawing can be used reliably in precise manufacturing.

Nomenclature

The terms "bar scale", "graphic scale", "graphical scale", "linear scale", and "scale" are all used. Bowditch defined only "bar scale" in its 1962 Glossary, but added a reference to "graphic scale" by its 2002 edition. Dutton used both terms in 1978. The International Hydrographic Organization's Chart No. 1 uses only "linear scale". The British Admiralty's Mariner's Handbook uses "scale" to describe a linear scale and avoids confusion by using "natural scale" for the fraction defined at scale (map).

See also Engineer's scale Logarithmic scale (useful e.g. when the data covers a large range of values)

References

Illustrations

Linear scale: A linear scale showing that one centimetre on the map corresponds to six kilometres
A linear scale showing that one centimetre on the map corresponds to six kilometres
Linear scale: Linear scale in both feet and metres in the center of an engineering drawing. The drawing was made 130 years after the bridge was built.
Linear scale in both feet and metres in the center of an engineering drawing. The drawing was made 130 years after the bridge was built.
Linear scale illustration
Linear scale: An architectural drawing with a simple linear scale showing feet and half feet.
An architectural drawing with a simple linear scale showing feet and half feet.

Worked examples

Example 1 — a first encounter with Linear scale

Start with the simplest possible case. Write down what Linear scale claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Linear scale before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Linear scale ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Linear scale

In research
Linear scale appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Linear scale in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Linear scale is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cartography, Scales, Technical drawing, so understanding it makes those chapters shorter.
In everyday life
Look for Linear scale outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Linear scale in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Linear scale means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Linear scale out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Linear scale in simple terms?

A linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing. A scale bar is common element of map layouts.

Why does Linear scale matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Linear scale?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Linear scale.

Tags

  • Cartography
  • Scales
  • Technical drawing

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