science

Orders of magnitude (length)

Orders of magnitude (length) 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 Orders of magnitude (length) rather than just read about it. In short: The following are examples of orders of magnitude for different lengths. Overview Detailed list To help compare different orders of magnitude, the following list describes various lengths between 1.6 × 10 − 35 {\displaystyle 1.6\times 10^{-35}} metres and 10 10 10 122 {\displaystyle 10^{10^{10^{122}}}} metres.

Key takeaways

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

Reference excerpt

The following are examples of orders of magnitude for different lengths.

Overview

Detailed list To help compare different orders of magnitude, the following list describes various lengths between 1.6 × 10 − 35 {\displaystyle 1.6\times 10^{-35}} metres and 10 10 10 122 {\displaystyle 10^{10^{10^{122}}}} metres. Metres are used in these tables to provide a common reference point, but metric prefixes above "k" are not commonly used with metres. So for example, 1.21 Gm would more commonly be written as 1.21 million km or (in scientific notation) 1.21 × 106 km. Interplanetary distances are also commonly measured in astronomical units. Distances on the interstellar or larger scale are typically measured in light-years or parsecs.

Subatomic scale

Atomic to cellular scale

Cellular to human scale

Human to astronomical scale

Astronomical scale

1 quectometre and less The quectometre (SI symbol: qm) is a unit of length in the metric system equal to 10−30 metres. To help compare different orders of magnitude, this section lists lengths shorter than 10−30 m (1 qm).

0 quectometres (0 meters) — gravitational singularity 1.6 × 10−5 quectometres (1.6 × 10−35 metres) – the Planck length (Measures of distance shorter than this do not make physical sense, according to current theories of physics.) 1 qm – 1 quectometre, the smallest named subdivision of the metre in the SI base unit of length, one nonillionth of a metre.

1 rontometre The rontometre (SI symbol: rm) is a unit of length in the metric system equal to 10−27 metres.

10 rontometres 10 rm – the length of one side of a square whose area is one shed, a unit of target cross section used in nuclear physics

1 yoctometre The yoctometre (SI symbol: ym) is a unit of length in the metric system equal to 10−24 metres.

2 ym – the effective cross-section radius of 1 MeV neutrinos as measured by Clyde Cowan and Frederick Reines.

1 zeptometre The zeptometre (SI symbol: zm) is a unit of length in the metric system equal to 10−21 metres. To help compare different orders of magnitude, this section lists lengths between 10−21 m and 10−20 m (1 zm and 10 zm).

2 zm – the upper bound for the width of a cosmic string in string theory. 2 zm – radius of effective cross section for a 20 GeV neutrino scattering off a nucleon 7 zm – radius of effective cross section for a 250 GeV neutrino scattering off a nucleon

10 zeptometres To help compare different orders of magnitude, this section lists lengths between 10−20 m and 10−19 m (10 zm and 100 zm).

100 zeptometres To help compare different orders of magnitude, this section lists lengths between 10−19 m and 10−18 m (100 zm and 1 am).

177 zm – de Broglie wavelength of protons at the Large Hadron Collider (7 TeV as of 2010)

1 attometre The attometre (SI symbol: am) is a unit of length in the metric system equal to 10−18 metres. To help compare different orders of magnitude, this section lists lengths between 10−18 m and 10−17 m (1 am and 10 am).

1 am – sensitivity of the LIGO detector for gravitational waves 1 am – upper limit for the size of quarks and electrons

10 attometres To help compare different orders of magnitude, this section lists lengths between 10−17 m and 10−16 m (10 am and 100 am).

10–100 am – range of the weak force 86 am – charge radius of a Bottom eta meson

100 attometres To help compare different orders of magnitude, this section lists lengths between 10−16 m and 10−15 m (100 am and 1 fm).

831 am – approximate proton radius

1 femtometre (or 1 fermi) The femtometre (SI symbol: fm) is a unit of length in the metric system equal to 10−15 metres. In particle physics, this unit is sometimes called a fermi, also with abbreviation "fm". To help compare different orders of magnitude, this section lists lengths between 10−15 metres and 10−14 metres (1 femtometre and 10 fm).

1 fm – diameter of a neutron, approximate range-limit of the color force carried between quarks by gluons 1.5 fm – diameter of the scattering cross section of an 11 MeV proton with a target proton 1.75 fm – the effective charge diameter of a proton 2.81794 fm – classical electron radius 3 fm – approximate range-limit of the nuclear binding force mediated by mesons 7 fm – the radius of the effective scattering cross section for a gold nucleus scattering a 6 MeV alpha particle over 140 degrees

10 femtometres To help compare different orders of magnitude, this section lists lengths between 10−14 m and 10−13 m (10 fm and 100 fm).

1.75 to 15 fm – diameter range of the atomic nucleus 10 fm – the length of one side of a square whose area is one barn (10−28 m2), a unit of target cross section used in nuclear physics 30.8568 fm – 1 quectoparsec (10−30 parsecs)

100 femtometres

To help compare different orders of magnitude, this section lists lengths between 10−13 m and 10−12 m (100 fm and 1 pm).

570 fm – typical distance from the atomic nucleus of the two innermost electrons (electrons in the 1s shell) in the uranium atom, the heaviest naturally occurring atom

1 picometre The picometre (SI symbol: pm) is a unit of length in the metric system equal to 10−12 metres (⁠1/1000000000000⁠ m = 0.000000000001 m). To help compare different orders of magnitude this section lists lengths between 10−12 and 10−11 m (1 pm and 10 pm).

1 pm – distance between atomic nuclei in a white dwarf 1 pm – reference value of particle displacement in acoustics 2.4 pm – the Compton wavelength of an electron 5 pm – shorter X-ray wavelengths (approx.)

10 picometres To help compare different orders of magnitude this section lists lengths between 10−11 and 10−10 m (10 pm and 100 pm).

25 pm – approximate radius of a helium atom, the smallest neutral atom 30.8568 pm – 1 rontoparsec 50 pm – Bohr radius: approximate radius of a hydrogen atom ~50 pm – best resolution of a high-resolution transmission electron microscope 60 pm – radius of a carbon atom 93 pm – length of a diatomic carbon molecule 96 pm – H–O bond length in a water molecule

100 picometres To help compare different orders of magnitude this section lists lengths between 10−10 and 10−9 m (100 pm and 1 nm; 1 Å and 10 Å).

… excerpt ends here. Continue reading the full article.

Illustrations

Orders of magnitude (length): The silk for a spider's web is 5–7 μm (0.00020–0.00028 in) wide. — The silk for a spider's web is 5–7 μm (0.00020–0.00028 in) wide.

Worked examples

Example 1 — a first encounter with Orders of magnitude (length)

Start with the simplest possible case. Write down what Orders of magnitude (length) 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 Orders of magnitude (length) 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 Orders of magnitude (length) 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 Orders of magnitude (length)

In research: Orders of magnitude (length) 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 Orders of magnitude (length) 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: Orders of magnitude (length) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Length, Lists by length, Orders of magnitude, so understanding it makes those chapters shorter.
In everyday life: Look for Orders of magnitude (length) 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 Orders of magnitude (length) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Orders of magnitude (length) means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Orders of magnitude (length) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Orders of magnitude (length) in simple terms?

The following are examples of orders of magnitude for different lengths. Overview Detailed list To help compare different orders of magnitude, the following list describes various lengths between 1.6 × 10 − 35 {\displaystyle 1.6\times 10^{-35}} metres and 10 10 10 122 {\displaystyle 10^{10^{10^{122…

Why does Orders of magnitude (length) 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 Orders of magnitude (length)?

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 Orders of magnitude (length).