Used and loved by millions
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com
by which are
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "by which are" is correct and usable in written English.
It can be used to introduce a clause that explains the means or method by which something is done or achieved. Example: "The methods by which are employed in this study are innovative and effective."
✓ Grammatically correct
Science
News & Media
Alternative expressions(7)
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified examples from authoritative sources
Exact Expressions
8 human-written examples
It ranked them by which are judged to be the most vulnerable to members' switching to competitors' programs.
News & Media
In Figure 4, the trellis diagram is preceded by and followed by which are two dummy nodes.
The photon trajectory is uniquely described by, which are scattering distance set, scattering zenith angle set, and scattering azimuth angle set for successive scatterings, respectively.
The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem.
For desire-based reasons theorists, normative talk, talk about (justifying) reasons, is effectively talk about desires, talk the beliefs we express by which are made true, if they are true, by facts about the desires of the people to whom we say reasons apply.
Science
[Charles S. Peirce, 'The Logic of Quantity' (1893: 7.127)] "[We must distinguish between the category of Natural Frontiers and] the category of Artificial Frontiers, by which are meant those boundary lines which, not being dependent upon natural features of the earth's surface for their selection, have been artificially or arbitrarily created by man".
Science
Human-verified similar examples from authoritative sources
Similar Expressions
52 human-written examples
The second is "best by", which is a communication from the manufacturer to the consumer.
News & Media
"In hiding," cracked a server who passed by, which was funny but then again not.
News & Media
Description of the process by which is converted into crude oil.
News & Media
Lots of locals stop by, which is why the food's so good.
News & Media
The "Feed Me Now" option simply sorts the restaurants by which is closest.
News & Media
Expert writing Tips
Best practice
Use "by which are" to clearly link a method or process to a subsequent explanation or description.
Common error
Avoid overuse of "by which are" in informal contexts, as it can sound stilted. Opt for simpler alternatives like "that are" or "which are" in casual writing.
Source & Trust
85%
Authority and reliability
4.3/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "by which are" functions as a relative clause connector, specifically indicating the means or method by which something is accomplished. Ludwig provides examples showing its use in introducing clauses that further define or explain the preceding noun.
Frequent in
Science
60%
News & Media
40%
Formal & Business
0%
Less common in
Encyclopedias
0%
Wiki
0%
Social Media
0%
Ludwig's WRAP-UP
In summary, the phrase "by which are" serves as a formal connector linking a noun to a descriptive clause, often detailing the methods or processes involved. Ludwig's analysis, based on a variety of sources, confirms its grammatical correctness but suggests that it's more appropriate for formal and scientific contexts. While it effectively adds precision, overuse can lead to a stilted tone, suggesting that alternatives such as "through which are" or "which are" may be more suitable in informal writing. The presence of this phrase in reputable sources such as The New York Times and scientific journals demonstrates its acceptability in academic and professional settings.
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
through which are
Emphasizes the channel or medium through which something passes or is accomplished.
by means of which are
Highlights the method or tool used to achieve a particular outcome.
whereby are
Indicates the method or process by which something is done or brought about.
according to which are
Specifies the rule or standard that governs a particular action or decision.
in accordance with which are
Stresses the compliance or conformity with a set of principles or guidelines.
by virtue of which are
Implies that something is a consequence or result of a particular quality or power.
on the basis of which are
Focuses on the foundation or rationale upon which something is based.
in terms of which are
Defines the framework or perspective from which something is considered or analyzed.
by reason of which are
Highlights the cause or justification for a particular event or situation.
dependent on which are
Indicates the conditions or factors that determine or influence a specific outcome.
FAQs
How can I use "by which are" in a sentence?
"By which are" is used to connect a noun phrase to a relative clause that describes a method or means. For example: "The methods "by which are" employed in this study are innovative."
What are some alternatives to "by which are"?
Depending on the context, you can use phrases like "through which are", "by means of which are", or simply "which are".
Is it always appropriate to use "by which are" in formal writing?
While generally suitable for formal writing, consider your audience. In some cases, a more straightforward construction might be preferable for clarity and conciseness. Opt for alternatives such as "that are" when appropriate.
What is the difference between "by which are" and "which are"?
"By which are" specifically indicates a method or means, whereas "which are" introduces additional information or describes attributes. "By which are" is more specific in its causal or instrumental implication.
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Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
85%
Authority and reliability
4.3/5
Expert rating
Real-world application tested