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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
the plane on which
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "the plane on which" is correct and usable in written English.
It can be used when referring to a specific surface or level in a metaphorical or literal sense, often in discussions about concepts or ideas. Example: "The plane on which we operate our business must be constantly evaluated for efficiency."
✓ Grammatically correct
Science
News & Media
Encyclopedias
Alternative expressions(20)
the earth on which
the foundation on which
the page on which
the level at which
the framework within which
the medium through which
on that day
the date on which
on the date that
when
the specific day
the occasion when
the data on which
the day that
When
the date of which
the occasion on which
the day on which
the date when
the area where
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
30 human-written examples
'Top,' the plane on which one could start detecting at least 20% of the field with stain-positive area for fibronectin fibers and one additional plane below.
Science
Airbus supporters said the trade panel had rejected some of the claims by the United States, including one that the A330-200 — the plane on which the EADS refueling tanker is based — also benefited from a loan tied to export sales.
News & Media
Off-balance was the plane on which Monk existed.
News & Media
(number) The z-coordinate of the plane on which to obtain the field.
Academia
Chief among these quirks is the dramatic twisting of the signal's polarization — the plane on which the waves oscillate.
News & Media
The plane on which they had planned to escape accompanied by Zaidan was located, and U.S. Pres.
Encyclopedias
Human-verified similar examples from authoritative sources
Similar Expressions
30 human-written examples
Traces of polonium have been found on the planes on which they are believed to have travelled between London and Moscow.
News & Media
Schulman, the author of the New York Times bestseller This Beautiful Life, follows Amy Reed, the newly minted PR chief at a Silicon Valley startup that allows people to explore their "multitudes" — the planes on which all their alternative life choices play out simultaneously.
Academia
In a show of pride from the grave, obituaries of Boeing employees typically include the model number of the planes on which the deceased worked.
News & Media
Once more the enemy fighters flash in, machine-guns shatter in violent burst, explosions of flak fly over the targets and planes shudder as bombs are dropped.But the fellows who sit in the cockpit of the one plane on which the actions center are a dull pair and are rendered even duller by poor acting and weak direction.
News & Media
All that had been excluded by the crop was the hostile speck of the enemy plane on which the Penguin one was swooping.
News & Media
Expert writing Tips
Best practice
Use "the plane on which" to precisely define a surface or level when discussing technical or abstract concepts. Clarity is key in these contexts.
Common error
Avoid using "the plane on which" in simple sentences where a more direct preposition like "on" or "where" would suffice. Overcomplicating simple ideas can obscure your meaning.
Source & Trust
84%
Authority and reliability
4.5/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "the plane on which" functions as a prepositional phrase modifying a noun. It specifies a particular surface, level, or area of focus. Ludwig examples showcase its use in diverse contexts, from technical descriptions to abstract concepts.
Frequent in
Science
40%
News & Media
35%
Encyclopedias
25%
Less common in
Formal & Business
0%
Wiki
0%
Reference
0%
Ludwig's WRAP-UP
In summary, "the plane on which" is a grammatically correct prepositional phrase used to specify a location, either literal or abstract. Ludwig AI confirms its validity. While its frequency is common, its formality lends itself to technical, scientific, and formal writing. Related phrases such as "the surface on which" or "the level at which" can serve as simpler alternatives in less formal contexts. Overusing this phrase in place of simpler constructions should be avoided. Usage patterns indicate that the phrase is common in science, news, and encyclopedic sources.
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
the surface on which
Replaces "plane" with "surface", emphasizing the two-dimensional aspect of the location.
the level at which
Substitutes "plane" with "level", focusing on a more abstract or hierarchical placement.
the medium through which
Replaces "plane" with "medium", highlighting the means by which something is conveyed or occurs.
the stage on which
Substitutes "plane" with "stage", implying a setting for events or actions.
the basis upon which
Changes the structure to emphasize the foundation or reason for something.
the framework within which
Replaces "plane" with "framework", indicating a structural or conceptual boundary.
the area where
Simplifies the phrase to indicate a general location.
the domain in which
Replaces "plane" with "domain", suggesting a specific field or sphere of activity.
the sphere of
A more concise alternative that emphasizes the area of influence or operation.
the field where
Similar to "area where", but can also imply a field of study or activity.
FAQs
How can I use "the plane on which" in a sentence?
Use "the plane on which" to specify a surface or level where something is located or occurs. For example, "The sketching plane that you choose will be "the plane on which" the runner will open out to the mold surface."
What are some alternatives to "the plane on which"?
Depending on the context, you can use alternatives such as "the surface on which", "the level at which", or simply "where" to convey a similar meaning.
Is "the plane on which" formal or informal?
"The plane on which" tends to be more formal. In informal contexts, simpler prepositions or relative clauses may be more appropriate.
When is it best to use "the plane on which" over simpler alternatives?
Use "the plane on which" when precision is necessary, particularly in technical, scientific, or abstract discussions. Simpler alternatives like "where" might lack the required specificity.
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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
84%
Authority and reliability
4.5/5
Expert rating
Real-world application tested