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
expanded at a constant rate
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "expanded at a constant rate" is correct and usable in written English.
It can be used in contexts involving growth, development, or change that occurs steadily over time. Example: "The company's revenue expanded at a constant rate over the last five years, demonstrating consistent growth."
✓ Grammatically correct
Science
News & Media
Academia
Alternative expressions(3)
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified similar examples from authoritative sources
Similar Expressions
60 human-written examples
In other words, if we assume that the Universe has been expanding at a constant rate since the Big Bang, then the rate of expansion tells us how far back in time the expansion started, which we take to be the beginning of the Universe.
Academia
If it has been expanding at a constant rate of 10 milliarcseconds a year, then it would take 1000 ± 260 years to reach a diameter of 20 arcseconds.
Wiki
Each individual plant's root system starts as a point and expands radially (i.e. as an expanding circle) with growth at a constant rate (by area).
Science
Genes, like languages, do not mutate at a constant rate.
News & Media
Molecular sequences rarely evolve at a constant rate.
Academia
Increase payouts at a constant rate and adjust for risk.
News & Media
Our first one samples at a constant rate and kept a steering state variable.
Academia
For example, a falling body accelerates at a constant rate, g.
Encyclopedias
This note is repeated at a constant rate of delivery in about 5-6 second intervals.
Academia
For this reason we recommend that boards increase payouts at a constant rate relative to performance.
News & Media
Obviously if sea level rise is accelerating, it's not increasing at a constant rate.
News & Media
Expert writing Tips
Best practice
When describing growth or change, ensure that "expanded at a constant rate" accurately reflects a steady and uniform progression over time. Use it when precision and consistency are important.
Common error
Avoid using "expanded at a constant rate" if the growth fluctuates, even slightly. Ensure data truly reflects uniformity before using this phrase. It's more precise than saying "increased steadily".
Source & Trust
88%
Authority and reliability
4.5/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "expanded at a constant rate" functions as a descriptive phrase, typically modifying a noun to indicate the manner in which something has grown or increased. This is supported by the examples provided, where Ludwig AI confirms its grammatical correctness.
Frequent in
Science
40%
News & Media
30%
Academia
30%
Less common in
Formal & Business
0%
Encyclopedias
0%
Wiki
0%
Ludwig's WRAP-UP
The phrase "expanded at a constant rate" is a grammatically correct and usable expression, as verified by Ludwig. It indicates a steady and uniform increase over time. While not exceedingly common, it finds usage across science, news media, and academic contexts. When writing, ensure that the context truly reflects a consistent rate of expansion to avoid misinterpretations. Alternatives include phrases like "grew steadily" or "increased uniformly".
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
increased at a uniform rate
Highlights the sameness of the rate of increase, focusing on the lack of variation.
grew at a steady pace
Emphasizes a consistent and regular increase without specifying the uniformity as strongly.
progressed at a consistent speed
Focuses on the continuous and unchanging nature of the speed of progression.
augmented at a linear progression
Mathematically precise, indicating a straight-line increase over time.
developed at a stable tempo
Suggests a balanced and unwavering rhythm of development, often used in more technical contexts.
advanced at an even keel
Implies a steady and balanced advancement, avoiding sudden changes or disruptions.
unfolded at a predictable rhythm
Emphasizes the anticipated and unchanging pattern of unfolding or growth.
escalated at a fixed increment
Highlights the methodical and predetermined nature of the increase.
marched forward at a constant velocity
Suggests a continuous and unwavering movement in a forward direction.
extended at a regular clip
Informal and suggests a brisk, but consistent, pace of expansion.
FAQs
How can I use "expanded at a constant rate" in a sentence?
You can use "expanded at a constant rate" to describe phenomena that grow or increase steadily over time. For example, "The universe "expanded at a constant rate" after the Big Bang, according to some theories."
What is a good alternative to "expanded at a constant rate"?
Alternatives include "grew steadily", "increased uniformly", or "progressed consistently". The best choice depends on the specific nuance you want to convey.
Is "expanded at a constant rate" the same as "grew exponentially"?
No, "expanded at a constant rate" implies a linear increase, while "grew exponentially" signifies an accelerating increase. They describe fundamentally different growth patterns.
When is it appropriate to use "expanded at a constant rate" in scientific writing?
Use "expanded at a constant rate" when describing phenomena where the rate of growth or increase remains the same over time. This is common in physics, biology, and economics when modeling linear growth.
Editing plus AI, all in one place.
Stop switching between tools. Your AI writing partner for everything—polishing proposals, crafting emails, finding the right tone.
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
88%
Authority and reliability
4.5/5
Expert rating
Real-world application tested