varies directly with

USAGE SUMMARY

The phrase "varies directly with" is correct and usable in written English.
It is typically used in mathematical or scientific contexts to describe a relationship where one variable increases or decreases in direct proportion to another variable. Example: "The speed of the car varies directly with the amount of fuel it consumes."

✓ Grammatically correct

Science

Encyclopedias

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

44 human-written examples

The case-fatality rate, as in typhus, varies directly with age.

Britannica

Dynamic type pumps obey the affinity laws: capacity varies directly with impeller diameter and speed, head varies directly with the square of impeller diameter and speed, and horsepower varies directly with the cube of impeller diameter and speed.

Rules of Thumb for Chemical Engineers A manual of quick, accurate solutions to everyday process engineering problems

Incubation time, which generally varies directly with size, ranges from 19 to 30 days or more.

Encyclopedia Britannica

Under the Minnesota law, the amount of the tax benefit varies directly with the amount of the expenditure.

Cornell University

Generally, the voltage varies directly with the frequency to keep the magnitude of the magnetic field constant.

Encyclopedia Britannica

Pycnoclines, or layers through which water density increases rapidly with depth, accompany such haloclines inasmuch as density varies directly with total salt content.

Encyclopedia Britannica

Human-verified similar examples from authoritative sources

Similar Expressions

16 human-written examples

It is found to vary directly with temperature.

Electrochimica Acta

Prevalence rates vary directly with both incidence and duration of disease.

Encyclopedia Britannica

Because manufacturing costs vary directly with weight, a comparison of the two trend lines in different periods is revealing.

Harvard Business Review

h was found to vary directly with oil temperature but inversely with sample size (p <0.05).

Food Research International

Maternal serum α-fetoprotein varied directly with viral load (P <.0001).

American Journal of Obstetrics and Gynecology

Expert writing Tips

Best practice

When using "varies directly with", ensure that the relationship you're describing is truly proportional. If the relationship is more complex, consider using a more nuanced phrase.

Common error

Avoid assuming that because one variable "varies directly with" another, one causes the other. Direct variation indicates a relationship, but not necessarily a causal one.

Linguistic Context

The phrase "varies directly with" functions as a relational expression, indicating a proportional relationship between two variables. As Ludwig AI confirms, this phrase is grammatically sound and commonly used. Examples include "voltage varies directly with frequency" and "density varies directly with salt content."

Expression frequency: Very common

Frequent in

Science

75%

Encyclopedias

10%

Academia

7%

Less common in

News & Media

5%

Formal & Business

2%

Wiki

1%

Ludwig's WRAP-UP

The phrase "varies directly with" is a grammatically correct and commonly used expression, particularly in scientific and academic writing. As confirmed by Ludwig AI, it effectively communicates a proportional relationship between two variables. Predominantly found in scientific contexts, the phrase indicates that as one quantity increases, the other increases proportionally. While useful for describing relationships, it's crucial to avoid implying causation solely based on this direct variation. Alternatives like "is directly proportional to" can offer a more formal or precise tone, depending on the context.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is directly proportional to

Uses mathematical terminology to indicate a proportional relationship.

increases proportionally with

Focuses on the increasing relationship between the two variables.

correlates positively with

Emphasizes the positive correlation, implying that as one increases, so does the other.

is in direct relation to

Highlights the direct relationship without necessarily implying strict proportionality.

scales linearly with

Indicates a linear relationship, a specific type of direct variation.

is dependent on

Broader term indicating a relationship where one quantity is influenced by another.

rises in tandem with

Suggests a simultaneous increase in both quantities.

grows alongside

Implies a parallel growth or increase.

is aligned with

Highlights the alignment in the trend between two variables.

is linked directly to

Emphasizes a clear and direct connection.

FAQs

How do I use "varies directly with" in a sentence?

Use "varies directly with" to describe a relationship where an increase in one quantity results in a proportional increase in another. For example, "The cost varies directly with the quantity ordered."

What's a good alternative to "varies directly with"?

Alternatives include "is directly proportional to", "increases proportionally with", or "correlates positively with". For instance, instead of "The intensity varies directly with the voltage", you could say "The intensity "is directly proportional to" the voltage".

Is it correct to say "varies directly with" or should I use another phrase?

"Varies directly with" is a correct and commonly used phrase, especially in scientific and mathematical contexts. However, you can also use more formal or precise alternatives like "is directly proportional to" for a more technical tone.

What is the difference between "varies directly with" and "varies inversely with"?

"Varies directly with" indicates that as one quantity increases, the other increases proportionally. "Varies inversely with" means that as one quantity increases, the other decreases proportionally. They describe opposite relationships. If A varies directly with B, increasing B increases A. If A varies inversely with B, increasing B decreases A.