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Prepositions after adjectives

Proportional to, in or with?

Proportional normally takes to when comparing relative size, amount, or degree.

Quick answer

Which preposition follows proportional?

Use proportional to for mathematical, statistical, or general comparisons. In and with may appear in surrounding phrases but are not the normal complement after proportional.

Pay should be proportional to experience.
The response was proportional to the threat.

Choose the pattern by meaning

These forms are not interchangeable. Choose the construction by meaning, not by which preposition appears most often.

1
proportional to + amount

Relationship between quantities

Use to when one thing changes in relation to another.

Costs are proportional to production volume.
2
directly proportional to + factor

Mathematical relationship

This pattern is common in science and mathematics.

Speed is directly proportional to distance travelled.

See the difference in context

The same subject can take different constructions because each sentence answers a different question.

Construction
Example
Meaning
proportional to
The fine was proportional to the damage.
Correct standard pattern for relative degree.
proportional in
The increase was proportional in all regions.
In all regions describes scope, not the adjective complement.
proportional with
The phrase proportional with is uncommon in modern standard English.
Usually replace with proportional to.

Common mistakes

Some combinations appear in real text but do not mean what learners often assume.

Using with instead of to

Proportional normally takes to.

✕ The tax is proportional with income. ✓ The tax is proportional to income.

Using in as the complement

In usually adds separate context information.

✕ The result is proportional in effort. ✓ The result is proportional to effort.

Quick practice

Choose the expression that matches the intended meaning.

1. The reward should be proportional ___ the risk.
2. In physics, force may be directly proportional ___ mass.
3. Which phrase is generally uncommon?

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Frequently asked questions

Is proportional to the standard phrase?

Yes. It is the normal and widely accepted pattern.

Can proportional be used in mathematics?

Yes. It is common in mathematical and scientific writing.

Is proportional with incorrect?

It is generally considered nonstandard or unnatural in modern English.

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