Corollary

Simple meaning

A corollary is a conclusion or result that follows so naturally from something already proven or accepted that it requires little or no additional argument.

Detailed meaning

In mathematics, a corollary is a theorem that follows so easily from a previous theorem that it barely needs its own proof. Prove Theorem A, and Corollary B comes along almost for free.

In everyday professional and intellectual language, a corollary is any direct, predictable consequence of a stated position or decision. If you accept the main idea, the corollary comes with it — you can't really reject one without rejecting the other.

The word is especially powerful in analytical writing and strategic conversation because it shows that your thinking goes beyond the surface:

• "If we agree that speed is the priority, a corollary is that we accept some quality risk."
• "A corollary of reducing headcount is that remaining staff take on more — that's not a separate decision, it's part of the same one."
• "The corollary to increasing transparency is that we must be comfortable with what gets revealed."

The plural is corollaries. You can also use it as an adjective: "the corollary implication" or "as a corollary result."

Picture this

Imagine you accept that the earth is round. A corollary follows almost immediately: if you travel in a perfectly straight line long enough, you'll eventually return to where you started. You didn't need to prove that separately — it flows directly from what you already accepted.

Or at work: if a company decides its priority is becoming the lowest-cost provider in a market, a corollary is that every process must be optimised for cost, not quality. That isn't a new decision — it's the first decision unfolding.

Where to use it

Use corollary when a consequence follows so naturally from a position that it should be accepted alongside it — not debated separately.

Where not to use it

Don't use corollary when the connection between two things is loose, debatable, or requires significant additional evidence. A corollary should feel nearly automatic — not argued for, but recognised.

5 example sentences

1. If we agree to expand into three new markets, a natural corollary is that our support team needs to scale proportionally.
2. The discovery that all humans share 99.9% of their DNA has a striking corollary: our differences are almost entirely cultural, not biological.
3. A corollary of accepting remote-first work is that management must shift from presence-based evaluation to outcome-based measurement.
4. In geometry, many famous corollaries follow from just a handful of fundamental theorems.
5. The corollary to "hire for attitude, train for skill" is that you must build genuinely strong training programmes, or the attitude is wasted.

Common mistakes

Similar & opposite words

Similar (synonyms)

Opposite (antonyms)

Memory trick

A short story to remember it

The strategy consultant had just finished presenting her recommendation: the firm should consolidate its twelve regional offices into four hub locations.

"I accept the recommendation," the CEO said. "But I want to understand the full picture. What are the corollaries?"

The consultant had prepared for this. "Three immediate ones," she said. "First: some top talent in the closed offices will leave rather than relocate — that's predictable. Second: the remaining hubs must have the infrastructure to absorb the load immediately, not eventually. Third: client relationships in removed regions must be actively managed, or we'll lose them."

The CFO nodded. "So accepting the consolidation means accepting all three of those realities. They're not separate risks — they're corollaries."

"Exactly," the consultant said. "You can't take the decision without taking what comes with it."

Practice quiz

Summary

Corollary is the precise word for a consequence so logically close to its source that it comes along almost for free. Understanding corollaries shows that your thinking doesn't stop at the main point — you follow ideas to their natural conclusions.