Began is the simple past and stands alone: "the meeting began at ten." Begun is the past participle and needs a helper verb — have, has, had, or a form of be: "the meeting has begun." If there is no helper verb, you want began.
The core difference
Both are past forms of begin, and the choice is decided entirely by whether a helper verb is present.
- began — no helper: He began the course last year.
- begun — with have/has/had: He has begun the course.
- begun — with be, forming the passive: Work has been begun.
The same pattern elsewhere
This is the identical shape as drank/drunk, rang/rung, sang/sung and swam/swum. If "I have drank" sounds wrong to you, "I have began" is wrong in exactly the same way, and the fix is the same.
The mistake in the wild
The common error is "has began" rather than "has begun". It is frequent in speech and is the one to watch for in writing.
Frequently asked questions
Is "has began" correct?
No. After has, have or had you need the participle: has begun.
How do I remember which is which?
Test with drank and drunk, which follow the same pattern. If the sentence would take drunk, it takes begun.
Which do I use with "was"?
Begun. A passive built on a form of be takes the past participle: work was begun.