Elton John once sang that sorry seemed to be hardest word but now scientists have found that the perfect apology requires more than just the word 'sorry' itself.

Based on the findings of a new study, researchers said there are six key elements to make one's apology more sincere and easy to accept with two being very critical in ensuring acceptance. They are accepting one's own fault and offering to repair the damage when making an apology, according to Ohio State University researchers.

The study looked at how 755 volunteers reacted to apologies that contained some or all of the six key elements in two separate parts.

The first part involved 333 adults acting out a fictional scenario where they were an accounting department manager interviewing a potential employee. The applicant had filed an incorrect tax return during their previous work but when asked during the fake interview about it, they apologised. The adults involved in the study then had to rate different apologies which contained one, three or all of the sorry elements listed above. The scale was between one (not at all) and five (very).

In the second part of the research, 422 undergraduates had the same scenario but this time they did not know what elements were within the apologies and had to rate it in a similar fashion.

The results were not exactly the same, but very similar, researchers said, and those apologies that contained more of the elements were rated higher than others.

"Apologies really do work, but you should make sure you hit as many of the six key components as possible," said Roy Lewicki, from the university's Fisher College of Business.

"Our findings showed that the most important component is an acknowledgement of responsibility," Mr Lewicki, who led the study, said. "Say it is your fault, that you made a mistake."

He added that an offer of repair was crucial because "one concern about apologies is that talk is cheap". But by offering to fix the damage, "you're committing to take action to undo the damage", he said.