How this calculation works
Count circular arrangements with rotations identified and clockwise order preserved.
THE FORMULA
(n−1)!A worked example
Fix one of six people and arrange the other five in 120 ways.
Good to know
Reflections count as distinct unless they coincide.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count circular arrangements with rotations identified and clockwise order preserved.
The primary result is labeled “Seatings up to rotation”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Reflections count as distinct unless they coincide.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Fix one of six people and arrange the other five in 120 ways.
Which rule does this calculator apply?
(n−1)!