How this calculation works
Evaluate a generalized figurate number from the number of sides and the term index.
THE FORMULA
P(s,n)=((s−2)n²−(s−4)n)/2A worked example
The fourth pentagonal number is (3×16−4)/2 = 22.
Good to know
Index zero gives zero.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Evaluate a generalized figurate number from the number of sides and the term index.
The primary result is labeled “Polygonal number”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Index zero gives zero.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
The fourth pentagonal number is (3×16−4)/2 = 22.
Which rule does this calculator apply?
P(s,n)=((s−2)n²−(s−4)n)/2