Common Ratio Calculator

About this calculator

The common ratio of a geometric sequence is the fixed number you multiply each term by to get the next one, found by dividing any term by the term immediately before it: r = a(n+1) ÷ a(n). Unlike an arithmetic sequence, where consecutive terms differ by a constant amount, a geometric sequence grows or shrinks by a constant factor, which is why sequences like 3, 6, 12, 24 (r = 2) or 100, 50, 25, 12.5 (r = 0.5) either compound upward or decay toward zero.

Students and teachers use the common ratio to identify and continue geometric sequences in algebra courses, while it also underpins real-world compounding models — a savings account compounding at a fixed rate, radioactive decay, or exponential population growth are all geometric sequences under the hood, with the common ratio playing the role of the growth or decay factor.

This calculator takes any two consecutive terms of a sequence and returns the common ratio, plus the next term the sequence would produce.