About the Common Ratio Calculator
Find the common ratio of a geometric sequence from two terms and their positions, plus the first term.
Also known as: find common ratio, geometric ratio, r in geometric sequence.
How to use this calculator
- Enter term value aₘ, position m, term value aₙ, position n.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Open “Step-by-step” to see how the answer was worked out.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
r = (aₙ / aₘ)^(1/(n − m))
Worked example
Using the values pre-filled in the calculator above:
- Term value aₘ = 6
- Position m = 2
- Term value aₙ = 162
- Position n = 5
the calculator returns:
- Common ratio r: 3
- First term a₁: 2
Working
r = (162 ÷ 6)^(1/3) = 3