When to use this calculator
Find a constant two-period growth rate equivalent to two different returns. Assumes sequential returns on the same investment with no intervening cash flow.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Geometric Sequence Calculator: Find a term in a sequence multiplied by a fixed ratio each step.
PUTTING IT INTO PRACTICE
Geometric Mean Growth Rate: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First period return (%) | 10 |
| Second period return (%) | -10 |
| Result | -0.501256 % |
- Check the input labels and enter the example values above.
- Apply the relationship: Equivalent rate (%) = (√((1+a/100)(1+b/100))−1) × 100.
- The result is -0.501256 %, rounded for display.
How to interpret your result
Assumes sequential returns on the same investment with no intervening cash flow.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the geometric mean growth rate calculator useful?
Find a constant two-period growth rate equivalent to two different returns. Assumes sequential returns on the same investment with no intervening cash flow.
How do I use the geometric mean growth rate calculator?
Enter first period return (%), second period return (%). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Equivalent rate (%) = (√((1+a/100)(1+b/100))−1) × 100.
What should I check before using the result?
Assumes sequential returns on the same investment with no intervening cash flow.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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