When to use this calculator
Solve the time needed to reach a target under constant compound growth. A target below the start produces a negative model time at a positive growth rate.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Matrix Trace Calculator: Calculate the trace of a three-by-three matrix from its diagonal.
PUTTING IT INTO PRACTICE
Logarithmic Growth Time: 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 |
|---|---|
| Starting amount | 100 |
| Target amount | 200 |
| Effective growth per period (%) | 100 |
| Result | 1 periods |
- Check the input labels and enter the example values above.
- Apply the relationship: Time = ln(target/start)/ln(1+rate/100).
- The result is 1 periods, rounded for display.
How to interpret your result
A target below the start produces a negative model time at a positive growth rate.
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 logarithmic growth time calculator useful?
Solve the time needed to reach a target under constant compound growth. A target below the start produces a negative model time at a positive growth rate.
How do I use the logarithmic growth time calculator?
Enter starting amount, target amount, effective growth per period (%). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Time = ln(target/start)/ln(1+rate/100).
What should I check before using the result?
A target below the start produces a negative model time at a positive growth rate.
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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