Find how many intervals it takes to grow from a starting value to a target value at a fixed growth rate per interval, using the compound growth formula FV = PV × (1 + r)n.
Quick Facts
Formula
n = ln(FV ÷ PV) ÷ ln(1 + r)
Solves the compound growth equation FV = PV × (1 + r)ⁿ for the number of intervals n.
Results
Calculated
Intervals to Reach Target
—
Number of intervals needed at this rate
Growth Multiple
—
Target value ÷ initial value
Total Growth
—
Percent change from initial to target
Doubling Time
—
Intervals for a value to double at this rate
Ready
Enter an initial value, target value, and growth rate per interval, then press Calculate.
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How to use this calculator
This calculator answers a single question: how many growth intervals does it take to get from a starting value to a target value at a fixed rate per interval? Enter your initial value, target value, and growth rate per interval, choose what an "interval" represents (years, quarters, months, weeks, or generic periods), then click Calculate.
The formula
The standard compound growth equation is FV = PV × (1 + r)n, where PV is the initial value, FV is the target (final) value, r is the growth rate per interval expressed as a decimal, and n is the number of intervals. Solving for n by taking the logarithm of both sides gives n = ln(FV ÷ PV) ÷ ln(1 + r) — exactly what this tool computes. The same math also gives the doubling time, ln(2) ÷ ln(1 + r), the number of intervals it takes any starting value to double at that rate (or the halving time, ln(0.5) ÷ ln(1 + r), when the rate is negative).
Interpreting the results
Intervals to Reach Target is the headline number: how many periods of compounding at your growth rate are needed to go from the initial value to the target. Growth Multiple is simply target ÷ initial (a multiple of 2.00× means the target is double the starting value). Total Growth expresses that same change as a percentage. Doubling Time is rate-only — it does not depend on your specific target, only on how fast the value compounds each interval. If the interval count comes back negative, the target sits on the wrong side of the growth path for the rate you entered; try flipping the sign of the rate or swapping which value is the target.
Frequently Asked Questions
What formula does this calculator use?
It solves the compound growth equation FV = PV × (1 + r)n for n, the number of intervals: n = ln(FV ÷ PV) ÷ ln(1 + r). PV is your initial value, FV is your target value, and r is the growth rate per interval as a decimal (5% becomes 0.05).
What does doubling time mean here?
Doubling time is how many intervals it takes any value to double at the entered growth rate, independent of your specific target: ln(2) ÷ ln(1 + r). It is closely related to the Rule of 72, a quick mental approximation of the same idea. If the rate is negative, the calculator reports a halving time instead.
Why did I get a negative number of intervals?
A negative result means the target value sits on the wrong side of the growth path: moving forward from the initial value at the entered rate takes you away from, not toward, the target. Check whether your target should be higher (for positive rates) or lower (for negative rates), or whether the rate's sign is correct.
Can the growth rate be negative?
Yes. A negative rate models decline instead of growth, as long as it stays above -100% (a value cannot fall below zero at -100% or worse). The same formula applies; the calculator then reports a halving time in place of a doubling time.