Quick answer
Doubling time t = ln 2 ÷ ln(1 + r), and the rule of 72 estimates it as 72 ÷ rate%. At 7% money doubles in 10.24 years (rule of 72: 10.29).
Enter an annual rate. The calculator returns the exact doubling time and the rule-of-72 estimate.
Related tools: Investment Calculator: Project investment growth from a rate of return you choose. Financial Calculator: Time-value-of-money solver for N, rate, present value, payment or future value. IRR Calculator: Internal rate of return of an investment from its yearly cash flows.
How to use the Doubling Time Calculator
- Enter annual rate (%) (between 0 and 1000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Annual rate | A number, in % | > 0, ≤ 1000 |
Formula and method
Formula
t = ln 2 ÷ ln(1 + r); Rule of 72: t ≈ 72 ÷ rate%
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Exact logarithmic result with the rule-of-72 estimate alongside.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Annual rate = 7.
| Result | Value |
|---|---|
| Years to double | 10.2448 |
| Rule of 72 | 10.2857 |
Example 2
Inputs: Annual rate = 100.
| Result | Value |
|---|---|
| Years to double | 1 |
| Rule of 72 | 0.72 |
The first line is the headline result (years to double). Below it the doubling Time Calculator lists rule of 72, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
How good is the rule of 72
It is accurate for rates between about 6% and 10%. At 7% the error is 0.04 years. At 2% the rule gives 36 years against an exact 35.0, and at 20% it gives 3.6 against 3.8.
Applications
Use it for savings growth, inflation (at 3%, prices double in 24 years) and population growth. The rate must be positive. For tripling use 114 ÷ rate.
How the result changes with annual rate
Holding every other input at the first worked example, this table changes only annual rate. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Annual rate | Years to double | Rule of 72 |
|---|---|---|
| 3.5 | 20.1488 | 20.5714 |
| 7 | 10.2448 | 10.2857 |
| 14 | 5.2901 | 5.1429 |
| 28 | 2.8079 | 2.5714 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Annual rate: entering "0" shows "Annual rate must be greater than 0." beside that field and no result.
Choosing between the Doubling Time Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [Financial Calculator](/finance/financial-calculator/) | solve for, periods per year and payments | Future value (FV) |
| [IRR Calculator](/finance/irr-calculator/) | initial investment and cash flows | IRR |
| [CAGR Calculator](/finance/cagr-calculator/) | beginning value, ending value and years | CAGR |
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- Rate must be positive
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for annual rate to confirm this.
Frequently asked questions
How long to double at 4%?
At 4% money doubles in ln 2 ÷ ln 1.04 ≈ 17.7 years; the rule of 72 gives 18.
What is the rule of 69.3?
A more accurate version for continuous compounding.
Does it apply to debt?
Yes, debt grows the same way when interest accrues.
What does the Doubling Time Calculator calculate?
Years for money to double at a given rate. It returns Years to double and Rule of 72.
What formula does the Doubling Time Calculator use?
t = ln 2 ÷ ln(1 + r); Rule of 72: t ≈ 72 ÷ rate%. Exact logarithmic result with the rule-of-72 estimate alongside.
What do I need to enter in the doubling Time Calculator?
You enter Annual rate (%).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Rate must be positive.
What is an example of a doubling Time result?
With annual rate 7, the years to double is 10.2448.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Rate must be positive.
Related calculators
- Investment Calculator — Project investment growth from a rate of return you choose.
- Financial Calculator — Time-value-of-money solver for N, rate, present value, payment or future value.
- IRR Calculator — Internal rate of return of an investment from its yearly cash flows.
- CAGR Calculator — Compound annual growth rate between two values.
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Mutual Fund Calculator — Growth of a fund investment after its expense ratio.
- Asset Allocation Calculator — Dollar amounts for a stock, bond and cash split.
- Capital Gains Calculator — Gain on a sale and tax at the rate you enter.
- Earnings per Share Calculator — Basic earnings per share.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.