People type this into search every day: rule of 72 calculator.
The Rule of 72 is a mental-math estimate. Investor.gov’s classroom page says to divide 72 by the annual rate of return. At 9%, 72 ÷ 9 = 8, so the balance doubles in about 8 years.
The Rule of 72 calculator prints that shortcut and the exact compound time next to it:
Years ≈ 72 ÷ annual rate
Exact years = ln(2) ÷ ln(1 + rate)
The exact line assumes one lump sum, compounded once a year. Fees, taxes, inflation, and later deposits are left out. Investor.gov’s compound interest glossary is the idea under both lines: interest on principal and on interest already earned.
These are labeled examples. They are not a forecast, and they are not personalized financial advice.
Fig 1
Shortcut beside the exact years
One rate, two clocks
72 divided by the rate is the estimate. The logarithm is the annual-compounding time for a lump sum.
Example 1: 9% and $10,000
This is the Investor.gov figure, and it is also the calculator default.
Inputs: annual rate 9%, starting amount $10,000.
Rule of 72: 72 ÷ 9 = 8 years
Exact time: ln(2) ÷ ln(1.09) = 8.04 years
Shortcut minus exact: 8 − 8.04 = −0.04 years
Doubled amount: 10,000 × 2 = $20,000.00
Calculator result
Rule of 72 doubling time
- Annual rate of return
- 9%
- Starting amount
- $10,000.00
8 years
Rule of 72 estimate to double
- Exact compound time
- 8.04 years
- Doubled amount
- $20,000.00
- Shortcut minus exact
- -0.04 years
The path of the lump sum, compounded once a year at 9%, is 10,000 × 1.09ⁿ.
| Year | Balance |
|---|---|
| 0 | $10,000.00 |
| 2 | $11,881.00 |
| 4 | $14,115.82 |
| 6 | $16,771.00 |
| 8 | $19,925.63 |
| 10 | $23,673.64 |
At year 8 the balance is $19,925.63, which is $74.37 short of $20,000. The exact 8.04 years is where 10,000 × 1.09^8.04 reaches $20,000. The rule’s “about 8 years” is the right reading of that gap.
Fig 2 · 1/6
$10,000 compounded once a year at 9%
The doubled target is $20,000
Balance
- Balance
| Point | Balance |
|---|---|
| 0y | $10k |
| 2y | $12k |
| 4y | $14k |
| 6y | $17k |
| 8y | $20k |
| 10y | $24k |
The lump sum starts at $10,000.
At year 8 it is $19,925.63. The exact double lands at 8.04 years.
Example 2: 6%
Inputs: 6%, $10,000.
Rule: 72 ÷ 6 = 12 years
Exact: ln(2) ÷ ln(1.06) = 11.90 years
Gap: 12 − 11.90 = 0.10 years
Doubled amount: $20,000.00
A 6% rate is a slower double than 9%. The shortcut is 0.10 years long, about five weeks. For a mental estimate, 12 years is the line to remember. The exact line is there when the weeks matter.
Example 3: 3%
Inputs: 3%, $10,000.
Rule: 72 ÷ 3 = 24 years
Exact: 23.45 years
Gap: 0.55 years
Doubled amount: $20,000.00
The gap is wider than at 6% or 9%. Half a year is still a small slice of a 24-year wait, and it is large enough that you should read the exact line if you are dating a goal. People also point this shortcut at inflation. Buying power is a different calculator. The inflation post divides today’s cash by (1 + inflation)^years. This page only doubles a balance.
Example 4: 2%, where the shortcut drifts
Inputs: 2%, $10,000.
Rule: 72 ÷ 2 = 36 years
Exact: 35.00 years
Gap: 1.00 year
Doubled amount: $20,000.00
Calculator result
Rule of 72 doubling time
- Annual rate of return
- 2%
- Starting amount
- $10,000.00
36 years
Rule of 72 estimate to double
- Exact compound time
- 35 years
- Doubled amount
- $20,000.00
- Shortcut minus exact
- 1 years
One year of error on a 35-year double is the low-rate warning. Investor.gov still teaches 72. The calculator puts the exact years beside it so you can see the miss.
Example 5: 1%, a wider miss
Inputs: 1%, $10,000.
Rule: 72 ÷ 1 = 72 years
Exact: 69.66 years
Gap: 2.34 years
Doubled amount: still $20,000.00
The shortcut is 2.34 years longer than annual compounding. At 1%, trust 69.66 years if you need the compound time. The 72-year line is only the mental estimate.
Fig 3 · 1/2
Rule of 72 next to the exact years
One lump sum, compounded once a year
Years to double
- Rule of 72
- Exact
| Category | Rule of 72 | Exact |
|---|---|---|
| 2% | 36 | 35 |
| 9% | 8 | 8 |
| 20% | 3.6 | 3.8 |
The Rule of 72 says 36, 8, and 3.6 years.
The exact times are 35.00, 8.04, and 3.80 years.
At 9% the two bars are the same height on the chart, because 8.04 years rounds to 8 at one decimal on the axis. The table in Example 1 keeps the 0.04. At 2% you can see the one-year gap. At 20% the rule is short, which is Example 8.
Example 6: 7.2% lands on 10 years
Inputs: 7.2%, $10,000.
Rule: 72 ÷ 7.2 = 10 years exactly.
Exact: 9.97 years
Gap: 0.03 years
Doubled amount: $20,000.00
7.2 is a convenient rate because the shortcut is a round decade. The compound time is about eleven days shorter (0.03 × 365 is about 11 days). For planning, 10 years and 9.97 years are the same conversation. For a contract date, use 9.97.
Example 7: 12%
Inputs: 12%, $10,000.
Rule: 72 ÷ 12 = 6 years
Exact: 6.12 years
Gap: 6 − 6.12 = −0.12 years
Doubled amount: $20,000.00
Above 9%, the shortcut starts coming in short. Here it is about six weeks early. The doubled dollar amount does not care. $10,000 still becomes $20,000. Only the clock moves.
Example 8: 20%, further off the shortcut
Inputs: 20%, $10,000.
Rule: 72 ÷ 20 = 3.6 years
Exact: 3.80 years
Gap: −0.20 years
Doubled amount: $20,000.00
A fifth of a year is 0.20 × 12 = 2.4 months. The rule says 3.6 years. Annual compounding says 3.80. At a high rate, read the exact line before you promise a date. The shortcut misses that compound date by 2.4 months.
Example 9: changing the starting amount does nothing to the years
Hold the rate at 9%. Change only the pile.
$1,000 start:
- rule: 8 years
- exact: 8.04 years
- doubled amount: $2,000.00
$10,000 start: same 8 and 8.04 years, doubled amount $20,000.00. That was Example 1.
$50,000 start:
- rule: 8 years
- exact: 8.04 years
- doubled amount: $100,000.00
Fig 4 · 1/3
What $1 of starting cash becomes
9% in every row. The years stay at 8. The dollars scale.
Doubled amount
$1,000 start
$2,000
$10,000 start
$20,000
$50,000 start
$100,000
A $1,000 start doubles to $2,000.
A $10,000 start doubles to $20,000.
A $50,000 start doubles to $100,000. Still 8.04 years on the exact line.
The years are a property of the rate. ln(2) ÷ ln(1.09) has no starting balance in it. A bigger pile doubles to a bigger number. It does not take longer under this formula.
Example 10: typing 0.09 instead of 9
The field wants the rate in percent. 9 means 9%. 0.09 means 0.09%.
Inputs: rate 0.09, starting amount $10,000.
Rule: 72 ÷ 0.09 = 800 years
Exact: 770.51 years
Gap: 29.49 years
Doubled amount: still $20,000.00, because doubling does not depend on the rate. The clock does.
Calculator result
Rule of 72 doubling time
- Annual rate of return
- 0.09%
- Starting amount
- $10,000.00
800 years
Rule of 72 estimate to double
- Exact compound time
- 770.51 years
- Doubled amount
- $20,000.00
- Shortcut minus exact
- 29.49 years
Example 1, with the rate typed as 9, was 8 years and 8.04 years. The decimal slip multiplies the estimate by 100. If the result is centuries and you meant a single-digit rate, check the percent.
Example 11: what rate doubles money in 10 years
Turn the shortcut around. Years are known. The rate is what you want.
Rule of 72: 72 ÷ 10 = 7.2%
That is Example 6 run backward. A 7.2% annual return doubles in 10 years on the shortcut, and in 9.97 years on the exact line.
Solve the exact formula for the rate instead:
(1 + rate)^10 = 2
1 + rate = 2^(1/10)
2^(1/10) = 1.071773...
rate = 0.071773..., which is 7.18% when rounded to two decimals.
The shortcut’s 7.2% is 0.02 percentage points above that exact annual rate. If you already have a starting balance and an ending balance, the CAGR calculator is the tool that connects them. The CAGR post walks (ending ÷ starting)^(1 ÷ years) − 1.
One limit belongs on the table. Later deposits are not in ln(2) ÷ ln(1 + rate). A monthly contribution can push a balance through the double sooner, and this page will not say when. The compound savings calculator is the one that starts with a balance and then adds a deposit. The compound interest post uses that monthly loop.
The examples side by side
| Example | Rate | Start | Rule of 72 | Exact years | Gap | Doubled amount |
|---|---|---|---|---|---|---|
| 1. Investor.gov | 9% | $10,000 | 8 years | 8.04 | −0.04 | $20,000 |
| 2. Six percent | 6% | $10,000 | 12 years | 11.90 | 0.10 | $20,000 |
| 3. Three percent | 3% | $10,000 | 24 years | 23.45 | 0.55 | $20,000 |
| 4. Two percent | 2% | $10,000 | 36 years | 35.00 | 1.00 | $20,000 |
| 5. One percent | 1% | $10,000 | 72 years | 69.66 | 2.34 | $20,000 |
| 6. A round decade | 7.2% | $10,000 | 10 years | 9.97 | 0.03 | $20,000 |
| 7. Twelve percent | 12% | $10,000 | 6 years | 6.12 | −0.12 | $20,000 |
| 8. Twenty percent | 20% | $10,000 | 3.6 years | 3.80 | −0.20 | $20,000 |
| 9a. Small start | 9% | $1,000 | 8 years | 8.04 | −0.04 | $2,000 |
| 9b. Larger start | 9% | $50,000 | 8 years | 8.04 | −0.04 | $100,000 |
| 10. Rate typed as 0.09 | 0.09% | $10,000 | 800 years | 770.51 | 29.49 | $20,000 |
| 11. Double in 10 years | 7.2% rule, 7.18% exact | 10 years at 7.2% | 10 years at 7.18% |
Open the Rule of 72 calculator with the rate in percent, not as a decimal. If the question is what a future sum is worth today, that is the discount in what is the present value of a future sum?.