Our free rule of 72 calculator shows how quickly money doubles at any interest rate. This short guide explains what the rule is, where it comes from, and how to use it without one.
What the Rule of 72 actually is
The rule of 72 is a quick way to work out how long an investment takes to double at a fixed annual growth rate. It turns a tricky compound-interest sum into a simple division you can do on the back of an envelope.
The exact doubling time comes from the natural logarithm in compound-interest maths: ln(2)/ln(1+r). When r is written as a decimal, that’s about 0.72 divided by the growth rate. That’s why 72 is the magic number.
Put £1,000 in an account paying 6% a year and divide 72 by 6. The result is 12 years. After 12 years you’ll have roughly £2,000. The precise figure is £1,000 × 1.06^12 ≈ £2,012, so the rule is off by about 0.6%.
The rule works best for rates between roughly 4% and 15%. Beyond 15% the error grows fast because the logarithm curve flattens. Below 4% it still gives a rough answer, but it’s less reliable for precise planning.
How to work it out without a calculator
- Enter the annual rate of return or interest.
- Read off how many years it takes to double your money.
- See the tripling and quadrupling times too.
- Try different rates to feel how much faster higher returns compound.
Years to double ≈ 72 ÷ rate · Triple ≈ 114 ÷ rate · Quadruple ≈ 144 ÷ rateRule of 72 vs Other Growth Rules
| Method | Formula | Use Case |
|---|---|---|
| Rule of 72 | 72 ÷ Interest Rate = Years to Double | Quick mental math for doubling time |
| Rule of 70 | 70 ÷ Interest Rate = Years to Double | Alternative to Rule of 72 |
| Rule of 69 | 69 ÷ Interest Rate = Years to Double | More precise for continuous compounding |
| Exact Calculation | ln(2) ÷ ln(1 + r) where r = rate | Precise doubling time |
Why this small trick changes big decisions
A couple in their forties once assumed a 5% savings rate would double their pension pot in 14 years. They didn’t realise the real growth rate after inflation was closer to 2%, so it actually takes 36 years. That gap can push retirement back a decade.
Know the rule and you can spot bad deals straight away. A 1% monthly fee on an investment sounds small, but 12% a year means your money doubles every six years instead of every twelve. Over a decade, half your gains vanish.
Three real cases, with numbers you can check
Pension fund at 7%
You have £25,000 in a pension earning 7% a year. Divide 72 by 7 to get about 10.3 years. After 10 years you’ll have roughly £50,000. Double-check: £25,000 × 1.07^10 ≈ £49,170, so the rule is only 1.7% low.
Odd rate with monthly compounding
A credit-card offer quotes 19.9% APR but compounds monthly. Treat it as 19.9 ÷ 12 = 1.658% a month. The rule gives 72 ÷ 1.658 ≈ 43 months to double. Exact maths: 1.01658^43 ≈ 2.006, so it’s spot on.
The slips that ruin the shortcut
| Common mistake | What to do instead |
|---|---|
| use the nominal rate without checking fees | Subtract annual fees from the quoted rate first, or you’ll overestimate growth. A fund at 8% with a 1% fee is really at 7%. |
| forget to adjust for compounding frequency | Convert the quoted rate to an effective annual rate before you divide 72. A 12% APR compounded monthly is about 12.68% effective, not 12%. |
| apply it to anything but doubling time | The Rule of 72 is only for doubling. For tripling use 114, for quadrupling use 144, but don’t invent new numbers. |
Free calculator and quick reference table
| Tool | What it does |
|---|---|
| Rule of 72 Calculator | Enter a rate to see how quickly compound growth doubles, triples and quadruples your money. |
Try the Rule of 72 Calculator
Skip the manual maths — enter your numbers and get the answer instantly.
Open the Rule of 72 Calculator →When to trust it and when to toss it out
Small differences in interest rate, term or timing can add up to large sums over the years. Before committing to any financial decision, run a few different scenarios so you can see the full picture and choose with confidence.
The three numbers to remember
- Always subtract fees from the quoted rate before using the rule.
- Switch to effective annual rates if the compounding isn’t yearly.
- Use 114 for tripling and 144 for quadrupling when you need more than doubling.
Questions fréquentes
How accurate is the Rule of 72?
Very close for rates between about 6% and 10%. At much higher or lower rates it drifts slightly from the exact answer, but it stays a reliable quick estimate. For precision, use a compound interest calculator.
Does it work for inflation too?
Yes. Divide 72 by an inflation rate to see how long it takes prices to double — or your money's buying power to halve. At 3% inflation, that is about 24 years.
Why 72?
72 is a convenient number that divides evenly by many rates (2, 3, 4, 6, 8, 9, 12) and closely matches the exact compounding maths in the common range of returns, which is why it became the standard rule of thumb.
