Doubling time is the cleanest mental model for understanding compound growth. Instead of asking "what's a 7% return?", you can ask "how long until my money doubles?" — and at 7% the answer is roughly 10 years, every time. This calculator applies both the Rule of 70 and the exact natural-log formula to any growth rate, showing you the doubling period in years and the growth curve year by year.
Use it for investment planning, population analysis, business growth projections, inflation tracking, or any other situation where a value compounds at a constant rate.
What is doubling time?
Doubling time is the time required for a quantity to double in size given a constant rate of growth. For exponential growth — where each period's increase is a fixed percentage of the current value — doubling time depends only on the rate, not the starting amount.
This independence is the elegant insight at the heart of compounding. A 7% annual return doubles ₹1 lakh in the same time it doubles ₹1 crore: about 10 years.
The Rule of 70 — and the Rule of 72
The Rule of 70 says:
The Rule of 72 is the close cousin:
Both are approximations of the exact formula ln(2) ÷ ln(1 + r), which equals 0.693 ÷ ln(1 + r). Since ln(2) ≈ 0.693 and ln(1 + r) ≈ r for small r, the result is approximately 0.693 ÷ r ≈ 69.3 ÷ rate(%). Rounding 69.3 up to 70 (or 72 for easier division) gives the practical shortcut.
The exact formula
- ln is the natural logarithm (base e).
- r is the growth rate expressed as a decimal (e.g. 0.07 for 7%).
- ln(2) ≈ 0.693147.
At 7% growth: 0.693 ÷ ln(1.07) = 0.693 ÷ 0.06766 = 10.245 years. The Rule of 70 says 10 years, off by less than 3 percent — close enough for mental math, but you'd want the exact form for precision work.
Worked example: doubling at 8% growth
Using the Rule of 70:
- Doubling time ≈ 70 ÷ 8 = 8.75 years
Using the Rule of 72:
- Doubling time ≈ 72 ÷ 8 = 9 years
Using the exact formula:
- Doubling time = ln(2) ÷ ln(1.08) = 0.693 ÷ 0.0770 ≈ 9.01 years
The Rule of 72 wins here. As a general rule, Rule of 72 is slightly more accurate for rates between 5% and 10%; Rule of 70 is slightly more accurate below 5%.
How to use this calculator
- Enter the growth rate as a percentage.
- Optionally enter a starting value to see the year-by-year growth curve.
- Read the doubling time — the calculator shows both the Rule of 70 approximation and the exact natural-log result, plus a chart showing the compounding path.
Doubling time at different growth rates
| Growth Rate | Rule of 70 | Rule of 72 | Exact (ln method) | Real-world example |
|---|---|---|---|---|
| 0.5% | 140 yrs | 144 yrs | 138.98 yrs | Aging populations |
| 1% | 70 yrs | 72 yrs | 69.66 yrs | World population growth (2024) |
| 2% | 35 yrs | 36 yrs | 35.00 yrs | India population (decades ago) |
| 3% | 23.3 yrs | 24 yrs | 23.45 yrs | Indian savings account |
| 5% | 14 yrs | 14.4 yrs | 14.21 yrs | Long-term US bond returns |
| 6% | 11.67 yrs | 12 yrs | 11.90 yrs | Indian inflation (recent) |
| 7% | 10 yrs | 10.29 yrs | 10.24 yrs | FD / PPF returns |
| 8% | 8.75 yrs | 9 yrs | 9.01 yrs | Corporate FD |
| 10% | 7 yrs | 7.2 yrs | 7.27 yrs | Index fund historical avg |
| 12% | 5.83 yrs | 6 yrs | 6.12 yrs | Indian equity mutual fund |
| 15% | 4.67 yrs | 4.8 yrs | 4.96 yrs | Strong small-cap fund |
| 20% | 3.5 yrs | 3.6 yrs | 3.80 yrs | Hyper-growth equity |
| 30% | 2.33 yrs | 2.4 yrs | 2.64 yrs | SaaS revenue scaling |
| 50% | 1.4 yrs | 1.44 yrs | 1.71 yrs | Viral-stage startup metrics |
| 100% | 0.7 yrs | 0.72 yrs | 1 yr (by definition) | Rule breaks down at extremes |
Note how the Rule of 70 and Rule of 72 diverge from reality at very low and very high rates. They are designed for the common 2–15% range.
When doubling time is useful
1. Investment planning
"Will I have enough by retirement?" becomes "how many doublings happen between now and retirement?". A 30-year-old investing in equity funds at 12% sees roughly 5 doublings by age 60 — ₹1 lakh becomes ~₹32 lakh. Use our SIP Calculator or Compound Interest Calculator for precise projections.
2. Inflation analysis
At 6% inflation (a typical recent Indian rate), the cost of goods doubles roughly every 11.7 years. A ₹40,000 monthly expense today becomes ₹80,000 in ~12 years — useful for retirement planning. Combine with our Inflation Calculator for specific projections.
3. Population & demographic forecasting
A country growing at 1% per year doubles in ~70 years. A city growing at 3% (typical for fast-growing Indian metros) doubles in ~23 years — the implication for infrastructure planning is obvious.
4. Business growth
A startup growing revenue 30% per year doubles every ~2.5 years. At 50% it's every 1.7 years. Doubling time turns growth-rate small-talk into a concrete planning horizon.
5. Biological growth
Bacterial colonies, social media virality, and epidemic spread all follow exponential laws with characteristic doubling times. The COVID-19 doubling time of 3–7 days early in the pandemic was a critical public-health metric.
6. Compound interest education
Doubling time is the most intuitive on-ramp to compound interest. New investors who can't visualize "12% per year" grasp "doubles every 6 years" instantly.
Nominal vs real doubling time
Don't forget inflation. A 7% nominal return looks like 10 years to double — but at 6% inflation, your real (purchasing- power) return is only 1%, with a real doubling time of 70 years.
| Nominal Rate | Inflation | Real Rate | Nominal Doubling | Real Doubling |
|---|---|---|---|---|
| 3% | 6% | −3% (shrinking) | 23 yrs | Never doubles in real terms |
| 7% | 6% | ~1% | 10 yrs | 70 yrs |
| 10% | 6% | ~4% | 7 yrs | 17.5 yrs |
| 12% | 6% | ~6% | 5.8 yrs | 11.7 yrs |
| 15% | 6% | ~9% | 4.7 yrs | 7.8 yrs |
Always plan in real terms when the horizon is more than a few years. Nominal doubling time alone overstates progress.
Halving time — the reverse
For declining values, the same math gives the halving period:
A currency losing 5% of its purchasing power per year halves its value in about 13.5 years. A car depreciating at 15% per year halves in about 4.3 years. Radioactive isotopes advertise their half-life — the same concept.
Common mistakes with doubling time
- Treating the approximation as exact. Rule of 70 is a shortcut, not a precise number. Use the natural- log formula when accuracy matters.
- Applying it to volatile growth. Doubling time assumes a constant rate. Stocks that average 12% with ±30% annual swings don't actually double every 6 years — they double over a longer effective period with a wider spread of outcomes.
- Forgetting inflation. Nominal doubling time can be misleading. Real doubling time is what matters for purchasing power.
- Adding doubling times. Two stages of growth don't add their doubling times — they multiply the values. A doubling followed by another doubling is 4×, not 4× the doubling time.
- Using it for short horizons. Below one full doubling period, the approximation has high relative error. Below 1 year, switch to absolute change.
- Ignoring fees and taxes. A 12% gross return is not the same as 12% net of expense ratio, securities transaction tax, and capital gains tax. Use after-cost returns for personal planning.
Doubling time myths vs reality
- Myth: "Money doubles every 7 years on average." Reality: Only at ~10% returns. Savings accounts at 3% take 23 years.
- Myth: "If I save twice as much, I double my money in half the time." Reality: Doubling time depends on the rate, not the amount. To halve the doubling time you need to double the growth rate.
- Myth: "High growth rates compound just like low ones." Reality: The Rule of 70 approximation breaks down above ~15%. At extreme rates, always use the exact formula.
Related calculators
- Compound Interest Calculator — the underlying forward math.
- SIP Calculator — for recurring monthly investments.
- CAGR Calculator — find the underlying growth rate from two values.
- Inflation Calculator — see how inflation halves your purchasing power.
- FD Calculator — apply doubling time to bank deposit returns.
- Percentage Increase Calculator — the single-step version for non-compounding changes.
- Percentage Change Calculator — for any before/after comparison.
The bottom line
Doubling time is the single most useful mental model for compound growth. Memorize a handful of key reference points — 7% doubles in 10 years, 12% in 6, 1% in 70 — and you can sanity-check almost any growth claim without a calculator. For precision, use the exact natural-log formula. And always plan in real terms — a doubling that the inflation rate outpaces isn't really a doubling at all.