About Rule of 72 Calculator

Applies the Rule of 72 to estimate either how many years an investment takes to double at a given interest rate, or what interest rate is needed to double money within a target number of years. Compares the Rule of 72 shortcut against the exact compound interest formula (using logarithms) and reports the accuracy percentage. Accepts an optional principal amount to show concrete dollar values.

• Two modes: “Years to Double” (enter rate, get years) and “Required Rate” (enter years, get rate)
• Exact calculation: years = ln(2) / ln(1 + r/100); rate = (2^(1/years) − 1) × 100
• Accuracy rating: Excellent (≥95%), Good (≥90%), Fair (below 90%)
• Optional principal input shows the doubled dollar amount
• Reference cards explain the formula and its optimal accuracy range (6–10%)

Frequently Asked Questions

When is the Rule of 72 inaccurate?

It is most accurate for rates between 6% and 10%, where the error is under 1%. At very low rates (1–2%) or very high rates (20%+), the approximation drifts. This calculator shows you exactly how far off it is by comparing against the precise logarithmic formula.

Why 72 and not some other number?

72 is a convenient approximation of 100 × ln(2) ≈ 69.3, rounded up because it has many divisors (1, 2, 3, 4, 6, 8, 9, 12, etc.), making mental division easy. Some finance texts use 69.3 or 70 for greater precision at the cost of harder arithmetic.