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Rule of 72 Calculator

Estimates the doubling time of an amount growing at a fixed annual rate with the Rule of 72, and compares it with the exact result ln 2 / ln(1 + r) for annual compounding and ln 2 / r for continuous compounding.

When to use

You want a quick mental-math estimate of how long money (or debt, or prices) takes to double at a given annual growth rate, plus the exact figure.

Do not use when: You need the balance after a specific number of years (use compound-interest) or the rate implied by two values (use cagr).

Formula

rule_of_72_years = 72 / annual_rate_percent; exact_years = ln(2) / ln(1 + annual_rate_percent/100); continuous_years = ln(2) / (annual_rate_percent/100)

The rule is a first-order approximation that is most accurate between about 6 % and 10 %; below that the Rule of 70 or 69.3 is closer, and at high rates the rule overstates the doubling time.

Inputs

Parameter	Type	Unit	Required	Description
`annual_rate_percent`	number	%	yes	Annual interest, return or inflation rate in percent; 8 means 8 %. Range: > 0, ≤ 100

Outputs

Output	Type	Unit	Description
`rule_of_72_years`	number	years	72 / annual_rate_percent.
`exact_years`	number	years	ln(2) / ln(1 + rate).
`continuous_years`	number	years	ln(2) / rate ≈ 69.3 / annual_rate_percent.
`rule_error_percent`	number	%	(rule_of_72_years − exact_years) / exact_years × 100.
`years_to_triple_exact`	number	years	ln(3) / ln(1 + rate).

Example

8 % per year: {"annual_rate_percent":8} → {"rule_of_72_years":9,"exact_years":9.01,"continuous_years":8.66,"rule_error_percent":-0.07}

6 % per year: {"annual_rate_percent":6} → {"rule_of_72_years":12,"exact_years":11.9,"continuous_years":11.55,"years_to_triple_exact":18.85}

GET https://tttkmbb.com/api/v1/calculate/rule-of-72?annual_rate_percent=8

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/rule-of-72 (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/rule-of-72 · Markdown: https://tttkmbb.com/finance/rule-of-72.md · JSON definition: https://tttkmbb.com/finance/rule-of-72.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="rule-of-72"
OpenAPI operationId: calculate_rule_of_72
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Rule of 72 (reference)
Investopedia – The Rule of 72: Definition, Usefulness and How to Use It (reference)

FAQ

Why 72 and not 69.3?

ln 2 ≈ 0.693 gives the exact continuous-compounding rule, but 72 has many divisors (2, 3, 4, 6, 8, 9, 12) and happens to correct for annual compounding near 8 %.

Does it work for inflation or debt?

Yes, any constant growth rate: at 3 % inflation prices double in about 24 years; at 18 % APR an unpaid credit-card balance doubles in about 4 years.

Related calculators

Compound Interest Calculator — Exact balance after any number of years.
CAGR Calculator — Growth rate implied by a starting and ending value.