Miracle Calculator — Littlewood's Law of Miracles
Based on Littlewood's Law, calculate how many days you should expect to wait before a "one-in-a-million" (or any rare) event happens to you, given how many significant events you notice each day.
Average wait for the first miraculous event at your daily rate
- 1
Per-event probability p = 1 ÷ N
1 ÷ 1,000,000 = 0.000001 - 2
Expected days = 1 ÷ (p × events/day)
1 ÷ (0.000001 × 28,800) = 34.7At this daily rate the first "miraculous" event is expected after this many days on average.
How does this calculator work?
Littlewood's Law: expected days to a miracle = 1 / (p × events_per_day), where p is the probability per event and events_per_day ≈ 28 800 (1/second awake for 8 h). For a one-in-a-million event, this gives ≈ 35 days — meaning such "miracles" should happen about once a month to a typical person.
Formula
How this is calculated
Mathematician J. E. Littlewood observed (in his 1953 Miscellany) that a "miracle" — an event with a probability of roughly one in a million — is far from rare. The reasoning: while alert and engaged, a person notices about one event per second, giving 8 hours × 3 600 ≈ 28 800 significant events per day. At a one-in-a-million per-event probability, you expect about 1 000 000 ÷ 28 800 ≈ 35 days between miracles.
Formally, this is the waiting-time problem for a Bernoulli process. Each event is independently miraculous with probability p = 1/N. The expected number of events until the first success is N, so the expected waiting time in days is N ÷ events_per_day = 1/(p × events_per_day). For small p the cumulative probability of having seen at least one miracle by day d follows P(d) = 1 − e^(−d/expected_days), an exponential CDF; the chart shows this curve over four times the expected wait.
The "events per day" figure is the most subjective input. Littlewood used 28 800 (one per second while awake), but you can lower it to 1 000 (one consciously noticed event per hour) or higher for people with hypervigilant attention. The calculator is agnostic about the value — adjust it to match your intuition of what counts as a distinct coincidence-eligible moment.
Frequently asked questions
Littlewood's Law states that individuals experience events at a rate of about one per second while awake (8 h/day ≈ 28 800/day). Defining a miracle as a one-in-a-million event, you should expect roughly one miracle every 35 days — so "miraculous" coincidences are actually statistically inevitable.
Littlewood used a broad definition — anything noticed or perceived: a face, a word, a sound, a thought. If you prefer only conscious coincidence-eligible moments (e.g. encounters with people), lower the events-per-day to a few hundred or thousand.
The law is a probabilistic observation, not a metaphysical claim. It shows that given a large enough base rate of daily observations, statistically improbable coincidences are expected to occur regularly — which can feel miraculous even when they're within the bounds of ordinary probability.
Also known as
TG we-Calculate Editorial Team. (2026). Miracle Calculator — Littlewood's Law of Miracles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/miracle-calculator
TG we-Calculate Editorial Team. "Miracle Calculator — Littlewood's Law of Miracles." TG we-Calculate. 2026. https://we-calculate.com/calculator/miracle-calculator.
TG we-Calculate Editorial Team, "Miracle Calculator — Littlewood's Law of Miracles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/miracle-calculator
@misc{wecalculate_miracle_calculator, title = {Miracle Calculator — Littlewood's Law of Miracles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/miracle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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