Miracle Calculator (Littlewood's Law)
According to Cambridge mathematician John Littlewood, a miracle is any event with a one-in-a-million probability. Because you consciously register roughly one event per second during every waking hour, statistically improbable surprises become almost inevitable over time. Enter a time period below and see exactly how many "miracles" probability predicts you will experience, and how long you need to wait for your next one.
Formula
Worked example
With 8 hours awake, 1 event per second, over 35 days: daily events = 8 x 3600 x 1 = 28,800. Total events = 28,800 x 35 = 1,008,000. Expected miracles = 1,008,000 / 1,000,000 = 1.008 - just over one miracle, confirming Littlewood's one-per-month finding.
What is Littlewood's Law of Miracles?
John Edensor Littlewood (1885-1977) was a Cambridge mathematics professor and one of the most eminent mathematicians of the twentieth century. In his 1953 collection "A Mathematician's Miscellany," he proposed what is now called Littlewood's Law: a person can expect to experience events of one-in-a-million probability at the rate of about one per month. His argument rests on a simple observation about the sheer volume of experience. If you are awake and active for eight hours each day and consciously register roughly one event per second - a glance, a sound, a thought, an interaction - then you accumulate about 28,800 events daily. Over 35 days that reaches 1,008,000 events, meaning a one-in-a-million event has a probability of occurring at least once that is greater than 50 percent. Littlewood was not endorsing the supernatural; he was using mathematics to show that extraordinary coincidences are statistically ordinary. This calculator lets you explore how the numbers change when you vary the time period, your waking hours, how many things you notice each second, and how rare you want the "miracle" to be.
How the calculation works
The formula has three parts. First, calculate your daily event count: hours awake per day multiplied by 3,600 seconds per hour, then multiplied by the number of events you register per second. Second, scale that to your chosen time period by multiplying daily events by the number of days. Third, divide the total event count by the miracle probability denominator (1,000,000 by default). The result is the expected number of miracles in that period. To find the average waiting time between miracles, divide the probability denominator by the daily event count. At Littlewood's defaults that gives 1,000,000 / 28,800 = 34.7 days, which he rounded to "about one per month." You can also reverse the question: if you want to know how long it would take to accumulate a certain number of miracles, multiply the waiting time by that count.
What counts as a miracle?
Littlewood chose one-in-a-million as a convenient threshold, but the concept generalises to any rare-event probability. In everyday life a "miracle" could be running into a specific acquaintance in a foreign city, guessing a random number correctly, or a chance encounter that changes your career. None of these feel impossible; what feels miraculous is the timing. The law helps explain why people who experience such a coincidence sometimes attribute it to fate or supernatural agency: the event genuinely had a low probability, but the number of opportunities in a lifetime makes at least one occurrence near-certain. The calculator lets you explore how the expected count changes as you adjust the rarity threshold. Move from one-in-a-million to one-in-ten-million and the expected frequency simply drops by a factor of ten, still producing many events over a lifetime.
The law of truly large numbers
Littlewood's Law is closely related to the law of truly large numbers, a principle stating that with enough observations, any sufficiently plausible event will happen to someone. In a country of 300 million people, a one-in-a-million daily event happens to about 300 people every day. When you read a news story about a remarkable coincidence - someone winning a lottery twice, or a patient recovering unexpectedly - you are almost certainly reading about one of those 300. The miracle calculator focuses on the individual perspective, showing how many such events you personally can expect given your own rate of experience. It is a useful reminder that our intuitions about probability are poor guides to how often rare events actually occur over long timescales.
Expected miracles by time period (Littlewood defaults)
| Period | Total events | Expected miracles | Days per miracle |
|---|---|---|---|
| 1 day | 28,800 | 0.029 | 34.7 |
| 1 week | 201,600 | 0.20 | 34.7 |
| 1 month (30 days) | 864,000 | 0.86 | 34.7 |
| 35 days (Littlewood) | 1,008,000 | 1.01 | 34.7 |
| 3 months | 2,592,000 | 2.59 | 34.7 |
| 6 months | 5,184,000 | 5.18 | 34.7 |
| 1 year | 10,512,000 | 10.5 | 34.7 |
| 10 years | 105,120,000 | 105 | 34.7 |
| 80 years (lifetime) | 840,960,000 | 841 | 34.7 |
Calculated using 8 waking hours/day, 1 event/second, and a 1-in-1,000,000 miracle threshold.
Frequently asked questions
What exactly is Littlewood's Law of Miracles?
Littlewood's Law is a statistical observation by Cambridge mathematician John Littlewood, first published in 1953. It states that a person should expect to experience events of one-in-a-million probability at the rate of roughly one per month. The reasoning is that if you register about one event per second during eight waking hours, you accumulate around 28,800 events per day. Over 35 days that is just over one million events, so a one-in-a-million coincidence becomes statistically expected at least once in that span.
Is this calculator claiming miracles are real?
No. Littlewood's Law is a mathematical argument, not a theological one. Littlewood himself wrote the law to challenge pseudoscientific claims by showing that improbable events are statistically inevitable given how many events we experience. The word "miracle" is used in the colloquial sense of a striking coincidence or surprising rarity, not as a supernatural claim.
Why does the calculator default to 8 hours awake?
Littlewood used 8 hours of active attention as a conservative estimate of the time during which a person is alert and registering discrete events. He excluded sleep and low-attention periods like routine commutes. You can raise or lower this in the calculator if your lifestyle differs - for instance, a highly alert 12-hour working day would roughly double the expected miracle count.
What if I change the miracle probability to something other than one in a million?
The formula scales linearly. If you use a probability of one in 100,000 (ten times more likely), you expect ten times as many miracles in the same period. If you use one in 10,000,000 (ten times rarer), you expect one-tenth as many. This lets you model anything from a moderately unlikely surprise (say, one in 10,000) to a genuinely exceptional event (one in a billion) and see how often each should appear in a lifetime.
How is this different from a lottery probability calculator?
A lottery calculator tells you the chance of a single specific event (winning a draw). Littlewood's approach counts all events across all categories that you might notice: a coincidence in conversation, an unexpected encounter, a surprising outcome at work. The total number of "lottery tickets" you hold is the total number of events you register, and that vastly larger pool is what makes rare individual outcomes common in aggregate.
Can I use this to predict a specific miraculous event?
No. The law says nothing about which event will occur or when. It only gives the expected number of one-in-a-million events across all possible categories of experience. Predicting the specific nature or timing of any individual coincidence is impossible; the law merely shows that some such event is overwhelmingly likely to occur in any long enough timeframe.