Mathematician J. E. Littlewood argued that miracles – events with a one-in-a-million chance – happen to each of us about once a month, simply because we experience so many events. It is a lesson about coincidences and the law of truly large numbers.
How to use the Miracle Calculator
- Period
- Hours awake per day
- Events noticed per second
- A miracle is a 1-in-N event: N =
Results update as you type, and everything is calculated in your browser.
How it works
Choose the period and adjust the assumptions: hours awake per day, events noticed per second and how rare an event must be to count as a miracle.
Inputs explained
| Field | What to enter |
|---|---|
| Period | Choose one: One day, One week, One month (30 days), One year … |
| Hours awake per day | A number |
| Events noticed per second | A number |
| A miracle is a 1-in-N event: N = | A number |
What each result means
- Events experienced = [Hours awake per day]×3600×[Events noticed per second]×[Period]
- Expected miracles = [Events experienced]÷[A miracle is a 1-in-N event: N =]
- Chance of at least one miracle = (1 – exp([Events experienced]×ln(1 – 1÷[A miracle is a 1-in-N event: N =])))×100
- Days between miracles on average = [A miracle is a 1-in-N event: N =]÷([Hours awake per day]×3600×[Events noticed per second])
Example values
How the main result changes when Hours awake per day changes and everything else stays at the example values above:
| Hours awake per day | Expected miracles |
|---|---|
| 4 | 0.432 |
| 6 | 0.648 |
| 8 | 0.864 |
| 10 | 1.08 |
| 12 | 1.296 |
| 16 | 1.728 |
Formula
Events = hours awake × 3,600 × frequency × days
Expected miracles = events / N, P(at least one) = 1 − (1 − 1/N)^events
Worked example
Inputs — Period: One month (30 days); Hours awake per day: 8; Events noticed per second: 1; A miracle is a 1-in-N event: N =: 1,000,000.
Results — Events experienced = 864,000; Expected miracles = 0.864; Chance of at least one miracle = 57.8527 %; Days between miracles on average = 34.7222 days.
Key terms
- Littlewood's law
- Expect a one-in-a-million event roughly monthly.
Frequently asked questions
What is Littlewood's law?
A person can expect to experience a one-in-a-million event about once a month.
Does this mean miracles are real?
It means rare coincidences are expected when there are many opportunities.
How many events per second is realistic?
Littlewood assumed one, which is a rough convention.
What is the law of truly large numbers?
With enough opportunities, any outrageous thing is likely to happen.