# Miracle Calculator

URL: https://speedycalculator.com/calculators/math/miracle/
Last updated: 2026-10-30

> The miracle calculator applies Littlewood's law: if you notice one event per second while awake and a "miracle" is a one-in-a-million event, how many miracles should you expect in a day, month, year or lifetime?

## Inputs

- Period
- Hours awake per day
- Events noticed per second
- A miracle is a 1-in-N event: N =

## Results

- Events experienced
- Expected miracles
- Chance of at least one miracle
- Days between miracles on average

## Formula

```
Events = hours awake × 3,600 × frequency × days
Expected miracles = events / N,  P(at least one) = 1 − (1 − 1/N)^events
```

## Explanation

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

FieldWhat to enterPeriodChoose one: One day, One week, One month (30 days), One year …Hours awake per dayA numberEvents noticed per secondA numberA 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 dayExpected miracles40.43260.64880.864101.08121.296161.728

## 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.

## FAQ

**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.


## Sources

- [Wolfram MathWorld – Littlewood's law](https://mathworld.wolfram.com/LittlewoodsLaw.html)