Murphy's Law Calculator
Calculate the probability of at least one failure across multiple opportunities. An educational probability and entertainment tool.
Murphy's Law Calculator
How the Calculation Works
How It Works: This calculator applies basic probability mathematics to estimate the likelihood that at least one failure will occur across multiple independent opportunities. It's based on the mathematical complement of "no failures."
Formulas:
- Probability of NO failures: (1 − p)^n
- Where p = individual failure probability (as a decimal), n = number of opportunities
- Example: (1 − 0.10)^5 = 0.9^5 = 0.59049 = 59.05%
- Probability of AT LEAST ONE failure: 1 − (1 − p)^n
- Example: 1 − 0.59049 = 0.40951 = 40.95%
- Expected number of failures: n × p
- Example: 5 × 0.10 = 0.50 expected failures
Key Assumptions: This calculation assumes all opportunities are independent (the outcome of one doesn't affect the others) and each has the same failure probability. Real-world scenarios may violate these assumptions.
Worked Example
Example: Event description: "Breaking my phone screen", failure probability: 10% per opportunity, opportunities: 5
- Probability of NO screen breaks: (0.90)^5 = 0.5905 = 59.05%
- Probability of AT LEAST ONE break: 1 − 0.5905 = 0.4095 = 40.95%
- Expected breaks: 5 × 0.10 = 0.50 (on average, you'd expect half a break across 5 opportunities)
- Interpretation: Even though each individual opportunity has only a 10% chance of a break, across 5 opportunities there's a 40.95% chance of experiencing at least one break.
How to Use This Calculator
How to Use This Calculator: Enter the failure probability as a percentage (0%–100%). This should represent the chance of failure in a single opportunity. Enter the number of opportunities (must be a whole number of at least 1). Optionally describe the event for personal context. Click "Calculate" to see the probability of no failures, the probability of at least one failure, and the expected number of failures.
Understanding Probabilities: If you flip a coin, there's a 50% chance of heads in one flip. But if you flip 10 times, the probability of getting at least one heads is over 99%. Similarly, small individual probabilities compound into higher probabilities across multiple opportunities.
Expected Failures: This number is a statistical average. If the expected value is 0.5, it doesn't mean you'll experience exactly half a failure. Instead, it means that across many scenarios with the same parameters, the average outcome approaches 0.5 failures per scenario.
Independence Assumption: This formula assumes each opportunity is independent—the outcome of one doesn't influence others. In real life, failures are often correlated. For example, if you're tired, you might be more likely to fail at multiple tasks. Use this as a rough estimate, not an exact prediction.
Real-World Application: This is useful for understanding risk across multiple attempts. Why does a small daily risk (like dropping my phone) become significant over years? Because you get thousands of opportunities, and the probability of experiencing the event at least once becomes very high.
Educational and Entertainment Use: This calculator is a tool for understanding probability and the concept behind Murphy's Law. It is not a scientific risk assessment tool for engineering, finance, or critical systems. For serious risk assessment, consult relevant professionals.
Informational Disclaimer: This calculator provides educational probability estimates based on entered parameters. Actual outcomes depend on complex real-world factors not captured by simple probability models. Use this for learning and entertainment, not for critical decisions or engineering safety assessments.
Last updated: October 1, 2026
Frequently Asked Questions
What does "40.95% chance of at least one failure" mean?
It means that across your specified number of opportunities, there's roughly a 40.95% probability that you'll experience the failure at least once. There's also a 59.05% chance you'll avoid failure in all opportunities.
How does the expected failure number work?
Expected value is a statistical average. If expected failures is 0.50 and you repeated this scenario many times, on average you'd experience 0.50 failures per scenario. It doesn't predict a fractional failure in a single scenario.
Why does a small probability add up to high odds?
Each additional opportunity multiplies the chances. A 10% daily failure rate means a 90% daily success rate. But (0.90)^365 ≈ 0.000063, meaning your annual success rate drops to essentially zero—virtually guaranteeing failure at least once per year.
Is this accurate for real-world situations?
This calculator works well when assumptions are met: independent opportunities and constant probabilities. Real-world scenarios often have correlated failures (being tired makes multiple failures more likely) or changing probabilities, so actual results may differ.
Is Murphy's Law real?
Murphy's Law ("anything that can go wrong will go wrong") is a humorous observation, not a physical law. However, this calculator shows mathematically why small risks compound: enough opportunities will eventually produce a failure. It's a lesson in probability, not fate.