STATISTICSProbability TheoryStatistics Calculator
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Risk Calculator

Free risk calculator. Cumulative risk, Poisson probabilities, risk comparison. Annual rates, lifetim

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

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RISK ASSESSMENTCumulative risk over time, Poisson event probabilities

Risk Over Time: Cumulative, Poisson, and Comparison

From heart attack risk to dice rolls — understand probability over time and compare risks fairly.

Relative Risk →Probability →

Real-World Scenarios — Click to Load

Risk Mode

e.g., 1.5 for 1.5%/year
Number of years
risk.sh
CALCULATED
$ risk --mode="cumulative"
Cumulative Risk
26.09%
Years to 50%: 46 â€ĸ Years to 90%: 153
Annual Rate
1.5%
Years
20
Share:
Risk Calculator Result
Cumulative: 26.09%
1.5%/year × 20 years
numbervibe.com/calculators/statistics/risk-calculator

Calculation Breakdown

COMPUTATION
Per-period probability
r = 0.0150
1.5% / 100
COMPUTATION
Cumulative risk formula
1 − (1−r)^T
P( ext{at} ext{least} ext{one} ext{in} T ext{periods})
RESULT
Cumulative risk
26.09%
1 − (1−0.0150)^{20}
RESULT
Years to 50%
46
RESULT
Years to 90%
153

Cumulative Risk Over Time

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • â€ĸ Cumulative risk over T years: P(at least one) = 1 − (1 − r)^T, where r is the annual probability
  • â€ĸ Poisson model: P(X=k) = e^(-Îģ) × Îģ^k / k!; P(â‰Ĩ1) = 1 − e^(-Îģ) for rare events
  • â€ĸ Absolute vs relative risk: A 1% vs 0.1% risk is a 10× ratio but small absolute difference
  • â€ĸ Risk perception is often skewed — people overestimate rare dramatic risks
  • â€ĸ Lifetime risk from annual rate: P(lifetime) = 1 − (1 − annual_rate)^years

Did You Know?

📊Cumulative risk grows faster than linear: 10% per year for 10 years ≈ 65% cumulative, not 100%Source: Probability theory
🎲P(at least one 6 in 4 rolls) = 1 − (5/6)^4 ≈ 51.8% — it's cumulative 'risk' over trialsSource: Dice probability
✈ī¸Flying is far safer than driving per mile; risk comparison helps put headlines in perspectiveSource: Transport safety
đŸĻ Annual flu risk ~15% means over 10 years cumulative risk of at least one infection ≈ 80%Source: CDC data
🌩ī¸Lightning strike ~1 in 500,000/year; over 80 years cumulative ≈ 0.016% — very lowSource: NOAA
💔Heart attack risk ~1.5%/year gives ~26% cumulative over 20 yearsSource: AHA

Expert Tips

Report absolute and relative

"50% increase" from 2% to 3% is different from 50% to 75%.

Use Poisson for rare events

Accidents, mutations, arrivals — when events are independent and rare.

Cumulative ≠ additive

10% per year for 10 years ≠ 100%; it's 1−(0.9)^10 ≈ 65%.

Compare like with like

Per trip vs per mile vs per hour — units matter for risk comparison.

Absolute vs Relative Risk

ScenarioAbsoluteRelative
Drug reduces risk 2%→1%1% ARR50% RRR
Risk 0.01%→0.001%0.009% ARR90% RRR
Flying vs driving (per trip)Both very lowDriving ~100× higher

Frequently Asked Questions

What is cumulative risk?

Probability of at least one event over a time period. P = 1 − (1 − r)^T where r is per-period probability and T is number of periods.

When do I use Poisson?

For rare, independent events: accidents, mutations, arrivals. Îģ = average events per period. P(â‰Ĩ1) = 1 − e^(-Îģ).

Why does cumulative risk not add up?

Each year you avoid the event, you start "fresh." P(no event in T years) = (1−r)^T, so P(at least one) = 1 − (1−r)^T.

What is relative risk increase?

(Risk_A − Risk_B) / Risk_B × 100%. A 10× ratio means 900% relative increase.

How do I interpret NNT from risk?

NNT = 1/ARR. If ARR = 2%, NNT = 50 — treat 50 to prevent one event.

Is flying safer than driving?

Per mile, flying is much safer. Per trip, both are very low. Compare same units.

What about the dice example?

P(6) = 1/6 per roll. Over 4 rolls: P(at least one 6) = 1 − (5/6)^4 ≈ 51.8%. Same formula as cumulative risk.

Why do people misperceive risk?

Availability heuristic, dread (nuclear vs car), control illusion. Numbers help: compare absolute and relative.

By the Numbers

1−(1−r)^T
Cumulative
e^(-Îģ)
Poisson P(0)
1−e^(-Îģ)
P(â‰Ĩ1)
A/B
Risk Ratio

Disclaimer: This calculator provides risk estimates for educational and general reference. Models assume independence and constant rates. Real-world risks vary. For health decisions, consult qualified professionals.

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