Conversion Rate CI Calculator
Calculate CI for conversion rates.
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Recommended for most cases. More accurate, especially for small samples or extreme proportions.
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What Is a Conversion Rate Confidence Interval?
A conversion rate confidence interval gives the range of plausible values for your true conversion rate based on observed data.
If 150 of 5,000 visitors converted (3.0%), the true rate isn't exactly 3.0%—sampling variability means the real rate might be 2.5% to 3.5%. The confidence interval quantifies this uncertainty.
Methods for Calculating CI
Wald (Normal Approximation)
The simplest method:
CI = p̂ ± z* × √[p̂(1-p̂)/n]
Pros: Simple, widely used Cons: Poor coverage for extreme proportions or small samples
Wilson Score
More accurate, especially near boundaries:
Uses an adjusted formula that "shrinks" toward 50%.
Pros: Better coverage, never produces impossible intervals Cons: Slightly more complex formula
Exact (Clopper-Pearson)
Based on the binomial distribution:
Pros: Guaranteed coverage, conservative Cons: Often too wide (conservative)
Agresti-Coull
Adds 2 "pseudo-successes" and 2 "pseudo-failures":
p̃ = (x + 2) / (n + 4) CI = p̃ ± z* × √[p̃(1-p̃)/(n + 4)]
Pros: Simple adjustment, good coverage Cons: Less familiar
Which Method to Use?
| Situation | Recommended Method |
|---|---|
| General use | Wilson or Agresti-Coull |
| Small n (< 30) | Wilson or Exact |
| Extreme rates (< 5% or > 95%) | Wilson |
| Large n, moderate rate | Any method works |
| Regulatory/conservative | Exact (Clopper-Pearson) |
This calculator uses Wilson by default for its robust performance.
Example Calculations
Standard conversion rate:
- n = 10,000 visitors
- x = 350 conversions (3.5%)
- 95% CI (Wilson): [3.15%, 3.88%]
Low conversion rate:
- n = 5,000 visitors
- x = 25 conversions (0.5%)
- 95% CI (Wilson): [0.33%, 0.74%]
Small sample:
- n = 100 visitors
- x = 8 conversions (8%)
- 95% CI (Wilson): [4.0%, 15.0%]
Interpreting the Interval
Width Indicates Precision
Narrow CI → precise estimate (large sample or moderate rate) Wide CI → imprecise (small sample or extreme rate)
For Decision Making
"Our conversion rate is 3.2% (95% CI: 2.8% to 3.6%)"
If a stakeholder asks "Is it above 3%?", you can say the data suggests yes, but values as low as 2.8% are plausible.
Comparing Rates
If two rates have non-overlapping CIs, they're likely different. If CIs overlap substantially, there may be no meaningful difference.
Formal comparison should use the CI for Difference in Proportions.
Applications
Marketing Reporting
"Email open rate: 22% (95% CI: 20%-24%)"
Shows stakeholders both the estimate and its uncertainty.
Baseline Establishment
Before A/B testing, establish baseline with confidence interval: "Current checkout rate: 2.8% ± 0.3%"
Quality Monitoring
If conversion drops outside the historical CI, investigate.
Capacity Planning
Use CI bounds for scenario planning:
- Optimistic: Upper bound of conversion rate
- Pessimistic: Lower bound
Factors Affecting CI Width
Sample Size
| n | 95% CI Width (at p̂ = 5%) |
|---|---|
| 100 | ±4.3% |
| 1,000 | ±1.4% |
| 10,000 | ±0.4% |
| 100,000 | ±0.13% |
Width ∝ 1/√n
Proportion Value
Maximum width at p̂ = 50%, minimum near 0% or 100%.
| Proportion | Width (n = 1,000) |
|---|---|
| 5% | ±1.4% |
| 20% | ±2.5% |
| 50% | ±3.1% |
Confidence Level
| Level | Multiplier | Width |
|---|---|---|
| 90% | 1.645 | Narrower |
| 95% | 1.960 | Standard |
| 99% | 2.576 | Wider |
Sample Size for Desired Precision
To achieve a specific CI half-width:
n ≈ (z*/E)² × p̂(1-p̂)
Where E is desired margin of error.
Example: Want ±1% margin at 95% confidence for p̂ = 10%
n ≈ (1.96/0.01)² × 0.10 × 0.90 = 3,458
Common Mistakes
Using Wald for Extreme Proportions
When p is near 0 or 1, Wald intervals can include impossible values (negative or > 100%) or be far too narrow.
Ignoring Sample Size
A CI of [3%, 7%] from n = 50 has different reliability than the same interval from n = 5,000.
Overinterpreting Point Estimates
"Conversion went from 3.2% to 3.4%—success!" But if both CIs overlap substantially, this might be noise.
Related Calculations
- Confidence Interval for Proportion — General proportion CI
- A/B Test Significance Calculator — Compare two rates
- Margin of Error Calculator — Half the CI width
- Sample Size for Two Proportions — Plan for precision
- Standard Error of Proportion — SE calculation
Summary
Conversion rate confidence intervals quantify uncertainty in observed rates. The Wilson method provides reliable intervals across sample sizes and proportion values, avoiding the pitfalls of simpler methods. Interval width depends primarily on sample size—more data yields more precision. Always report conversion rates with confidence intervals to communicate not just the estimate but how much trust to place in it.