95 Percent CI Calculator for Data Science

Calculator Inputs

Calculation mode

Interval method

Decimal places

Confidence level

Optional units label

Population standard deviation

Raw sample values

Example: 12.4, 13.1, 11.9, 12.8, 13.5

Sample mean

Sample standard deviation

Sample size

Number of successes

Sample size

Example Data Table

Case	Input type	Method	Estimate	Lower 95% bound	Upper 95% bound
Website latency sample	Raw data, n = 8	Student t mean interval	12.7750	12.2027	13.3473
Survey score summary	Mean = 52.4, SD = 8.1, n = 40	Student t mean interval	52.4000	49.8099	54.9901
A/B test conversion	84 successes from 120	Wilson proportion interval	0.7000	0.6117	0.7748

Formula Used

Mean, unknown population standard deviation:
95% CI = x̄ ± t_{0.975, n-1} × (s / √n)

Mean, known population standard deviation:
95% CI = x̄ ± 1.96 × (σ / √n)

Proportion, Wald interval:
95% CI = p̂ ± 1.96 × √(p̂(1 − p̂) / n)

Proportion, Wilson score interval:
Center = (p̂ + z² / 2n) / (1 + z² / n)
Adjustment = z × √((p̂(1 − p̂) + z² / 4n) / n) / (1 + z² / n)
95% CI = Center ± Adjustment

Use the t method for mean intervals when population spread is unknown. Use Wilson for proportion work when samples are small or proportions are near boundaries.

How to Use This Calculator

Choose whether you want a mean interval from raw data, a mean interval from summary values, or a proportion interval.
Select the interval method that matches your assumptions.
Enter your sample values, summary statistics, or successes and sample size.
Add optional units and choose decimal precision.
Click Calculate 95% CI to show the interval above the form.
Review the summary cards and Plotly graph, then export the results as CSV or PDF if needed.

FAQs

1. What does a 95 percent confidence interval mean?

It is a range built from sample data using a repeatable method. Over many similar samples, about 95 percent of those intervals would contain the true population parameter.

2. When should I use the t interval for means?

Use the t interval when estimating a population mean and the population standard deviation is unknown. That is the most common real-world case for sample-based mean inference.

3. When is the z interval appropriate?

Use the z interval when the population standard deviation is known or treated as known from a trusted external source. It is also the default base for common proportion intervals.

4. Why is the Wilson interval often better for proportions?

Wilson usually behaves better with small samples and proportions near 0 or 1. It avoids some unrealistic bounds and instability that can appear with the simpler Wald method.

5. Does a narrower interval always mean better data?

Not always, but it usually signals more precision. Larger samples, lower variability, and better measurement quality often shrink interval width and improve estimate stability.

6. Can I use raw data and summary statistics interchangeably?

Yes for mean intervals, if the summary statistics were computed correctly from the same sample. Raw data gives transparency, while summary mode is faster when observations are unavailable.

7. Why can interval bounds differ from the sample estimate symmetry?

Some methods, especially Wilson for proportions, create intervals that are not centered exactly on the observed proportion. That improves coverage performance under difficult sampling conditions.

8. Should I round the result heavily in reports?

Avoid excessive rounding. Keep enough decimals to preserve interpretability and prevent overlapping intervals from appearing identical when they are actually different in the underlying analysis.