Confidence Interval Calculator

Use our free confidence interval calculator to compute CI for a population mean (known or unknown σ) or proportion with any confidence level.

Math

Type

Confidence level (%)

Sample size (n)

Sample mean (x̄)

Std dev (σ or s)

Sample proportion (p̂)

Formula

A confidence interval gives a range of plausible values for a population parameter. Uses the z-critical value computed dynamically from the standard normal distribution.

x̄ ± z × σ/√n (mean), p̂ ± z × √(p̂(1-p̂)/n) (proportion)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select the CI type.
2Enter the confidence level (e.g., 95).
3Enter sample size and the relevant statistics.
4Click Calculate.

Examples

95% CI for mean (n=100, x̄=50, σ=15)

1.SE = 15/10 = 1.5
2.z = 1.96
3.ME = 1.96 × 1.5 = 2.94
4.CI: 47.06 to 52.94

Result: 2.9400

95% CI for proportion (n=200, p̂=0.6)

1.SE = √(0.6×0.4/200) ≈ 0.0346
2.z = 1.96
3.ME ≈ 0.0679
4.CI: 0.5321 to 0.6679

Result: 0.0679

Frequently Asked Questions

A range of values that likely contains the true population parameter.

The half-width of the CI: z × SE.

The z-score corresponding to the desired confidence level.

If repeated samples were taken, 95% of CIs would contain the true parameter.

Use known σ if population σ is known; otherwise use sample s (large n ≈ z).

Related Calculators

Sample Size Calculator Z Score Calculator Normal Distribution Calculator Mean Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-14

Confidence Interval Calculator

Formula

How It Works

Examples

95% CI for mean (n=100, x̄=50, σ=15)

95% CI for proportion (n=200, p̂=0.6)

Frequently Asked Questions

What is a confidence interval?

What is margin of error?

What is z-critical?

95% CI meaning?

Known vs unknown σ?

Related Calculators

Confidence Interval Calculator

Formula

How It Works

Examples

95% CI for mean (n=100, x̄=50, σ=15)

95% CI for proportion (n=200, p̂=0.6)

Frequently Asked Questions

What is a confidence interval?

What is margin of error?

What is z-critical?

95% CI meaning?

Known vs unknown σ?

Related Calculators