Confidence Interval Calculator

Calculate confidence intervals for a population mean from sample mean, standard deviation, and sample size.

Calculator Inputs

Average of sample.
Spread.
Number of observations.
Confidence.

Calculated Results

95% Confidence Interval
[47.06, 52.94]
Margin of Error (+/-) +/- 2.94
Sample Mean 50.00
Critical Value (Z) 1.960
Values calculate live as you adjust inputs.

About Confidence Interval Calculator

What is the Confidence Interval Calculator?

The Confidence Interval Calculator is an enterprise-grade calculation tool designed to compute exact mathematical, financial, or scientific parameters based on peer-reviewed formulas.

How to Use This Calculator

  1. Enter your primary input variables in the input fields above.
  2. Select your desired measurement units or options.
  3. Click Calculate to instantly view live outputs, step-by-step mathematical breakdowns, and formulas.

Mathematical Formula & Derivation

Our calculation engine implements verified equations approved by academic literature, WHO guidelines, IRS tax codes, or BIPM metric standards.

Frequently Asked Questions

Q: Is this calculator free to use?
A: Yes! OmniCalc Ultra provides 100% free, private, client-side calculations with zero tracking.

Scientific & Academic References

  • International System of Units (SI) Standards
  • NIST Engineering & Mathematical Reference Handbooks

What is Confidence Interval Calculator?

Estimates the plausible range of values within which the true population mean is expected to fall with specified probability.

How to Use This Calculator

  1. Enter sample mean, standard deviation, and sample size n.
  2. Choose confidence level.
  3. View interval lower and upper bounds.

The Mathematical Formula & Variables

CI = Sample Mean +/- Z * (StdDev / sqrt(n))

Step-by-Step Worked Example

Scenario: Sample mean 50, standard deviation 15, n = 100, 95% confidence.

  1. Standard error = 15 / sqrt(100) = 15 / 10 = 1.5.
  2. Margin of error = 1.96 * 1.5 = 2.94.
  3. Interval = 50 +/- 2.94 = [47.06, 52.94].

Result: [47.06, 52.94]

Frequently Asked Questions

How does larger sample size affect confidence intervals?

Larger sample sizes reduce the standard error, making the confidence interval narrower and more precise.