INPUTS
CONFIDENCE INTERVAL CALCULATOR
Confidence interval calculator for a mean or a proportion.
Get a 90%, 95% or 99% confidence interval from summary statistics, with the standard error, critical value, margin of error and a sentence you can use in your results chapter.t INTERVAL
METHOD
Confidence interval formulas, worked examples, and reporting
What is a confidence interval?
A confidence interval is a range of values that is likely to contain the true population value, such as a population mean. A 95% interval means that if you repeated the study many times, about 95% of the intervals would contain the true value. Narrow intervals mean a more precise estimate.
Formula for a mean
CI = M ± t(α/2, n − 1) × SD ÷ √nUse the t distribution because the population standard deviation is estimated from the sample.
Worked example: 95% CI for a mean
M = 50, SD = 10, n = 25.
- Standard error: 10 ÷ √25 = 2.00.
- t critical for df = 24 at 95%: 2.064.
- Margin of error: 2.064 × 2.00 = 4.13.
- Interval: 50 − 4.13 = 45.87 to 50 + 4.13 = 54.13.
- Report: M = 50.00, 95% CI [45.87, 54.13].
Formula for a proportion (Wilson score)
(p̂ + z²/2n ± z√(p̂(1 − p̂)/n + z²/4n²)) ÷ (1 + z²/n)For 45 of 120 respondents (37.5%), the 95% Wilson interval is 29.4% to 46.4%. The simpler Wald interval, p̂ ± z√(p̂(1 − p̂)/n), gives 28.8% to 46.2% but is less accurate for small samples.
How to report it (APA style)
Put the interval in square brackets after the estimate with the same number of decimals: M = 50.00, 95% CI [45.87, 54.13], or 37.5%, 95% CI [29.4%, 46.4%].
References
- Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25(1), 7–29.
- Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209–212.
- Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133.
ABOUT THIS TOOL
Confidence Interval Calculator
Calculate a 90%, 95% or 99% confidence interval for a mean from M, SD and n, or for a proportion with the Wilson score and Wald methods, with every step shown.
- Report a 95% CI for a scale mean in your results chapter
- Give a CI for the percentage of respondents who agreed
- Check the precision of a survey estimate
KEY FUNCTIONS
t-based interval for a meanWilson score and Wald intervals for a proportion90%, 95%, 99% or custom confidenceStandard error, critical value and margin of error
USE IN YOUR THESIS
Cite this calculator and export your results
APA 7 reference for software or an online tool. Cite the statistical method in your text as well.
SolveGrid. (2026). Confidence Interval Calculator [Online calculator]. https://solvegrid.online/confidence-interval-calculator
LEARN THE METHOD
Guides for this calculator workflow
GUIDEStandard deviation formulaCompare sample and population standard deviation, variance, mean deviations, quartiles, and spread.Read →GUIDESlovin's formula for sample size (with examples)Use n = N ÷ (1 + N·e²) to find a thesis sample size, compare it with Cochran's formula, and write it up correctly.Read →
±→σ→n→
Margin of Error Calculator
Work out the margin of error of a survey from the sample size and confidence level, for a percentage or a mean, with an optional finite population correction for small populations.
Statistics Calculator
Analyse raw data, frequency tables, grouped intervals, or paired X/Y values using descriptive statistics, sample and population standard deviation, variance, quartiles, IQR, outlier checks, and regression results.
Sample Size Calculator
Find the minimum sample size for a survey or thesis using Slovin/Yamane or Cochran's formula, with confidence level, margin of error, population size, response-rate adjustment, and a copy-ready methods sentence.