Confidence Interval Calculator
Build confidence intervals for a sample mean or proportion at 90%, 95% and 99% levels. Get the margin of error and interval bounds.
Confidence interval
97.06 – 102.94
95% confidence
Margin of error
± 2.94
Sample size
100
If you repeated the survey many times, about 95% of intervals built this way would contain the true value.
Confidence Interval Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Build confidence intervals for a sample mean or proportion at 90%, 95% and 99% levels. Get the margin of error and interval bounds. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: confidence interval calculator · 95 confidence interval · margin of error calculator
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard statistical formulas as defined in textbooks and statistical software. All calculations are performed instantly in your browser using JavaScript — no data is sent to any server.
Formulas follow the conventions used in academic statistics, including population and sample variants where they differ.
When to Use This Calculator
Use the confidence interval calculator whenever you have a sample estimate and want to quantify its uncertainty — survey percentages, average spending, blood test means, production measurements or market research figures. Indian media routinely quote polls with intervals like ±3%, and this calculator reproduces exactly those numbers from the sample size, proportion and confidence level. Researchers use it to report results the way journals require, and businesses use it to decide whether a measured difference between two periods is real or within sampling noise. The mean mode covers continuous data such as weights, yields and incomes, while the proportion mode handles percentages like market share or vaccination coverage — both producing the margin of error and bounds in a single calculation without consulting tables.
How to Use This Calculator
- Step 1: Choose whether your estimate is a sample mean or a sample proportion (percentage).
- Step 2: Enter the sample mean (plus standard deviation for the mean mode) or the percentage observed.
- Step 3: Enter the sample size n — the number of observations behind the estimate.
- Step 4: Choose the confidence level and read the interval, margin of error and bounds.
Worked Example
A tea brand surveys 100 consumers in Assam and finds a mean daily consumption of 100 grams with a standard deviation of 15 grams. Entering mean = 100, sd = 15, n = 100 at 95% confidence gives a margin of error of 2.94 grams, so the interval is 97.06 to 102.94 grams — the brand can claim average consumption lies in this range with 95% confidence. In proportion mode, a poll finding 40% support from 1,000 respondents gives a 95% interval of about 36.96% to 43.04%.
Tips and Common Mistakes
- •Tip 1: The margin of error shrinks with the square root of the sample size — quadruple n to halve it.
- •Tip 2: Use 90% for exploratory work and 99% when a wrong estimate is costly, such as in regulatory filings.
- •Tip 3: Report the interval width together with the point estimate — the width communicates the uncertainty.
- ✗Mistake 1: Saying 'there is a 95% chance the true value is inside this interval' — the interval is fixed; the method has the 95% success rate.
- ✗Mistake 2: Building intervals for badly biased samples — a non-random sample with a tiny interval is still wrong.
Frequently Asked Questions
What is a confidence interval?
A confidence interval is a range built from a sample that is likely to contain the true population value. A 95% confidence interval means that if you repeated the survey many times, about 95% of the intervals would contain the true mean or proportion. The width shows how precise your estimate is.
How do I build a 95% interval for a mean?
Enter the sample mean, the standard deviation and the sample size. The calculator uses the formula mean ± 1.96 × sd ÷ √n. For example, a mean of 100 with standard deviation 15 and n = 100 gives a margin of error of 2.94, so the 95% interval is 97.06 to 102.94.
Why do larger samples give narrower intervals?
The margin of error is proportional to 1 ÷ √n, so quadrupling the sample size halves the margin. That is why surveys with a few hundred respondents quote margins like ±3%, while studies with a few thousand can quote ±1%. This calculator lets you see the effect instantly by changing n.
Can I calculate an interval for a percentage like a poll share?
Yes — switch to proportion mode and enter the percentage directly, such as 40% vote share from a sample of 1,000. The calculator uses the Wald formula p ± z × √(p(1−p)/n) and clamps the result between 0% and 100%. For 40% with n = 1,000, the 95% interval is about 36.96% to 43.04%.
What do 90%, 95% and 99% intervals mean for decision-making?
Higher confidence gives wider intervals: the z-values are 1.645, 1.96 and 2.576 respectively. A 99% interval is more likely to contain the truth but is less precise, which is why regulators and quality teams often use 95% as a balanced default. Choose the level based on how costly a wrong estimate would be.
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