Confidence interval calculator
Estimate intervals with explicit distribution and sample assumptions.
Як карыстацца Confidence interval calculator
The Confidence interval calculator takes a sample mean, a known population standard deviation, a sample size and a confidence level from 50 to 99.99% and returns the lower bound, upper bound, margin of error and z value. It computes a normal z interval, mean ± z × σ / √n. It is not a t interval for a standard deviation estimated from the sample.
- Enter the requested values in the settings panel.
- Adjust the basic settings, then open Advanced mode for export and fine-tuning options. Custom settings stay active when the panel is closed.
- Run confidence interval calculator, review the output, then use the available copy or download controls.
Што падтрымлівае гэты інструмент
Calculates a normal z interval for a mean with known population standard deviation. This is not a t interval for an estimated sample deviation.
- Sample mean
- Range: -1000000000000 to 1000000000000
- Known population standard deviation
- Range: 0 to 1000000000000
- Sample size
- Range: 1 to 10000000
- Confidence (%)
- Range: 50 to 99.99
Абмежаванні і апрацоўка
Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.
Частыя пытанні
What is the formula for a confidence interval for a mean?
The margin of error is z × σ / √n, and the interval is the sample mean minus and plus that margin. With a mean of 50, σ of 10, n of 100 and 95% confidence, z is about 1.96, so the interval is roughly 48.04 to 51.96.
When should I use a t interval instead?
Use a t interval when the population standard deviation is unknown and estimated from your sample, especially with small samples. This calculator always uses the normal z critical value, which assumes σ is known and gives narrower intervals than a t interval would.
How does the confidence level change the interval?
Higher confidence uses a larger z critical value, which widens the interval. The calculator finds z from the standard normal distribution at 0.5 + confidence/200, so 90%, 95% and 99% give about 1.645, 1.960 and 2.576.
Where is my input processed?
This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.
What are the input limits?
Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.