Confidence Level and Alpha Calculator

Enter either value as a proportion, and the calculator returns its complement together with the area in each tail for a two-sided procedure. It is a quick way to check common settings such as 95% confidence and alpha 0.05 without mixing percentages, proportions, or one-sided conventions.

Convert a confidence level into alpha

A confidence level describes the central share of a reference distribution retained by a two-sided confidence procedure. The significance level, written as alpha, is the share left outside that central region. Their relationship is direct: alpha equals one minus the confidence level. For example, a confidence level entered as 0.95 leaves alpha equal to 0.05. This calculator expects proportions rather than percentage notation, so enter 0.90, 0.95, or 0.99 instead of 90, 95, or 99. The distinction matters because treating 95 as a proportion would put the input far outside its valid range. When you provide `confidence_level`, the result repeats the normalized confidence level, calculates alpha, and divides alpha equally between the left and right tails. This makes the assumptions visible and gives you all three values needed when setting up a conventional two-sided interval or hypothesis test. Values at exactly zero or one are rejected because they imply a degenerate confidence procedure with no central area or no tail area.

Convert alpha back into confidence and tail areas

If a textbook, protocol, or analysis plan specifies alpha first, the reverse calculation is just as simple: the confidence level equals one minus alpha. An alpha of 0.01 corresponds to a confidence level of 0.99, while an alpha of 0.10 corresponds to 0.90. For the two-sided convention used here, alpha is shared equally, so each tail contains alpha divided by two. With alpha 0.05, the left tail area is 0.025 and the right tail area is 0.025. Those tail values are often what you need before looking up symmetric critical values or explaining how a confidence interval relates to a two-sided test. Enter only `alpha` when working in this direction. Providing both alpha and confidence level is rejected even if the two numbers appear consistent, because accepting two sources of truth can hide rounding differences and contradictory inputs. The output uses stable decimal rounding so common complements such as 1 minus 0.9 appear cleanly instead of exposing binary floating-point artifacts.

Use the result with the correct statistical convention

The calculator deliberately reports equal left and right tail areas, which is the standard allocation for a two-sided confidence interval or two-sided significance test based on a symmetric tail split. It does not compute a critical value, p-value, margin of error, sample size, or interval endpoints; those require a distribution and usually additional information such as degrees of freedom or a standard error. It also does not reinterpret alpha for a one-sided test. In a one-sided procedure, the entire alpha is normally placed in one tail, so the equal tail values returned here should not be copied into that design. Use the output as a precise conversion and a transparent check of notation before moving to the next statistical step. Both accepted inputs must be finite numeric proportions strictly between zero and one. Strings such as "95%", missing values, `NaN`, infinity, and boundary values are invalid. Via the API, each request costs $0.002; the deterministic calculation uses no network access and stores no input data.