# Confidence Level Calculator

Confidence level calculator and confidence level formula for the following confidence intervals: **mean, two means, proportion, two proportions**.

The tool doesn't count empty cells or non-numeric cells.

### Confidence level calculator

The confidence level calculator determines the confidence level by using the margin of error and sample size. The confidence level represents the level of certainty that the true value of the parameter will be within the confidence interval. Researchers often aim for a confidence level of 0.95. The online confidence level calculator provides the formulas and a step-by-step guide for calculating the confidence level.

### Confidence level formula

For a two-tailed confidence interval:

Confidence Level(CL) = 1 - 2*Min(P, 1 - P)

#### Mean confidence level formula

##### Unknown standard deviation

S.E = | S |

√n |

T(n - 1)= | MOE |

S.E |

P = P(x ≤ T(n - 1))

##### Known standard deviation

S.E = | σ |

√n |

Z = | MOE |

S.E |

P = P(x ≤ Z)

#### Mean difference confidence level formula

T(df) = | MOE |

S.E |

P = P(x ≤ T(df))

##### Unknown standard deviation

###### Equal variances

In this case use the pooled variance

S_{p}^{2} = | (n_{1} - 1)S_{1}^{2} + (n_{2} - 1)S_{2}^{2} |

n_{1} + n_{2} - 2 |

SE = S_{x̄1 - x̄2} = S_{p}√( | 1 | + | 1 | ) |

n_{1} | n_{2} |

df = n₁ + n₂ - 2

###### Unequal variances

SE = S_{x̄1 - x̄2} = √( | S_{1}^{2} | + | S_{2}^{2} | ) |

n_{1} | n_{2} |

df = | ( | S_{1}^{2} | + | S_{2}^{2} | )^{2} |

n_{1} | n_{2} | ||||

S_{1}^{4} | + | S_{2}^{4} | |||

n_{1}^{2}(n_{1} - 1) | n_{2}^{2}(n_{2} - 1) |

#### Proportion confidence level formula

Z = MOE√( | n | ) |

p(1-p) |

P = P(x ≤ Z)

#### Confidence level formula for the difference between two population proportions

S.E=√( | p̂₁(1 - p̂₁) | + | p̂₂(1 - p̂₂) | ) |

n₁ | n₂ |

Z= | MOE |

S.E |

P = P(x ≤ Z)

### How to use the confidence interval calculator?

**Confidence interval type**- choose the required type of confidence interval:**Mean - unknown SD**- When you use the sample standard deviation to estimate the population standard deviation. In this case, the calculator applies the T distribution..**Mean - known SD**- When you know the population standard deviation, in this case the calculator applies the normal distribution.**Mean difference - unknown SD****Mean difference - known SD****Proportion**- calculate the confidence level for the ratio of the required events to the total events.**Two proportions**- calculate the confidence level for the difference between two proportions**The population standard deviation (σ)**- is determined by preliminary knowledge from another study.**Rounding**- when the number is bigger than one the calculator rounds to the required decimal places, but when the number is smaller than one, it rounds to the required significant figures. For example, when you choose 2, it will format 88.1234 to 88.12, and 0.001234 to 0.0012.**Step by step**- show the solution steps