Online Calculators > Math Calculators > Margin of Error Calculator

Margin of Error Calculator

Margin of Error Calculator to calculate the margin of error (MOE) percent for a survey or an experiment.

MOE Calculator

Confidence Level (a) *
Sample Size (n) *
Proportion Percentage (p) *
Population Size (N)
Result * population size must be greater than the sample size

Margin of Error Formula

Following is the margin of error formula on how to calculate margin of error for any experiment. There are two formulas for margin of error, with and without a popular size.

Margin of Error Formula = z * √p * (1 - p) / √n, where
z = Confidence Level
p = Proportion Percentage
n = Sample Size

To include population size in the the experiment, use the following margin of error formula.

Margin of Error Formula With Population Size = z * √p * (1 - p) / √(N - 1) * n / (N - n), where
z = Confidence Level
p = Proportion Percentage
n = Sample Size
N = Population Size

Confidence Level Table

To find the z score value from the confidence level, use the confidence level table below.

Confidence Level z
70% 1.04
75% 1.15
80% 1.28
85% 1.44
90% 1.645
91% 1.70
92% 1.75
93% 1.81
94% 1.88
95% 1.96
96% 2.05
97% 2.17
98% 2.33
99% 2.576
99.5% 2.807
99.9% 3.29
99.99% 3.89

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