Jeff Sauro • December 14, 2007

Hover over the normal curve to display the area and z-score.To enter specific values use the Z-Score to Percentile Calculator or the Percentile to Z-Score Calculator.Two-Tailed Area Under the Normal Curve

The values presented above are computed by adding up all the area under the curve(the shaded area) from the point where the mouse is hovering to its opposite-signed point. For example, by hovering over 1σ the area between -1σ and 1σ is shaded and represents about 68% of the area of the curve. This corresponds to a Z-Score of 1. The area above 1σ and below -1σ is 1 minus the proportion of area covered or about 32%. Contrast the area generated from these Z-score with the area generated below. Add any mean and standard-deviation in the boxes. As an example, a mean of 100 and SD of 16 (similiar to the distribution of IQ scores) has been added to the input boxes. We can then see that 95% of the IQ tests scores should fall between 68 and 132. To enter specific values use the Z-Score to Percentile Calculator.

Download an Excel version of the Normal Curve Graph or take a Crash course in Z-Scores

One-Tailed Area Under the Normal Curve

The values presented are computed by adding up all the area under the curve(the shaded area) from negative infinity to the point where the mouse is hovering. For example, by hovering over 1σ about 84% of the area is shaded. This corresponds to a Z-Score of 1. The area above 1σ is 1 minus the proportion of area covered or about 16%. As an example, a mean of 100 and Standard Deviation of 16 (similiar to the distribution of IQ scores) has been added to the input boxes. So for example, if you scored a 132 on an IQ test, you would have an IQ higher than over 97% of the population (a z-score of 2). To enter specific values use the Percentile to Z-Score Calculator.

A Note about the Calculations & Decimal Precision

The values presented in the graphs above are approximations derived from the work of Abramowitz & Stegun. If you need precision to more that 3 decimals you are encouraged to consult multiple published tables of Z-Values.If you need to look up specific values then you will most likely find it easier to use the Z-Score to Percentile Calculator and the Percentile to Z-Score Calculator9 Biases That Affect Survey Responses

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