As in the title, I'm looking to fin what's the relationship between the total height of the normal distribution curve and the height at the point where x=standard deviation. At the plot below the height seems to be around 0.63*total height, where total height is given by ~0.4/sigma, but how to get it mathematically?

Thanks

https://en.wikipedia.org/wiki/Standard_deviation#/media/File:Standard_deviation_diagram.svg

I'm looking to find what's the relationship between the total height of the normal distribution curve and the height at the point where x=standard deviation. At the plot below the height seems to be around 0.63*total height, where total height is given by ~0.4/sigma, but how to get it mathematically?

https://en.wikipedia.org/wiki/Standard_deviation#/media/File:Standard_deviation_diagram.svg