Normal Distribution Calculator

This normal distribution calculator works out probabilities and the density for the famous bell-shaped curve, given any mean and standard deviation. The normal distribution describes a huge range of real measurements, from heights and birth weights to exam marks and measurement errors, which is why it sits at the heart of statistics. It is fully described by two numbers: the mean, which fixes the centre of the curve, and the standard deviation, which sets how wide it spreads. You enter the mean, the standard deviation and a value x, and the calculator returns the probability density at x, the cumulative probability of being below x, the probability of being above x, and the z-score that places x on the standard scale. The probability below a value is the area under the curve to its left, which is what statistical tables give and what you use to answer questions like the chance a result falls under a threshold. A useful guide is the 68, 95, 99.7 rule: about 68 percent of values lie within one standard deviation of the mean, 95 percent within two and 99.7 percent within three. The probabilities use an accurate approximation of the normal curve, so they match printed tables closely. Enter a mean, standard deviation and value to see the results straight away.