# Steepness

The term **steepness** is often used in technology for the rise of a characteristic . From a mathematical point of view, the slope is the slope or the difference quotient of the characteristic line or curve . The slope angle of the characteristic curve, on the other hand, depends on the scales of the coordinate axes.

For example, the following is referred to as steepness:

- a parameter of measuring electrodes . When measuring the pH value, it indicates how large the measured voltage difference is when the concentration of an analyte changes by a decade order of magnitude (10
^{1}). According to the Nernst equation , these ideally 59 mV per order (cheating, for a single electron -transfer, in a two-electron transfer corresponding to half. 29.5 mV, and 29.5 mV / pH, both at 25 ° C or 298.16 K ). Today, standard electrodes achieve a slope of 59 mV per order of magnitude over wide concentration and pH ranges.

- a characteristic of electron tubes : the slope indicates the ratio of anode current change to a grid voltage change, see Barkhausen's tube formula and transconductance . It is specified here in mA / V (milliamps per volt) and is a measure of the gain factor for a given working resistance. In the adjacent figure, the slope is maximum in A operation.

- the form of a probability density function or other distribution functions , see also arching (statistics) .