Thursday, November 24, 2016

Area under the Curve (AUC)

The idea that the area under the temperature curve could be an indicator on how much total energy the beans might have receive during the roasting process popped up already some years ago. While the rate-of-rise (RoR) of a temperature curve, calculated as the first (discrete) derivation, gives the current "speed" of the temperature increase and allows to predict the future, the area-under-the-curve (AUC) describes the past.


To some extent one can expected that beans that received a similar amount of energy would have been roasted to a similar degree. That same energy can be supplied by a short hot roast or a longer gentle roast at lower temperatures. Within a certain range, one can assume that both type of roasts would taste similar if the total energy supplied is comparable.

The Area under the Curve (AUC) value of a roast is an indicator of its total supplied energy. It computes as the area underneath the bean mass temperature (BT) curve and above a certain base temperature, starting from the begin of the roast or a certain well-defined point into the roast (like the yellow point marked DRY in Artisan) up to the end of the roast (marked as DROP in Artisan). Assuming that the AUC of a profile correlates well enough to the totally received energy by the roast, it could serve as a measure for consistency.

Artisan did always calculate the RoR of the bean temperature (BT) and the environmental temperature (ET) and in recent versions also calculated the area between the base temperature of 0 degrees and the BT and ET curves, as well as the area between BT and ET, named ETBTa. It turned out that using (randomly) 0 degree as base temperature might not result in a productive measure. However, a recent discussion on the forum discussed the potential use of such a measure, working with a higher base temperature of 110C, to determine the point to stop a roast. To enable some experimentation with this idea, the ETBTa calculation of previous versions as been replaced by a rather flexible support for the AUC concept in Artisan v1.0.

To simplify things for now and to make the AUC values comparable, Artisan computes it always in C*min, even if Artisan operates in Fahrenheit mode. The area is taken between the BT signal and a base temperature a freely set as reference. The computation can be limited to start from CHARGE, TP (turning point), DRY (dry end) or FCs (first crack start). The base temperature can alternatively be derived dynamically from the BT at the start of the AUC computation.

The AUC computation can be configured via the Statistics dialog (menu Config >> Statistics), where one can choose the event to mark the start of the computation (From) and the base temperature. If the "From Temp" flag is ticked, the base temperature is taken dynamically from the AUC start event.

The total AUC of a profile under the given configuration is displayed as x-axis label underneath the roast curves. The main mode of that characteristics label displays the date/time, beans, batch size, weight loss and color. Its second mode displays the maximum environmental temperature (max ET or MET), the average RoR taken from TP on, and the AUC value in C*min. A right-click on the characteristics label toggles between those two modes.

Main mode of the characteristics

MET/RoR/AUC mode of the characteristics

The statistics bar above the temperature curves displays the AUC values per phase if activated via the AUC flag in the configuration dialog.

LCD and Target

If the LCD flag is ticked in the configuration dialog, Artisan adds another LCD, next to the phases LCDs, showing the running AUC during recording. A right-click on that LCD toggles its mode between this running AUC, the distance to the target AUC as specified in the configuration dialog (blue if below the target and red otherwise) and the running AUC computed from the FCs onwards. Especially the target mode supports the roast master to drop a roast at a specific AUC target. That target is taken from the background profile if one is loaded and the "Background" flag is ticked in the configuration dialog.


A final tool implemented in Artisan is the AUC guide. Similar to the projection lines of Artisan that predict the future of the main temperature curves based on the current rate-of-rise, a thin vertical ruler is rendered at that point in time where the target AUC will be reached, taking the current AUC and rate-of-rise into account.


  • The AUC value of a roast profile as currently implemented in Artisan is not an absolute value, but depends on the given arguments for the start event and base temperature parameter. So only if those configurations are equal, the resulting AUC values can be compared between roast profiles.
  • If one selects a visual marker, like the yellow point (DRY) as start point and also to define the base temperature, the AUC readings should be comparable across machines, even if the probe of one machines generally reads lower than the other. This is because even if probes vary absolutely due their dimension or different placement, they often show a similar temperature increases.
  • While the AUC is for sure correlated with the total energy supplied to the beans, it cannot account for all those complex physics that are involved in the energy transfer during the roast. Time will show how useful this measure is to decide when to drop a roast or to improve consistency in roasting.


  1. Cool! That´s a very nice feature !
    But, Marko Is it available just for mac users? I don´t have it on my PC. I am with artisan 1.0.0

    1. Available for all platforms. You need the latest build v1.0.0b4 and enable the AUC features with in the statistics dialog (menu Config >> Statistics).

  2. This is pretty cool! The area under the temperature curve gives the average amount of energy through the roast chamber at a specific point in time. This process would be considered an unsteady heat transfer (complicated math), but if you did a transient analysis of the typical coffee bean coupled with change in moisture content (change in C_v, mass, and density) you could automate the roasting process more reliably.

  3. Thanks. It's a nice post about area under the curve. I really like it :). It's really helpful. Good job.