# How degree days are computed

There are two main ways to compute degree-day figures: (a) an approximation based on daily maximum and minimum temperatures; and (b) continuous integration using frequent temperature measurements.

## (a) The maximum-minimum method

The calculation requires daily measurements of maximum and minimum outside air temperatures ( T_{max} and T_{min} ) and a 'base temperature' T_{base}, nominated by the user as an estimate of the outside air temperature at which no artificial heating (or cooling) is required. In the UK T_{base} for heating has commonly been set at 15.5^{o}C, but other base temperatures can be adopted.

The degree-day figure for a given month or week is the accumulated total of daily results over the period in question.

The daily result for **heating** degree days, D_{h}, is selected from the following formulae, using the first one that matches:

Condition | Formula used |
---|---|

T_{min}>T_{base} |
D_{h}=0 |

(T_{max}+T_{min})/2>T_{base} |
D_{h}=(T_{base}-T_{min})/4 |

T_{max}>=T_{base} |
D_{h}=(T_{base}-T_{min})/2-(T_{max}-T_{base})/4 |

T_{max}<T_{base} |
D_{h}=T_{base}-(T_{max}+T_{min})/2 |

The daily result for **cooling** degree days, D_{c}, is selected from the following formulae, using the first one that matches:

Condition | Formula used |
---|---|

T_{max}<T_{base} |
D_{c}=0 |

(T_{max}+T_{min})/2<T_{base} |
D_{c}=(T_{max}-T_{base})/4 |

T_{min}<=T_{base} |
D_{c}=(T_{max}-T_{base})/2-(T_{base}-T_{min})/4 |

T_{min}>T_{base} |
D_{c}=(T_{max}+T_{min})/2-T_{base} |

Note that in North America a more simplistic algorithm is employed which ignores the third and fourth conditions in each of the above tables.

The maximum-minimum method is sometimes incorrectly referred to as the 'British Gas Method' but its use dates back to the 1920s and the methodology has its roots in the work of a nineteenth-century agronomist who developed it for the purposes of crop-growth correlation.

This method was used by the UK government for the computation of free heating degree-day figures from the 1960s to the end of the last century and, for the purposes of continuity, is the method still employed for most published degree-day values.

## (b) the continuous-integration method

Continuous integration tends to give more accurate results for two reasons. One is mathematical: it takes proper account of the shape of the temperature profile through the day (compared with the max-min method which assumes a square-wave profile). The other is that it is based on logged temperatures, which implicitly are more likely to be measured local to the buildings that are being monitored.

The essence of the continuous-integration method is frequent measurement. For simplicity of explanation, let's consider heating degree days. Say that the temperature T is measured every hour and the difference between that and the base temperature T_{base} is recorded. If (T_{base}-T) is greater than zero, it is added to a running total. This represents the number of degree-hours. At the end of the required interval - usually a week or a month - the degree-hours value is divided by 24 to convert to degree-days. For cooling degree days the logic is inverted: we record (T-T_{base}) instead and add that to a running total.