Cooling degree days:
formula and worked example

Counting the heat that air-conditioning has to remove

Cooling degree days are the summer counterpart to heating degree days. Each day is scored by how far its mean temperature rose above a chosen base. A day that stays below the base scores zero, because a building at that outdoor temperature needs no mechanical cooling.

The value is useful because air-conditioning load rises with the gap between outdoor and indoor conditions. Summing daily scores over a month or season gives a single severity figure that you can compare with metered cooling energy, which lets you tell a hot summer from a wasteful building.

Comparing it with the heating version is instructive. Heating demand has a fairly clean relationship with outdoor temperature, while cooling also responds to sunshine and humidity. The cooling index is therefore a rougher guide, but still the most widely available way to put summers on a common scale.

The daily formula and its inputs

• Mean temperature: usually the midpoint of the day's high and low, or an average of hourly values.
• Base temperature: the outdoor level above which the building starts to need cooling. It depends on the building's insulation, occupancy, equipment heat and the thermostat setpoint.
• Result: degree days for that single day, to be summed over the period of interest.

Notice that the order of subtraction is the reverse of the heating version. Getting that wrong turns a hot day into a negative number that the zero floor then erases.

Weather services often publish ready-made monthly totals for several base temperatures. If you take one of those, check the base and the method, since a total built on a base of 22 degrees cannot be compared with one built on 25.

Worked example: mean 30, base 24

On a hot afternoon the day's mean temperature is 30 degrees, and the building's cooling base is 24.

1. 1Mean temperature: 30.
2. 2Base temperature: 24.
3. 3Difference: 30 − 24 = 6.
4. 4The positive result is kept, so the day scores 6 cooling degree days.

A 90-day hot season averaging 6 degree days per day totals 540. A neighbouring city with a total of 270 would be expected to need roughly half the cooling energy for a similar building, all else being equal.

The day in the example is a single point. To see the effect of a heatwave, imagine a week at a mean of 33: each day scores 9, so the week totals 63, against 42 for a week of ordinary days at 6 each.

What the totals tell you about a building

Cooling degree days work best as a normaliser. If a shop's electricity bill went up 15% in a summer with 20% more cooling degree days, the building actually became a little more efficient even though the bill rose.

• Compare energy per degree day between summers to see real performance change.
• Compare cities to understand why a branch in a hot region has a higher cooling bill.
• Check after a retrofit: if energy per degree day falls, the upgrade is working.

Humidity is not captured. Two days with the same dry-bulb mean can need very different amounts of cooling if one is humid, so in damp climates the index understates the load.

For equipment sizing the index is less useful than a design peak temperature, since a chiller must cope with the hottest hours, not the seasonal total. Degree days speak to energy over time, while peak conditions speak to capacity at a moment. Keep the two ideas apart.

How sensitive the total is to the base

Raising the base from 24 to 26.4 takes the day's score from 6 to 3.6, a fall of 40% from a 10% rise in the base. Over a summer, a higher base cuts the total sharply, which is why it must be chosen to fit the building and kept consistent. A well-insulated office with few internal gains has a higher base than a crowded shop with heavy lighting.

The practical conclusion is that a degree or two of thermostat discipline matters. A building run with a setpoint a couple of degrees higher effectively has a higher base, and its cooling degree days, and its energy, shrink accordingly.

Errors to avoid

• Subtracting the other way round, which produces negative values that vanish at the floor.
• Averaging a month's temperature first, which hides the hot afternoons that should drive the score.
• Using one base for every building when internal gains differ widely.
• Ignoring humidity in tropical or coastal locations.
• Mixing Celsius and Fahrenheit sources.

Putting cooling degree days to work

Collect daily mean temperatures from a nearby weather station, choose a base, and sum the daily values for each month. Plot monthly electricity against that total. A tight line means the building is predictable, and points above it point to something worth investigating, such as equipment left running at night.

• Download daily mean temperatures for your location.
• Pick a base that matches the building.
• Sum the daily scores by month.
• Divide metered cooling energy by the monthly total.
• Track that ratio year on year.