Calculating Degree Days with Wolfram|Alpha

Sunday is the United States’ Independence Day, and one of the hottest days of the year in this part of the country. Many Americans will celebrate the day with outdoor activities such as barbecues, parades, and fireworks. Chances are that after all the corn on the cob and fun in the sun, they’ll be looking to celebrate with some air conditioning, too! All that cooling will require a few degree days!

What’s a degree day? A degree day quantifies the amount of heating or cooling required to heat or cool an inside space.

Suppose you want to maintain an inside temperature of 65°F. This 65°F is called the base temperature. (65°F might sound cool, but this artificially low number is used because the actual temperature in the building will be raised by bodies and other inside sources of heat.) If the weather forecast for Champaign is as hot as expected for U.S. Independence Day—definitely above 65°F—then you’ll need to cool the building. The amount of cooling required is the difference between the base temperature and the outdoor temperature, multiplied by the time over which the temperature is different. If it is cooler outside than 65°F then you’ll need to heat the building, again by an amount equal to the product of the temperature difference and the time.

To make sense out of that, just type “degree days” into Wolfram|Alpha.

The temperature history pod contains a plot of the temperature over the time period of the calculation—one month back by default. If you are used to using Wolfram|Alpha to check the weather this plot should look familiar, but with some differences. The horizontal red line across the plot is the base temperature. The part of the plot that is above the red line is shaded in blue. That’s because when the temperature is above the base temperature, you have to cool the building. The number of cooling degree days is the area of the blue region. Similarly, the number of heating degree days is the area of the red region, which extends from the red baseline down to temperatures below the base temperature.

In North America it is typical to use a base temperature of 65°F for both heating and cooling, but in Europe one often uses a base temperature of 15.5°C for heating and 18°C for cooling. Wolfram|Alpha lets you use any base temperatures you want.

Wolfram|Alpha also shows you how the number of degree days changes with the base temperature. The “Base temperature dependence” pod shows us that two years ago on July 4, the number of cooling degree days is more than halved by using a base temperature of 70°F instead of 65°F. This gives you an idea of how much energy you can save by raising the thermostat in the summer.

Degree days aren’t used for just heating and cooling. Degree days are also used in agriculture. Plants need warmth to grow. Cold-blooded insects and other pests that feed on crops also thrive in the heat.

For example, roughly speaking, corn requires about 2800 degree days to reach maturity, using a base temperature of 50°F. So the hotter it is, the quicker the corn will mature—but the more air conditioning we humans will want. This means that a growing degree day is the same as a cooling degree day! The results pod below shows that there have been 1470 (Fahrenheit) degree days since April 1. As that’s about half of 2800, it looks like any corn planted here in Champaign in early April is about halfway to maturity.

Think about that as you eat your corn on the cob while celebrating the Fourth of July. Assuming you’re having corn and not partaking in a hot dog eating contest.