Turn on the television any morning and you will see meteorologists talking about the day’s weather forecast. In addition to telling you what the weather conditions will be like (sunny, cloudy, rainy, muggy), they also tell you the day’s forecast for high and low temperatures. A hot summer day may reach 100° in Philadelphia, while a cool spring day may have a low of 40° in Seattle.

If you have been to other countries, though, you may notice that meteorologists measure heat and cold differently outside of the United States. For example, a TV weatherman in San Diego may forecast a high of 89°, but a similar forecaster in Tijuana, Mexico, which is only 20 miles south, may look at the same weather pattern and say that the day’s high temperature is going to be 32°. What’s going on here? The difference is that the two countries use different temperature scales.

Measuring Temperature on Two Scales

Fahrenheit and Celsius are two different scales for measuring temperature.

Converting Between the Scales

By looking at the two thermometers shown, you can make some general comparisons between the scales. For example, many people tend to be comfortable in outdoor temperatures between 50°F and 80°F (or between 10°C and 25°C). If a meteorologist predicts an average temperature of 0°C (or 32°F), then it is a safe bet that you will need a winter jacket.

Sometimes, it is necessary to convert a Celsius measurement to its exact Fahrenheit measurement or vice versa. For example, what if you want to know the temperature of your child in Fahrenheit, and the only thermometer you have measures temperature in Celsius measurement? Converting temperature between the systems is a straightforward process as long as you use the formulas provided below.

How were these formulas developed? They came from comparing the two scales. Since the freezing point is 0° in the Celsius scale and 32° on the Fahrenheit scale, we subtract 32 when converting from Fahrenheit to Celsius, and add 32 when converting from Celsius to Fahrenheit.

There is a reason for the fractions [latex]\frac{5}{9}[/latex] and [latex]\frac{9}{5}[/latex], also. There are 100 degrees between the freezing (0°) and boiling points (100°) of water on the Celsius scale and 180 degrees between the similar points (32° and 212°) on the Fahrenheit scale. Writing these two scales as a ratio, [latex]\frac{F{}^\circ }{C{}^\circ }[/latex], gives [latex]\frac{180{}^\circ }{100{}^\circ }=\frac{180{}^\circ \div 20}{100{}^\circ \div 20}=\frac{9}{5}[/latex]. If you flip the ratio to be [latex]\frac{\text{C}{}^\circ }{\text{F}{}^\circ }[/latex], you get [latex]\frac{100{}^\circ }{180{}^\circ }=\frac{100{}^\circ \div 20}{180{}^\circ \div 20}=\frac{5}{9}[/latex]. Notice how these fractions are used in the conversion formulas.

The example below illustrates the conversion of Celsius temperature to Fahrenheit temperature, using the boiling point of water, which is 100° C.

The two previous problems used the conversion formulas to verify some temperature conversions that were discussed earlier: the boiling and freezing points of water. The next example shows how these formulas can be used to solve a real-world problem using different temperature scales.

You could have converted 250°F to °C instead, and then found the difference in the two measurements. (Had you done it this way, you would have found that [latex]250^{\circ}\text{F}=121.1^{\circ}\text{C}[/latex], and that 121.1°C is 1.1°C higher than 120°C.) Whichever way you choose, it is important to compare the temperature measurements within the same scale, and to apply the conversion formulas accurately.

Summary

Temperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. A Celsius thermometer will measure the boiling point of water at 100° and its freezing point at 0°; a Fahrenheit thermometer will measure the same events at 212° for the boiling point of water and 32° as its freezing point. You can use conversion formulas to convert a measurement made in one scale to the other scale.