Fahrenheit degree (difference)
Temperature differenceexact by definition
The Fahrenheit degree used as a temperature difference. A Fahrenheit degree is exactly five-ninths the size of a Celsius degree or kelvin, so an interval of one F° is an interval of 5/9 K, with no offset. The factor is exact by definition, since the Fahrenheit scale is defined off the kelvin by exactly 5/9.
Watch out: This is the single most common temperature error in engineering work. 10 °C is 50 °F, but a RISE of 10 C° is a rise of 18 F°. When converting a delta-T, multiply by 1.8 and stop. Do not add 32. Adding the offset to an interval will inflate a 10-degree rise into a 50-degree one and wreck any load calculation downstream.
| 1 F° | 0.55555556 C° |
Written F° with the degree sign trailing, to distinguish it from °F meaning a temperature reading. North American HVAC practice is built on this unit: the classic hydronic design spread is 20 F°, and the standard air-side rule of thumb, 1.08 × cfm × ΔT for sensible heat in BTU per hour, expects ΔT in Fahrenheit degrees.
About the fahrenheit degree (difference)
Every heat-transfer equation in North American practice runs on this unit. The heat carried by a water loop is \(Q = 500 \times \text{gpm} \times \Delta T\) in BTU per hour, and that 500 is a packaging of water's density and specific heat that only works if \(\Delta T\) is in Fahrenheit degrees. The air-side equivalent, \(Q = 1.08 \times \text{cfm} \times \Delta T\), is the same idea. A boiler sized on a 20 F° drop and a chiller sized on a 10 F° rise are both quoting intervals, not temperatures.
The conversion is a multiplication and only a multiplication. \(\Delta T_C = \Delta T_F \times 5/9\), and \(\Delta T_F = \Delta T_C \times 9/5\). The 32 that appears when you convert a temperature reading is the offset between where the two scales put their zeros, and it cancels the instant you take a difference. Concretely: a 20 F° design spread is an 11.1 C° spread. It is not 20 × 5/9 + 32, which would be 43, a number with no physical meaning at all.
If you want a memory aid, note that the two questions have different shapes. "What temperature is it?" needs both a scale factor and an offset, because the scales disagree about zero. "How much did it change?" needs only the scale factor, because both scales measure change in steps of their own size and the disagreement about zero never enters.