Temperature Rise and the Sensible Heat Airflow Formula

Why this matters

A gas furnace tells you how much air its blower is moving every time it fires, if you know how to ask. Output heat goes into the air and shows up as temperature rise, and with two thermometers and the rating plate you can turn that rise into CFM in under a minute. It is the cheapest airflow estimate on the truck and the one most often done wrong: the supply probe in sight of the heat exchanger, the input number used where the output belongs, the sea-level constant used at 6,000 ft, or the whole method carried into cooling where it does not apply. This card owns the formula, its assumptions and its sanity check. Measuring the rise itself on a furnace is a sibling procedure; see related: How to Measure Temperature Rise on a Gas Furnace.

The formula and where 1.08 comes from

For sensible heat added to or removed from air:

BTU per hour = 1.08 x CFM x temperature difference (F)

so

CFM = BTU per hour / (1.08 x temperature difference)

The 1.08 is not a magic number. It is three things multiplied together for standard air (the basis the ASHRAE Handbook, Fundamentals uses for this constant), which is dry air at sea level near 70 F with a density of 0.075 lb per cubic foot:

• 0.075 lb per cubic foot (density)
• x 60 minutes per hour (turns CFM into cubic feet per hour)
• x 0.24 BTU per lb per F (specific heat of air)
• = 1.08 BTU per hour, per CFM, per degree F

Every assumption inside it matters later. The density term is where altitude enters, the specific heat is where it stops being exact for very humid air, and "sensible" is why it cannot be used with total cooling capacity.

The worked calculation

A 96 percent AFUE two-stage condensing furnace on high fire, read from the rating plate and measured on a fall commissioning visit. Rating plate values are illustrative; read yours.

RATING PLATE (ILLUSTRATIVE)
Input, high fire          60,000 BTU/h
Output capacity, high     57,600 BTU/h
Temperature rise range    35 to 65 F

MEASURED, HIGH FIRE, 15 MIN STEADY
Return air (before filter)      70 F
Supply air (past first elbow)  122 F
Rise    122 F - 70 F          =  52 F

AIRFLOW
CFM = Output / (1.08 x Rise)
    = 57,600 BTU/h / (1.08 x 52 F)
    = 57,600 BTU/h / 56.16 BTU/h per CFM
    = 1,026 CFM

CHECK, OTHER DIRECTION
1.08 x 1,026 CFM x 52 F = 57,620 BTU/h
(matches output within rounding)

Why output, not input. Input is the gas energy the burners consume. Output is what ends up in the air after flue losses. Using the 60,000 input instead of the 57,600 output would claim 1,068 CFM (60,000 / 56.16), overstating airflow by about 4 percent here and by about 25 percent on an 80 percent furnace, where input and output differ much more.

Why the rise matters on its own. A 52 F rise sits inside the 35 to 65 F plate range, 17 F above the bottom and 13 F below the top. The plate range is a heat exchanger limit, not an airflow suggestion: too little rise means the flue products cool enough to condense where a non-condensing heat exchanger cannot handle it, too much rise means the heat exchanger runs hot enough to trip the limit and shorten its life. Rise is judged against the rating plate first; CFM is the bonus. The plate itself is read per Furnace Rating Plate Read Before Start-Up.

Low fire is its own calculation

On a two-stage furnace, low fire has its own output and the blower drops to its own low-fire airflow, so the high-fire answer says nothing about it. This furnace's plate lists low fire at 40,000 BTU/h input and 38,400 BTU/h output (the same 96 percent). On low fire the measured rise was 45 F: CFM = 38,400 / (1.08 x 45) = 38,400 / 48.6 = 790 CFM. Check: 1.08 x 790 x 45 = 38,394 BTU/h. The 45 F rise also has to sit inside the plate's range (some plates print a separate low-fire range; use it where printed). A low-fire rise below the bottom of the range is the condition that condenses flue gas in a heat exchanger not built for it.

The assumption underneath: the furnace is firing at its rated output

Rated output assumes rated input, which assumes the correct manifold pressure and gas of the expected heating value. A furnace under-fired by 10 percent puts 10 percent less heat into the air; the rise drops, and the formula, fed the rated output, reports about 11 percent more airflow than is really there (rated output divided by a rise 0.90 as large is 1.11 times the true figure). If the airflow number matters, confirm the firing rate first by clocking the meter, per How to Clock a Gas Meter to Check Furnace Input, and set manifold pressure per How to Set Gas Manifold Pressure on a Furnace. If the meter says the furnace is burning 54,000 BTU/h of gas against a 60,000 rating, scale the output by the same 90 percent before dividing: 57,600 x 0.90 is 51,840 BTU/h.

Altitude: the constant is a sea-level constant

At altitude, air is less dense, so each CFM carries fewer pounds and absorbs less heat per degree. The 1.08 scales with density. At about 5,000 ft, air density is roughly 83 percent of sea level, so the constant is about 0.90 (1.08 x 0.83).

Run the same furnace's numbers at 5,000 ft as if they had been measured there, with 0.90 in place of 1.08: 57,600 / (0.90 x 52) = 57,600 / 46.8 = 1,231 CFM. Using 1.08 would have reported 1,026, understating actual volume flow by about a sixth. Two other things move at the same time, and the formula does not know about either: a furnace at altitude is usually derated in input per the maker's high-altitude instructions, so its output is lower than the sea-level plate figure, and the maker's fan table may already be stated in standard CFM. Use the derated output and the corrected constant together, and say which you used on the ticket.

Sanity check against the fan table

The formula and the fan table are independent estimates of the same quantity, which is what makes them useful together. The fan table method (total external static plus the blower's speed tap, read off the maker's airflow chart) is a sibling procedure; see related: How to Estimate Blower Airflow From Static and the Fan Table.

On this furnace, total external static measured 0.50 in. w.c. on the heating tap, and the maker's table gives about 1,080 CFM at 0.50 in. on that tap. Against the formula's 1,026 CFM, the two differ by 54 CFM (1,080 minus 1,026), about 5 percent of the table figure. Two methods with different error sources landing within about 10 percent of each other is good agreement; take the figure and move on.

When they disagree by a lot, one of the methods is wrong, and the usual suspects are known:

• Supply probe in radiant view of the heat exchanger, or in the plenum before the air has mixed, reads high, inflates rise and makes the formula report too little air.
• Return probe after a humidifier bypass or near a return leak pulls in warm supply air or attic air and distorts the rise.
• Furnace under-fired or over-fired, as above.
• Static read in the wrong place, such as across the filter rack in one reading and not the other, pushes the fan table estimate off.
• The wrong fan table: the table for a different cabinet width, or for a different motor program on an ECM blower.

Electric heat gives you a measured output

Electric resistance heat is the one case where you measure output directly rather than trusting a plate. Every watt into a heating element becomes heat in the air: watts x 3.412 = BTU per hour.

An air handler with a 10 kW kit, all stages on, blower steady: measured 236 V and 40.5 A at the strip feed. 236 x 40.5 = 9,558 W. 9,558 x 3.412 = 32,612 BTU/h. Rise measured 30 F. CFM = 32,612 / (1.08 x 30) = 32,612 / 32.4 = 1,007 CFM. Check: 1.08 x 1,007 x 30 = 32,627 BTU/h, which closes within rounding. The blower motor's own heat also ends up in the air and adds slightly to the rise, so this estimate is a little high by the motor's share. The kit's minimum airflow requirement is owned by Heat Strip Kit Sizing and Circuit Field Card; do not run strips below it to get a cleaner reading. The strip feed is 240 V and energized while you read it: clamp the insulated feed conductors where they are exposed by design, keep hands and the clamp jaw out of the element chamber, and wear the voltage-rated gloves and eye protection your shop's NFPA 70E program calls for.

Where the formula does not belong

Cooling with total capacity. In cooling, the coil removes both sensible and latent heat, and the air temperature drop reflects only the sensible part. Dividing a 36,000 BTU/h nominal rating by 1.08 x the temperature split assigns latent heat to a temperature change it did not cause, and overstates airflow. The formula works in cooling only with a measured or known sensible capacity, which is rarely in hand on a service call. Measuring delivered cooling capacity properly is a sibling procedure; see related: How to Measure Delivered Cooling Capacity With Wet Bulb and Airflow.

A heat pump in heating. Heat pump heating output varies with outdoor temperature and is not on the indoor unit's plate, so there is no fixed output to divide. You can use the formula backwards with a known airflow to estimate heating output, which is how sibling performance checks use it.

Mixing units. CFM, F and BTU per hour go together. Metric (watts, L/s, degrees C) uses a different constant. Do not mix a watt figure into the 1.08 form without converting it first, as the electric heat example does.

What the number is for

The airflow from the formula is a check, not a setting. The cooling airflow choice belongs to Airflow Per Ton Targets and What Moves Them, the blower tap belongs to How to Set Blower Speed Taps for Cooling and Heating Airflow, and the static that limits both belongs to Static Pressure Budget Across a Residential System. The formula's job is to tell you whether what the furnace is doing agrees with what you set.

References

• ASHRAE Handbook, Fundamentals (current edition): properties of moist air and the standard-air basis of the sensible heat constant.
• Furnace rating plate, installation manual and fan table (output capacity, temperature rise range, high-altitude derate).
• See related: How to Measure Temperature Rise on a Gas Furnace; How to Estimate Blower Airflow From Static and the Fan Table; How to Clock a Gas Meter to Check Furnace Input; Furnace Rating Plate Read Before Start-Up; Airflow Per Ton Targets and What Moves Them.