The Sensible Heat Formulas for Air and Water

Why this matters

Two short formulas let a tech estimate heat moved without any instrument fancier than a thermometer: BTU/h = 1.08 x CFM x temperature difference for air, and BTU/h = 500 x GPM x temperature difference for water. They turn a temperature rise across a furnace into an airflow estimate, a boiler's output into the flow its loop needs, and a suspicious reading into a number that either fits the equipment or does not. Both are routinely misused, because the 1.08 and the 500 look like laws of nature and are really bundles of assumptions. Unpack the bundle and you know when the formula holds, when it drifts, and when it is answering a different question from the one you asked.

What is inside 1.08 and 500

Sensible heat is heat that changes a temperature, as opposed to latent heat, which changes moisture between vapor and liquid without moving the thermometer. For any stream the rule is the same: heat rate = mass flow x specific heat x temperature difference. The constants just pre-multiply the field units into that.

AIR   BTU/h = 1.08 x CFM x dT(F)

  0.075 lb/ft3     density of standard air
x 60    min/h      CFM is per minute, answer is per hour
x 0.24  BTU/lb-F   specific heat of air
= 1.08  BTU-min/h-ft3-F

WATER BTU/h = 500 x GPM x dT(F)

  8.33  lb/gal     density of water near 60 F
x 60    min/h
x 1.0   BTU/lb-F   specific heat of water
= 500   (499.8, rounded)

WORKED
1.08 x 1,200 CFM x 20 F =  25,920 BTU/h
500  x 10 GPM    x 20 F = 100,000 BTU/h

Every condition baked into the constant travels with it. The 1.08 assumes standard air, 0.075 lb per cubic foot, which is sea-level air near 70 F. The 500 assumes water near 60 F with a specific heat of 1.0. Move away from those and the constant moves, whatever the formula's tidy look suggests.

Worked example: airflow from a furnace temperature rise

The most common field use runs the air formula backwards. A gas furnace is rated 80,000 BTU/h input at 95 percent efficiency, so its output is 80,000 x 0.95 = 76,000 BTU/h. After the burner has run long enough for the rise to settle, the tech reads 68 F in the return and 118 F in the supply, out of line of sight of the heat exchanger so radiant heat does not inflate the supply reading. The rise is 118 - 68 = 50 F.

Solve for airflow:

• CFM = BTU/h / (1.08 x dT)
• CFM = 76,000 / (1.08 x 50) = 76,000 / 54 = 1,407 CFM.
• Check forward: 1.08 x 1,407 x 50 = 75,978 BTU/h, which rounds back to the 76,000 we started with.
• Rough estimate: 1.08 x 50 is about 54, and 76,000 / 54 is a bit under 1,500. Agrees.

Report it as about 1,400 CFM, not 1,407. The input is a rated figure, the efficiency is a rated figure, and the rise is two thermometer readings each good to perhaps a degree or so; a 2 F error in a 50 F rise is 4 percent of the answer, which is about 56 CFM. An airflow figure carried to the last digit from inputs like these claims a precision nothing in the calculation has. Measurement Resolution and Honest Rounding covers how far to trust it.

The estimate is useful mostly as a cross-check. If the furnace's rating plate gives a permitted rise range and the measured rise sits inside it, airflow is in a sane band. If the rise is near the top of the range, the formula says airflow is low, and the next stop is the filter, the coil, and the duct. It does not say which; that interpretation is the job of What a Delta-T Is Actually Telling You.

Worked example: flow a boiler loop needs

A boiler delivers 100,000 BTU/h of output to a hydronic loop designed for a 20 F drop between supply and return. How much water has to move?

• GPM = BTU/h / (500 x dT)
• GPM = 100,000 / (500 x 20) = 100,000 / 10,000 = 10 GPM.
• Check forward: 500 x 10 x 20 = 100,000 BTU/h.

This is why hydronic design starts from a design temperature drop. Halve the drop to 10 F and the same heat needs 20 GPM; double it to 40 F and it needs 5 GPM. The pump, the pipe size and the head all follow from that one choice. In the field, it runs the other way: with a known flow and two pipe temperatures you can estimate what a loop is delivering. A zone moving 4 GPM with a 15 F drop is delivering 500 x 4 x 15 = 30,000 BTU/h. If the boiler is firing 100,000 BTU/h of output into three zones and the zone drops add up to far less, either the flow figures are guesses or heat is going somewhere you have not measured.

When the constant moves

Altitude. Air gets thinner as you go up, so a cubic foot carries less mass and less heat. At about 5,000 ft air is roughly 14 percent less dense than at sea level, which brings 1.08 down to about 1.08 x 0.86 = 0.93. Redo the furnace example at that elevation and 76,000 / (0.93 x 50) = 1,634 CFM. Using 1.08 at altitude understates the airflow by that same 14 percent, because the formula assumes the air is heavier than it is. A furnace installed at altitude also carries its own derating of input, so the 76,000 itself may be lower; the installation manual sets that, not this card.

Hot water. At 180 F water weighs about 8.1 lb per gallon instead of 8.33, which pulls the 500 down to about 8.1 x 60 = 486. Nearly 3 percent, enough to matter in a design calculation and usually lost in the noise of a field estimate.

Glycol. An antifreeze mix carries less heat per pound than water, and its density differs too. Both numbers move the constant, and the direction for the common mixes is down: a glycol loop needs more flow than a water loop to move the same heat at the same drop. Take the specific heat and density from the fluid supplier's data for that concentration, multiply them with 60 as above, and use that constant. Using 500 on a glycol loop overstates the heat a measured flow delivers.

Very hot or very cold air. The 0.075 is also a temperature assumption. Air at 140 F is about 12 percent lighter than air at 70 F. Inside the range of comfort heating and cooling the effect is small next to measurement error, which is why the 1.08 survives. In a make-up air heater or an industrial dryer it does not.

Sensible only, and what that leaves out

Across a cooling coil the air formula measures only the sensible part of what the coil is doing: the temperature drop. A coil also removes moisture, and that latent heat does not show up on a thermometer at all. In humid weather the latent share can be a large fraction of the total, so 1.08 x CFM x dT across a wet coil can come in well under the system's capacity while the system is working perfectly.

Put numbers on it. A nominal 3-ton system (36,000 BTU/h) moves 1,200 CFM and the tech measures a 20 F drop across the coil. The air formula gives 1.08 x 1,200 x 20 = 25,920 BTU/h. That is 25,920 / 36,000 = 72 percent of the nominal rating, and a reader who forgets the formula is sensible-only calls the system 28 percent short. On a humid day the other 10,080 BTU/h may well be going into condensate running down the drain, which is the coil doing its job. Two more things keep that comparison loose: the 36,000 is a rating-condition figure, not what the coil delivers at today's indoor and outdoor conditions, and the 1,200 CFM is itself an estimate unless it was measured. The sensible figure is real; calling it a shortfall needs a total-heat measurement.

Total heat on a wet coil uses a different formula: BTU/h = 4.5 x CFM x the change in enthalpy (heat content, in BTU per pound of dry air), where 4.5 is the same 0.075 lb/ft3 x 60 min/h without the specific heat, because enthalpy already carries it. Enthalpy comes from wet-bulb readings and a psychrometric chart or calculator. The point for this card is narrower: if a cooling capacity check uses 1.08, it is a sensible-capacity check, and the sentence reporting it says so.

The slips that break these formulas

• A temperature difference converted with 32. A 10 C rise is an 18 F rise. Plug 50 into the formula because someone converted the difference like a reading, and the heat comes out nearly three times too large. Temperature Conversion and the Delta-T Rule owns this one.
• Readings taken before the rise has settled. A furnace's rise climbs for several minutes after ignition. A reading in the first minute or two understates it and so overstates airflow.
• Mixed-air readings. A supply thermometer in a spot where some return air bypasses, or a return reading near a supply register, shrinks the measured rise and inflates the CFM.
• CFM per minute, BTU per hour. The 60 inside each constant is the minutes-to-hours step. A writer who builds the formula by hand and forgets it lands sixty times low.
• Rated input used as output. Furnace and boiler plates usually state input. The heat the air or water actually picks up is input times efficiency, so using input overstates the airflow or flow by the efficiency loss.

How to check an answer before you act on it

Run it forward. Every backward solve (CFM from heat, GPM from heat) has a forward version, and plugging the answer back in should return the heat you started from.

Compare it with a second, independent figure. A furnace airflow from the rise can be compared with what the blower's table predicts at the measured external static pressure, or with a duct traverse. Two methods landing within about 10 percent of each other is a reasonable field agreement; one method alone is an estimate. When they disagree badly, the formula is rarely the problem: one of the readings feeding it is.

And say which constant you used. "1,400 CFM at standard air" and "1,630 CFM corrected for 5,000 ft" are both honest; "1,400 CFM" at altitude without the qualifier is a number the next tech will trust and should not.

References

• Furnace and boiler installation manuals for rated output, temperature rise range and altitude derating
• Glycol supplier data for specific heat and density at the mix concentration
• See related: What a Delta-T Is Actually Telling You; Temperature Conversion and the Delta-T Rule; Energy and Power Units: BTU, Kilowatts, Tons and Horsepower; How to Average a Duct Traverse into CFM