What the sensible heat equation tells you
The sensible heat equation is the single most-used piece of arithmetic in HVAC. It links three quantities — how much air you move, how much you change its temperature, and how much heat that transfers — so that knowing any two gives you the third.
Sensible means heat you can measure with a thermometer: it changes the dry-bulb temperature of the air and nothing else. Heat that evaporates or condenses water changes the moisture content without changing the dry-bulb temperature, and that is latent heat, which needs the latent heat equation instead. The two together make total heat, and the ratio between them is the sensible heat ratio.
Three questions get answered with this equation every working day. How much cooling is my coil actually delivering? How much air do I need to move to satisfy a 24,000 BTU/h sensible load at a 20 °F split? And what temperature rise should I measure across this furnace at its rated output and nameplate airflow? All three are the same equation rearranged.
Where 1.08 comes from, and why it is not a constant
Start from first principles. Heat carried by a mass flow is Q = ṁ × c_p × ΔT. You measure air in volume per minute, not mass per hour, so convert:
- 60 converts minutes to hours.
- 0.075 lb/ft³ is the density of standard air, which turns cubic feet into pounds.
- 0.24 BTU/lb·°F is the specific heat of dry air at constant pressure.
Multiply: 60 × 0.075 × 0.24 = 1.08. That is the whole derivation.
Now look at which of those three can move. Specific heat is essentially fixed for the range HVAC works in — moist air at typical conditions is nearer 0.244, which is why some references use 1.10 instead of 1.08, a 1.9% difference that is smaller than most field measurements. The 60 is arithmetic. Density is the term that moves, and it moves a long way.
Density falls with elevation because there is less atmosphere pressing down, and it falls with temperature because warm air expands. From the ideal gas law, ρ = 144 P ÷ (53.35 T) with pressure in psia and temperature in degrees Rankine. Feed in the standard atmosphere and you find that 0.075 lb/ft³ corresponds to sea level at about 69 °F — which is why the sea-level row of the reference table below reads 1.078 rather than exactly 1.080.
The practical consequence: at 5,280 ft the constant is about 0.888, so a duct system in Denver moving 1,000 CFM at a 20 °F split carries 17,800 BTU/h, not 21,600. Ignore that and you undersize the airflow by 18%.
Worked example: sizing airflow for a 36,000 BTU/h sensible load
A Manual J calculation gives a room a sensible cooling load of 36,000 BTU/h. You intend to run a 20 °F supply-to-return split at sea level.
- Pick the constant. Sea level, room-temperature air, so k = 1.08.
- Rearrange. CFM = Q ÷ (k × ΔT).
- Substitute. 36,000 ÷ (1.08 × 20) = 36,000 ÷ 21.6 = 1,666.7 CFM.
- Sanity-check against tonnage. 36,000 BTU/h is 3.0 tons of sensible load. 1,666.7 ÷ 3.0 = 556 CFM per ton of sensible capacity — high, which tells you this is a dry-climate load with very little latent content.
Now repeat it at 5,280 ft.
- Pressure. P = 14.696 × (1 − 6.8754×10−6 × 5,280)5.2559 = 14.696 × 0.963705.2559 = 12.100 psia.
- Density. ρ = 144 × 12.100 ÷ (53.35 × 529.67) = 1,742.4 ÷ 28,258 = 0.06166 lb/ft³.
- Constant. 60 × 0.06166 × 0.24 = 0.8879.
- Airflow. 36,000 ÷ (0.8879 × 20) = 2,027 CFM.
The same load at the same split needs 22% more air in Denver. That extra airflow also costs static pressure, which is why high-altitude duct systems get sized generously — see the duct velocity calculator for the penalty.
How to read the answer
When you solve for BTU/h, you are measuring what the equipment is doing right now, not what it is rated to do. Two thermometers and an airflow measurement give a real capacity figure. If it comes out well under the nameplate, the problem is nearly always airflow or refrigerant charge, and the delta-T calculator is the next step.
When you solve for CFM, sanity-check the answer against CFM per ton. Residential cooling equipment is designed around 350–450 CFM per ton of total capacity, with 400 as the usual default; humid climates run toward 350 to get more moisture removal and dry climates toward 450. If this equation asks for 600 CFM per nominal ton, either the load is unusually dry or the design split you chose is too small. The CFM per ton calculator makes that check directly.
When you solve for ΔT, compare it to the range the equipment is built for. A gas furnace carries a nameplate temperature rise range, typically something like 30–60 °F, and running outside it is a code and warranty problem, not just an efficiency one. A cooling coil normally shows a 16–22 °F dry-bulb split depending on entering humidity.
One caution that catches people out: this equation only describes sensible heat. On a wet cooling coil a large fraction of the work is latent, so the BTU/h this equation returns is genuinely less than the total capacity of the coil. It is not an error — you are measuring one of the two components.
Sensible heat constant by elevation
| Elevation (ft) | Pressure (psia) | Density (lb/ft³) | Constant | % of 1.08 |
|---|---|---|---|---|
| 0 | 14.696 | 0.07489 | 1.078 | 99.9% |
| 1,000 | 14.173 | 0.07222 | 1.040 | 96.3% |
| 2,000 | 13.664 | 0.06963 | 1.003 | 92.8% |
| 3,000 | 13.171 | 0.06712 | 0.967 | 89.5% |
| 4,000 | 12.692 | 0.06468 | 0.931 | 86.2% |
| 5,000 | 12.228 | 0.06231 | 0.897 | 83.1% |
| 6,000 | 11.777 | 0.06002 | 0.864 | 80.0% |
| 7,000 | 11.340 | 0.05779 | 0.832 | 77.1% |
| 8,000 | 10.916 | 0.05563 | 0.801 | 74.2% |
Every row assumes 70 °F air. Raising the air temperature lowers density further: at 130 °F in a furnace supply plenum the sea-level constant falls to about 0.99.
Where this equation gets misused
- Applying it to a wet coil and calling the answer total capacity. On a cooling coil that is condensing water, sensible heat is typically 65–80% of the total. The remainder needs the latent equation with the same airflow and the humidity ratio change.
- Using 1.08 above 2,000 ft. The error is roughly 3.5% per 1,000 ft of elevation and it always runs the same way — the real constant is smaller, so the real capacity is lower than 1.08 suggests.
- Measuring temperature in the wrong place. Take the return reading upstream of any duct leakage and the supply reading far enough from the heat exchanger that radiant heat does not hit the probe. A supply probe in line of sight of a furnace heat exchanger reads high.
- Guessing the CFM. Every number this equation returns is only as good as the airflow. Blower table lookups against measured static pressure, a flow hood, or a TrueFlow-style plate all beat an assumption of nameplate airflow.
- Confusing the constant with 4.5 or 4,840. 4.5 (= 60 × 0.075) converts CFM to pounds of dry air per hour, 4,840 is the latent constant, and 1.08 is the sensible one. They share a derivation but are not interchangeable.
- Ignoring the specific-heat convention. Some references use 1.10 because they take moist air at 0.244 BTU/lb·°F. Either is defensible; pick one and stay consistent within a calculation.
Where the numbers come from
The air-side sensible heat equation and its constant are given in the ASHRAE Handbook—Fundamentals, Chapter 1, along with the standard-atmosphere pressure relation used for the altitude correction here. Load calculations feeding the sensible load input are normally produced under ACCA Manual J for residential work; the airflow that comes out of this equation feeds ACCA Manual D duct design.
The family of air-side equations
Three constants cover almost all air-side work, and they are all the same conversion with a different property attached.
Sensible: Q = 1.08 × CFM × ΔT. Dry-bulb temperature change only.
Latent: Q = 4,840 × CFM × ΔW, with ΔW the humidity ratio change in pounds of water per pound of dry air. The 4,840 is 60 × 0.075 × 1,076, where the last term is the latent heat of vaporisation.
Total: Q = 4.5 × CFM × Δh, with Δh the enthalpy change in BTU per pound of dry air. This one is the honest way to measure a wet coil, because it captures sensible and latent together in a single measurement — see the moist air enthalpy calculator.
All three take the same density correction, because 60 × ρ is the common factor. If you correct 1.08 for altitude, correct 4,840 and 4.5 by the same ratio.
On the water side of a hydronic system the analogous equation is Q = 500 × GPM × ΔT, built exactly the same way from minutes, pounds per gallon and specific heat. The hydronic GPM calculator handles that one, including the correction for glycol.