Latent Heat Load from Humidity Ratio Difference: The Moisture Mass Behind the Cooling Duty and the Condensate It Produces

Why Latent Load Is a Mass-Transfer Problem Wearing a Heat Equation

Latent cooling load is written as a heat rate in BTU per hour or kilowatts, but the physical event underneath is the condensation of a mass of water, and every term in the equation exists to convert pounds of moisture per hour into an energy rate.

Air carries water vapor, and a cooling coil removes some of it by chilling the air below its dew point so the vapor condenses on the fins. The energy involved is the latent heat of vaporization released as that vapor turns to liquid, roughly a thousand BTU for every pound of water (2,326 kJ per kg). The load therefore depends on how much dry air passes the coil and how much water each pound of that air gives up — not on the temperature drop. A coil can produce a large latent load with almost no temperature change if the entering air is humid, and none at all if the air never reaches its dew point.

The calculator takes the airflow, the entering and leaving humidity ratios, and the air density, computes the humidity-ratio difference, converts it to a latent heat rate, and reports the moisture removal rate that goes with it. The Sensible Heat Ratio article treated the latent load as a known input and showed how its share decides equipment selection; this article computes that input from the air's own moisture content. The second output, the moisture rate, is often the more practical number, because it sizes condensate drains, sets dehumidifier duty in pounds or kilograms per hour, and translates directly into gallons in a pan. ASHRAE expresses moist-air latent heat through the humidity-ratio difference, which is the fundamental variable in every latent-load calculation.

Calculator Inputs: Airflow, Two Humidity Ratios, and Air Density

The calculator collects one airflow, two moisture states, and an optional density, then returns the difference, the load, and the moisture rate.

Unit System. Imperial (CFM, lb/lb, BTU/hr, lb/hr) or Metric (m³/s, kg/kg, kW, kg/h). The physics is identical; the Imperial path lumps two constants together while the metric path keeps them visible.

Airflow Rate [CFM or m³/s]. Volume airflow through the coil or airstream. Typical commercial air handler: 1,000 to 20,000 CFM (0.5 to 9.4 m³/s).

Entering Humidity Ratio W_in [lb/lb or kg/kg]. Mass of water vapor per mass of dry air entering the coil. Typical humid-climate mixed air: 0.011 to 0.016 lb/lb.

Leaving Humidity Ratio W_out [lb/lb or kg/kg]. The same quantity leaving the coil, bounded below by saturation at the coil's apparatus dew point. Typical: 0.007 to 0.010 lb/lb.

Air Density ρ [kg/m³]. Standard air is 1.202 kg/m³ (0.075 lb/ft³). Adjust for altitude and temperature.

Outputs are Humidity Ratio Difference ΔW (lb/lb or kg/kg), Latent Heat Load QL (BTU/hr or kW), and Moisture Removal Rate (lb/hr or kg/h).

ΔW = W_in − W_out → latent heat load → moisture removal rate

Both ratios on the same basis:

Enter both as mass ratios in the same unit. The humidity ratio is dimensionless
(mass of water per mass of dry air), so the numeric value is identical in lb/lb and kg/kg.

Where the humidity ratios come from:

From a psychrometric calculation or chart, given dry-bulb and one moisture property
(wet-bulb, dew point, relative humidity, or enthalpy).
Entering conditions come from the mixed-air state; leaving conditions from the coil selection.

The calculator does not account for sensible load, total cooling load, coil bypass factor, apparatus dew point, a leaving-air saturation check, outside-air mixing, infiltration moisture generation, condensate carryover or re-evaporation, room relative humidity from a load balance, or equipment latent capacity at real conditions. It is a screening latent-load estimate.

Humidity Ratio Is Not Relative Humidity

The single most consequential input error in latent-load work is entering relative humidity where humidity ratio belongs, because the two describe moisture in fundamentally different ways and differ by three orders of magnitude in numeric value.

The distinction:

Humidity ratio W: mass of water vapor per mass of dry air [lb/lb or kg/kg]
  An absolute measure. Typical indoor air: 0.008 to 0.012.
Relative humidity RH: vapor pressure as a percentage of saturation at that temperature [%]
  A relative measure. Typical indoor air: 40 to 60.

Why relative humidity cannot drive the equation:

Air at 50% RH holds very different amounts of water at 60°F (16°C) and at 90°F (32°C),
because saturation rises steeply with temperature.
The same percentage describes different moisture masses.
Latent load depends on the mass, so the equation needs the absolute measure.

The magnitude of the error:

Entering 50 (percent) where 0.0100 (lb/lb) belongs inflates the result by a factor of 5,000.
The output is absurd rather than subtly wrong, which is the one mercy of this mistake.

Converting when only relative humidity is known:

Humidity ratio follows from dry-bulb temperature and relative humidity through the
saturation pressure relation: W = 0.622 × p_v / (p_atm − p_v), with p_v = RH × p_sat(T).
A psychrometric calculator or chart performs this step.

Related moisture measures:

Dew point: the temperature at which the air's vapor would saturate; a direct proxy for W
Wet-bulb: an evaporative measure combining temperature and moisture
Grains per pound: the humidity ratio in grains, 7,000 grains to the pound

A practical check:

A humidity ratio should be a small decimal, roughly 0.002 to 0.030 for building air.
A value above 0.05 or below 0.001 signals a unit or conversion error.

Per ASHRAE Handbook Fundamentals, Psychrometrics chapter, humidity ratio is the mass of water vapor per mass of dry air, an absolute measure, while relative humidity is a percentage of saturation at a given temperature. Latent load depends on moisture mass, so the calculation requires the humidity ratio.

The Humidity-Ratio Difference and Why It Looks So Small

The driving quantity is the difference between entering and leaving humidity ratios, a number in the third or fourth decimal place, and its small appearance disguises how much energy it represents when multiplied by a full airstream.

ΔW = W_in − W_out   [lb water per lb dry air, or kg/kg]

Typical magnitudes:

Light dehumidification: ΔW 0.001 to 0.002
Standard comfort coil in a humid climate: ΔW 0.003 to 0.005
Deep dehumidification, DOAS on outdoor air: ΔW 0.006 to 0.012

Why the numbers are small:

Even saturated air at 90°F (32°C) carries only about 0.031 lb of water per lb of dry air.
Air is mostly dry air by mass; the moisture is a fraction of a percent to a few percent.
The differences across a coil are therefore small decimals by nature.

Why the small number still matters:

The airstream is large. At 1,200 CFM (0.566 m³/s) the coil processes roughly
5,400 lb of dry air per hour (2,449 kg/h).
Removing 0.0035 lb of water from each pound gives about 19 lb of water per hour (8.6 kg/h),
and each pound of condensed water releases roughly a thousand BTU.

The mass-flow bridge:

Dry air mass flow (Imperial) = CFM × 60 min/hr × 0.075 lb/ft³ = 4.5 × CFM  [lb/hr]
At 1,200 CFM: 4.5 × 1,200 = 5,400 lb/hr of dry air (2,449 kg/h)
Water removed = 5,400 × 0.0035 = 18.9 lb/hr (8.57 kg/h)

Precision matters at this scale:

Rounding ΔW from 0.0035 to 0.004 overstates the load by 14%.
Carry four decimal places on humidity ratios; the third decimal is not enough.

In grains:

0.0035 lb/lb equals 24.5 grains per pound, a more legible figure for field work.

Per ASHRAE Fundamentals, the humidity-ratio difference across a coil typically runs 0.001 to 0.012 lb/lb, small because air is mostly dry air by mass. Multiplied by the dry-air mass flow of 4.5 × CFM lb/hr it becomes pounds of water per hour, and each pound carries about a thousand BTU. Carry four decimals.

The Latent Load Equation in Both Unit Systems

The two unit systems express the same physics in different packaging, one with a lumped constant and one with the density and latent heat written out.

Imperial:

QL = 4,840 × CFM × ΔW

QL  = latent heat load [BTU/hr]
CFM = airflow [ft³/min], typical 400 to 20,000
ΔW  = humidity ratio difference [lb water per lb dry air], typical 0.001 to 0.012
4,840 = lumped constant embedding standard air density and latent heat

Metric (SI):

QL = ρ × h_fg × q × ΔW

QL   = latent heat load [kW]
ρ    = air density [kg/m³], standard 1.202
h_fg = latent heat of vaporization [kJ/kg], fixed at 2,454
q    = airflow [m³/s], typical 0.2 to 10
ΔW   = humidity ratio difference [kg water per kg dry air]

The same three ideas run through both:

Volume airflow × density = mass flow of air
Mass flow of air × ΔW = mass flow of water
Mass flow of water × latent heat = energy rate

Why the Imperial form hides them:

The 4,840 collapses the 60 minutes per hour, the 0.075 lb/ft³ density, and the
1,076 BTU/lb latent heat into one number, which is convenient and opaque.
The metric form keeps density and latent heat visible and adjustable.

The practical difference:

Metric lets you change air density directly for altitude.
Imperial requires scaling the constant itself.

An order-of-magnitude check:

1,000 CFM (0.472 m³/s) at ΔW 0.004 gives 4,840 × 1,000 × 0.004 = 19,360 BTU/hr (5.67 kW),
about 1.6 tons.
A useful mental anchor: roughly 5 BTU/hr per CFM per 0.001 of ΔW.

Per ASHRAE Fundamentals, the Imperial form QL = 4,840 × CFM × ΔW and the SI form QL = ρ × h_fg × q × ΔW express the same chain, volume to air mass to water mass to energy. The metric form keeps density and latent heat explicit; the Imperial constant lumps them.

Where 4,840 Comes From: The Provenance of the Imperial Constant

The 4,840 is not an arbitrary lookup value; it is the product of three physical quantities, and knowing them is what lets an engineer judge when the constant no longer applies.

The derivation:

60 min/hr           × 0.075 lb/ft³           × 1,076 BTU/lb           = 4,842 ≈ 4,840
(time conversion)     (standard air density)   (latent heat near 70°F / 21°C)

Step by step:

CFM × 60 = cubic feet per hour of air
× 0.075 lb/ft³ = pounds of dry air per hour (this is the familiar 4.5 × CFM)
× ΔW = pounds of water per hour
× 1,076 BTU/lb = BTU per hour

The 4.5 intermediate:

60 × 0.075 = 4.5, the standard air mass-flow factor.
The same 4.5 sits inside the sensible constant 1.08 (4.5 × 0.24 BTU/lb·°F specific heat)
and inside the total-enthalpy constant 4.5 itself.
The three familiar HVAC constants share one parent.

Why the provenance matters:

Each embedded quantity is an assumption.
Standard density assumes sea level and roughly 70°F (21°C); latent heat assumes a temperature.
Change the assumption and the constant changes.

The constant family:

Sensible: 1.08 × CFM × ΔT       (embeds 4.5 and specific heat 0.24)
Latent:   4,840 × CFM × ΔW      (embeds 4.5 and latent heat 1,076)
Total:    4.5 × CFM × Δh        (embeds 4.5 alone, enthalpy carries the rest)

Recognizing the family makes the equations one idea rather than three memorized forms.

Per ASHRAE Fundamentals, the Imperial latent constant is 60 min/hr × 0.075 lb/ft³ × 1,076 BTU/lb, approximately 4,840. Its 4.5 core is shared with the sensible constant 1.08 and the total-heat constant 4.5. Each embedded value is an assumption about air density and latent heat.

The Grains Form and Which Latent Heat the Constant Carries

Field practice often states moisture in grains per pound rather than decimal pounds, producing a second form of the equation, and the small spread between its published constants traces directly to which latent heat value was chosen.

The grains conversion:

1 lb of water = 7,000 grains (1 kg = 15,432 grains)
ΔW 0.0035 lb/lb = 0.0035 × 7,000 = 24.5 grains per pound

The grains form:

QL = 0.68 × CFM × Δgrains        [BTU/hr]

Where 0.68 comes from:

4,840 / 7,000 = 0.691
Using the coil-temperature latent heat instead: 4.5 × 1,061 = 4,775; 4,775 / 7,000 = 0.682
Published values of 0.68 and 0.69 differ only by which latent heat was assumed.

The two latent heat values:

1,076 BTU/lb (2,503 kJ/kg): latent heat of vaporization near 70°F (21°C), inside the 4,840 constant
1,061 BTU/lb (2,468 kJ/kg): an approximation nearer coil condensation temperature, used for mass
The two differ by about 1.4%.

Consistency of the calculator's own outputs:

The heat load uses the 4,840 constant (1,076 basis).
The moisture removal rate divides by 1,061 (coil-condensation basis).
The derived water mass therefore differs by roughly 1.4% from a strict single-constant
derivation, which is inside screening tolerance and worth knowing when comparing tools.

A cross-check with the grains form:

0.68 × 1,200 CFM × 24.5 grains = 19,992 BTU/hr (5.86 kW)
0.69 × 1,200 × 24.5 = 20,286 BTU/hr (5.94 kW)
4,840 × 1,200 × 0.0035 = 20,328 BTU/hr (5.96 kW)
All three agree within 2%, the spread being entirely the latent-heat assumption.

Per ASHRAE Fundamentals and standard HVAC practice, the grains form QL = 0.68 × CFM × Δgrains is the same equation scaled by 7,000 grains per pound. Published constants of 0.68 and 0.69, and latent heats of 1,061 and 1,076 BTU/lb, differ by about 1.4%, well inside screening tolerance.

Moisture Removal Rate: The Condensate the Coil Actually Produces

The second output converts the heat rate back into the mass it came from, and that number is what sizes condensate drains, rates dehumidifiers, and tells an operator how much water to expect in a pan.

The two forms:

Imperial: ṁ_water = QL / 1,061           [lb/hr]
Metric:   ṁ_water = ρ × q × ΔW × 3,600   [kg/h]

The metric form is the direct mass path:

ρ × q = kg of air per second
× ΔW = kg of water per second
× 3,600 = kg of water per hour
No latent heat is needed, because the quantity never converts to energy and back.

The Imperial form is the reverse path:

It divides the energy rate by the latent heat to recover the mass.
The 1,061 BTU/lb (2,468 kJ/kg) divisor is the coil-temperature approximation.

Worked, on the Imperial example:

QL 20,328 BTU/hr / 1,061 = 19.16 lb/hr (8.69 kg/h)

Converting to volume, the practical unit:

Water weighs 8.34 lb per US gallon (1.0 kg per litre).
19.16 / 8.34 = 2.30 gallons per hour (8.7 litres per hour)
Over an eight-hour occupied period, roughly 18 gallons (70 litres) into the drain pan.

Why the volume matters:

Condensate drain and trap sizing, pump capacity, and pan overflow risk all follow the volume rate.
A drain sized for a mild climate can be overwhelmed in a humid one at the same tonnage.

Dehumidifier ratings:

Standalone dehumidifiers are rated in pints or litres per day at stated conditions.
19.16 lb/hr is about 460 lb per day (209 kg per day),
roughly 55 gallons or 209 litres per day,
a figure that immediately shows whether portable equipment is plausible.

A sanity check against the air itself:

The moisture rate must be less than the water the entering air carries:
5,400 lb/hr dry air × 0.0130 lb/lb = 70 lb/hr (31.8 kg/h) of water entering.
Removing 18.9 lb/hr is 27% of it.

Per ASHRAE and manufacturer practice, the moisture removal rate converts the latent load back to mass, sizing condensate drains, pumps, and dehumidifier duty. At 8.34 lb per gallon, 19.16 lb/hr is 2.30 gallons per hour, about 18 gallons (70 litres) over an eight-hour period.

Air Density and the Altitude Correction the Constants Hide

Both equations rest on an assumed air density, and because density falls with elevation, the constants that look universal are sea-level values that overstate the load in mountain installations.

The density assumption:

Standard air: 0.075 lb/ft³ (1.202 kg/m³) at sea level, roughly 70°F (21°C)
The Imperial 4,840 embeds it; the metric form takes it as an explicit input

Density with elevation:

2,500 ft (762 m):   roughly 0.0685 lb/ft³ (1.098 kg/m³), about 9% below standard
5,000 ft (1,524 m): roughly 0.0625 lb/ft³ (1.001 kg/m³), about 17% below standard
7,500 ft (2,286 m): roughly 0.0570 lb/ft³ (0.913 kg/m³), about 24% below standard

Correcting the Imperial constant:

Scale by the density ratio: 4,840 × (ρ_actual / 0.075)
At 5,000 ft: 4,840 × (0.0625 / 0.075) = 4,840 × 0.833 = 4,033
Using the sea-level 4,840 at 5,000 ft overstates the latent load by about 20%.

Correcting in metric:

Enter the actual density directly. The equation needs no other change.

Why thinner air carries less moisture load:

The load depends on the mass of dry air passing, not its volume.
Thinner air means fewer pounds per CFM, so fewer pounds of water per CFM at the same ΔW.

The temperature effect:

Density also falls as temperature rises, though the effect over normal coil entering
conditions is smaller than a few thousand feet of elevation.

The same correction applies elsewhere:

The sensible constant 1.08 and the total-heat 4.5 scale by the identical density ratio,
because all three share the 4.5 core.

Per ASHRAE Fundamentals, the constants assume standard sea-level air density. At 5,000 ft (1,524 m), density runs about 17% low and the Imperial constant falls to roughly 4,033; using 4,840 there overstates the latent load by about 20%. The metric form takes density as a direct input.

The Coil Dew Point Floor: Leaving Humidity Ratio Is Not a Free Choice

The leaving humidity ratio entered into the calculation is bounded by physics, because air cannot leave a coil drier than saturation at the coil's effective surface temperature, and real coils never reach even that limit.

The floor:

W_out cannot fall below the saturation humidity ratio at the coil's apparatus dew point.
Apparatus dew point is the effective surface temperature the coil presents to the air.
Typical chilled-water and DX coils: 45 to 55°F (7 to 13°C).

Saturation values across that range:

45°F (7°C):  W_sat ≈ 0.0063 lb/lb
50°F (10°C): W_sat ≈ 0.0077 lb/lb
55°F (13°C): W_sat ≈ 0.0092 lb/lb

Why real coils stay above the floor:

Some air passes between the fins without touching a wet surface, the bypass fraction.
That bypassed air leaves at its entering moisture content and mixes with the treated air,
so the mixed leaving state sits above saturation at the apparatus dew point.
Bypass factors commonly run 0.05 to 0.20 depending on rows and fin spacing.

The sanity check on the worked example:

W_out 0.0095 lb/lb corresponds to saturation at roughly 56°F (13°C).
That is consistent with a coil whose apparatus dew point sits near 50°F (10°C) with some bypass.
An entered W_out of 0.005 would imply an apparatus dew point near 38°F (3°C), unrealistic
for a comfort coil and a signal that the input is wrong.

Reaching deeper dehumidification:

Lower leaving moisture requires a colder coil, more rows to cut bypass,
or a desiccant stage, each with its own energy and equipment consequence.

The entering side has no such floor:

W_in is whatever the mixed air carries, set by outdoor conditions and the outdoor-air fraction.

Per ASHRAE Handbook HVAC Systems and Equipment, the leaving humidity ratio is bounded below by saturation at the coil's apparatus dew point, and bypass air raises the actual leaving state above that limit. A leaving value implying an apparatus dew point far below 45°F (7°C) indicates an input error.

Airflow Against Difference: Many Combinations, One Load

Because the load is a product of airflow and moisture difference, the same latent duty arises from many combinations, and the choice between them is a real design decision rather than an arithmetic detail.

The product relationship:

QL = constant × CFM × ΔW
Halve the airflow and double ΔW: the same load.
Lines of equal latent load are hyperbolas on an airflow-versus-ΔW plot.

Worked equivalence:

1,200 CFM (0.566 m³/s) × ΔW 0.0035 = 20,328 BTU/hr (5.96 kW)
600 CFM (0.283 m³/s)   × ΔW 0.0070 = 20,328 BTU/hr (5.96 kW)
2,400 CFM (1.133 m³/s) × ΔW 0.00175 = 20,328 BTU/hr (5.96 kW)

What differs between them:

High airflow, small ΔW: a warmer, shallower coil, less dehumidification per pass,
higher fan energy, and a leaving state closer to the entering state.
Low airflow, large ΔW: a colder, deeper coil, a lower apparatus dew point,
more moisture per pass, lower fan energy, and a risk of overcooling the supply air.

The dew point constraint picks the winner:

The high-difference option needs a leaving humidity ratio that may sit below the coil's floor.
The low-difference option may not reach the room's required supply moisture at all.
The feasible band is narrower than the arithmetic suggests.

The sensible side constrains it further:

Airflow is usually already fixed by the sensible load and the supply temperature difference.
In most designs the latent calculation checks whether that airflow, at an achievable ΔW,
covers the moisture, rather than choosing airflow freely.

Where the freedom is real:

Dedicated outdoor air systems decouple the two: a small airflow at a large ΔW
handles the ventilation moisture, leaving the space equipment to handle sensible load.

Per ASHRAE practice, equal latent loads trace hyperbolas across airflow and humidity-ratio difference. The coil dew point floor limits the high-difference end and the sensible load usually fixes airflow, so the calculation typically verifies a chosen airflow rather than selecting one. Dedicated outdoor air systems exploit the low-flow, high-difference corner.

How the Latent Load Feeds the Sensible Heat Ratio

This calculation produces one of the two numbers the sensible heat ratio divides, which is how a moisture estimate turns into an equipment-selection decision.

The connection:

SHR = Q_sensible / (Q_sensible + Q_latent)
This calculator supplies Q_latent.

The worked link:

Q_latent 20,328 BTU/hr (5.96 kW) from the worked example.
With a sensible load of 60,000 BTU/hr (17.58 kW):
Q_total = 80,328 BTU/hr (23.54 kW); SHR = 60,000 / 80,328 = 0.747, standard comfort band.
With a sensible load of only 30,000 BTU/hr (8.79 kW):
Q_total = 50,328 BTU/hr (14.75 kW); SHR = 30,000 / 50,328 = 0.596, below the 0.65 threshold,
indicating enhanced dehumidification.

The same moisture, two conclusions:

The latent load is identical in both cases. What changed is the sensible load beside it.
A latent figure means nothing about equipment until it sits next to its sensible partner.

Why compute latent separately:

Many load tools report a total and a sensible figure, leaving latent as the remainder.
Computing latent directly from moisture content is an independent check on that remainder,
and it catches ventilation moisture that summary tools sometimes understate.

Boundary consistency:

Both loads must come from the same boundary, room-only or coil-total including ventilation.
The Sensible Heat Ratio article covers that distinction and the related heat factors.

Equipment matching:

The moisture removal rate compares directly against a coil's rated latent capacity
or a dehumidifier's rated pounds per hour at design conditions, a check that
total tonnage cannot provide.

Per ASHRAE and ACCA Manual S, the latent load computed here is the input the sensible heat ratio divides. The same 20,328 BTU/hr gives a ratio of 0.75 beside a 60,000 BTU/hr sensible load and 0.60 beside a 30,000 BTU/hr one, with opposite equipment conclusions. Keep both loads on one boundary.

Worked Example: 1,200 CFM at a 0.0035 Difference to 20,328 BTU per Hour

A commercial cooling coil handles humid-climate mixed air at 1,200 CFM (0.566 m³/s), entering at a humidity ratio of 0.0130 lb/lb and leaving at 0.0095 lb/lb. The question is the latent duty and the condensate it produces.

Step 1. Humidity-ratio difference.

ΔW = 0.0130 − 0.0095 = 0.0035 lb/lb (0.0035 kg/kg, 24.5 grains per pound)

Step 2. Dry-air mass flow.

ṁ_air = 4.5 × 1,200 = 5,400 lb/hr (2,449 kg/h)

Step 3. Latent heat load.

QL = 4,840 × 1,200 × 0.0035 = 20,328 BTU/hr (5.96 kW)

Step 4. Convert to tons.

20,328 / 12,000 = 1.69 tons of latent duty

Step 5. Moisture removal rate.

ṁ_water = 20,328 / 1,061 = 19.16 lb/hr (8.69 kg/h)

Step 6. Cross-check by the mass path.

5,400 lb/hr × 0.0035 = 18.9 lb/hr (8.57 kg/h)
The 19.16 figure is 1.4% higher, the 1,076-versus-1,061 constant spread.
Both are correct within screening tolerance.

Step 7. Condensate volume.

19.16 / 8.34 lb per gallon = 2.30 gallons per hour (8.7 litres per hour)
About 18 gallons (70 litres) over an eight-hour occupied period.
Size the drain, trap, and any condensate pump for this rate.

Step 8. Leaving-state sanity check.

W_out 0.0095 lb/lb saturates at roughly 56°F (13°C).
Consistent with a coil apparatus dew point near 50°F (10°C) with normal bypass. Plausible.

Step 9. Grains cross-check.

0.68 × 1,200 × 24.5 = 19,992 BTU/hr (5.86 kW), within 2% of 20,328.
The spread is the latent-heat assumption, not an error in either form.

Step 10. Result.

ΔW 0.0035 lb/lb, latent load 20,328 BTU/hr (5.96 kW, 1.69 tons),
moisture removal 19.16 lb/hr (8.69 kg/h, 2.30 gal/hr, 8.7 L/hr).
Compare against the coil's rated latent capacity at the design entering wet-bulb,
and size the condensate drain for 2.3 gallons per hour.

The decision is a coil selected on rated latent capacity at 1,200 CFM and the design entering wet-bulb — not on total tonnage. The Sensible Heat Ratio Calculator combines this figure with the sensible load to give the split, the Humidity Ratio Calculator produces the two moisture inputs, and the Condensate Pump Sizing Calculator handles the 2.3 gallons per hour this coil sheds.

Metric Worked Example and the Two-Constant Discrepancy

Step 1. The inputs.

Airflow 1.0 m³/s (2,119 CFM), W_in 0.014 kg/kg, W_out 0.010 kg/kg
ρ 1.202 kg/m³ (0.075 lb/ft³), h_fg 2,454 kJ/kg

Step 2. Humidity-ratio difference.

ΔW = 0.014 − 0.010 = 0.004 kg/kg (0.004 lb/lb, 28 grains per pound)

Step 3. Latent heat load.

QL = 1.202 × 2,454 × 1.0 × 0.004 = 11.80 kW (40,263 BTU/hr, 3.36 tons)

Step 4. Moisture removal rate by the direct mass path.

ṁ_water = 1.202 × 1.0 × 0.004 × 3,600 = 17.31 kg/h (38.16 lb/hr)

Step 5. Condensate volume.

17.31 kg/h = 17.3 litres per hour (4.57 gallons per hour)
A substantially larger drain duty than the Imperial example, at nearly twice the airflow.

Step 6. Cross-checking the two unit systems.

Running the same case through the Imperial form:
2,119 CFM × 4,840 × 0.004 = 41,024 BTU/hr (12.02 kW) against the metric 40,263 BTU/hr (11.80 kW).
A 1.9% difference.

Step 7. Where the difference comes from.

The Imperial constant carries a latent heat of 1,076 BTU/lb (2,503 kJ/kg).
The metric constant 2,454 kJ/kg equals about 1,055 BTU/lb.
The 2% spread in results is exactly the 2% spread in the assumed latent heat.
Air density is effectively identical between the two (0.075 lb/ft³ is 1.201 kg/m³).

Step 8. Which value to prefer.

Neither is more correct in general; each is the latent heat at a different reference temperature.
For screening, the spread is immaterial. For equipment comparison, use one basis consistently
and state it, so two tools are not compared across different assumptions.

Step 9. The practical rule.

Stay within one unit system for a given project's latent calculations.
Converting a result between systems reproduces the constant spread as an apparent discrepancy.

Step 10. Result.

1.0 m³/s at ΔW 0.004 gives 11.80 kW (40,263 BTU/hr) and 17.31 kg/h (38.16 lb/hr).
The 2% gap against an Imperial recomputation is the latent-heat assumption, not an error.

Per ASHRAE Fundamentals, the metric case gives 11.80 kW and 17.31 kg/h. Recomputing in the Imperial form differs by about 2%, tracing entirely to latent heat values of 1,076 against 1,055 BTU/lb. Keep one basis per project and state it.

Application Boundaries: Psychrometric State, Bypass, Outside Air, Humidity Proof

The calculator covers the latent heat rate and moisture mass rate from an airflow and a humidity-ratio difference, coil latent-load screening, dehumidification and DOAS estimating, and a first-pass check before psychrometric design. Several neighboring questions fall outside that scope.

Sensible and Total Load. The calculator returns only the latent portion. Sensible load and total cooling load are separate calculations, and the split between them is the sensible heat ratio.

Psychrometric State Points. It takes humidity ratios as given. Deriving them from dry-bulb with wet-bulb, dew point, relative humidity, or enthalpy requires a psychrometric calculation.

Apparatus Dew Point and Bypass Factor. The coil's effective surface temperature and its bypass fraction determine what leaving humidity ratio is actually achievable. Neither is computed here; both bound the input.

Outside-Air Mixing. Mixing outdoor and return air to produce the coil entering state is not modeled. Enter the mixed-air humidity ratio, or run outdoor air separately as a dedicated stream.

Infiltration and Internal Moisture Generation. Moisture entering the space through leakage, occupants, and processes is not generated by the calculator; it must already be represented in the entered humidity ratios or handled as a separate airstream.

Condensate Carryover and Re-Evaporation. At high face velocity, condensate can be entrained into the airstream and re-evaporate downstream, returning moisture to the air. Not modeled.

Room Relative Humidity. A latent load does not by itself predict the resulting indoor humidity, which requires a moisture balance on the space including all sources, the airflow, and the leaving-air moisture.

Equipment Latent Capacity. Rated coil latent capacity varies with entering wet-bulb, airflow, and staging. Manufacturer expanded ratings at the design point govern selection; this figure is the requirement, not the capability.

Altitude and Non-Standard Density. The Imperial constant assumes sea-level standard air; correct it by the density ratio, or use the metric form with the actual density.

Latent Heat Constant Basis. Results carry a roughly 2% spread depending on the assumed latent heat; state the basis when comparing tools.

Per ASHRAE Fundamentals and ACCA Manual S, latent-rate screening is the calculator's scope. Sensible and total load, psychrometric state derivation, apparatus dew point and bypass, outside-air mixing, moisture generation, carryover, room humidity prediction, and equipment latent capacity require separate analysis. A qualified engineer completes the selection.

Latent Heat Load Calculator

Standards and References

• ASHRAE Handbook, Fundamentals (2021), Psychrometrics chapter. Humidity ratio definition, moist-air property relations, saturation humidity ratios, and the latent heat of vaporization values behind the constants.
• ASHRAE Handbook, Fundamentals (2021), Nonresidential Cooling and Heating Load Calculations chapter. Latent load components and the standard air constants 1.08, 4,840, and 4.5.
• ASHRAE Standard 62.1-2022, Ventilation for Acceptable Indoor Air Quality. Minimum outdoor air rates by occupancy category and floor area, the code driver behind the ventilation moisture burden.
• ASHRAE Handbook, HVAC Systems and Equipment (2020), Air-Cooling and Dehumidifying Coils chapter. Apparatus dew point, bypass factor, rated latent capacity, and condensate carryover.
• ASHRAE Handbook, HVAC Applications (2023). Natatorium, commercial kitchen, and dedicated outdoor air system moisture loads, the applications where latent duty dominates.
• ASHRAE Standard 55-2023, Thermal Environmental Conditions for Human Occupancy. The indoor humidity context within which a latent-load target is judged.
• ACCA Manual J (8th ed), Residential Load Calculation. Residential latent load, occupant moisture allowances, and infiltration moisture.
• ACCA Manual S, Residential Equipment Selection. Selection against rated latent capacity at design conditions rather than against nominal tonnage.
• ASHRAE psychrometric standard air properties. Density 0.075 lb/ft³ (1.202 kg/m³), 7,000 grains per pound, and latent heat values of 1,076 and 1,061 BTU/lb (2,503 and 2,468 kJ/kg, 2,454 kJ/kg in the SI form).
• Manufacturer coil expanded ratings and dehumidifier performance data. Rated latent capacity and moisture removal at stated entering conditions and airflow, the source for actual equipment capability.

FAQ

Related Calculators

• Sensible Heat Ratio Calculator: The split this latent load feeds, deciding whether standard equipment can control humidity (article).
• Humidity Ratio Calculator: Produces the entering and leaving moisture values this calculation subtracts.
• Psychrometric Calculator: Full air-state analysis behind the apparatus dew point and the leaving-air condition.
• Condensate Pump Sizing Calculator: Sizes the pump for the moisture removal rate this calculation produces.
• Dehumidifier Sizing for Pools Calculator: Natatorium evaporation, the highest latent loads in building design.
• Ventilation Rate Calculator: Outdoor air quantity per ASHRAE Standard 62.1, usually the dominant moisture source.
• Cooling Load Calculator: The sensible side of the total cooling load.
• CFM Calculator: Airflow, the other factor in the latent product.