Enter the partial pressure of water vapor and the total air pressure into the calculator to determine the grains of moisture per pound of dry air.
Grains of Moisture Formula
The following formula calculates grains of moisture per pound of dry air from partial pressure, derived from the ideal gas law applied to a mixture of dry air and water vapor (Dalton’s Law of Partial Pressures):
G = 0.62198 \times \frac{P_w}{P - P_w} \times 7000Variables:
- G = grains of moisture per pound of dry air (gr/lb)
- P₀ = partial pressure of water vapor (inHg)
- P = total barometric pressure (inHg)
- 0.62198 = ratio of molecular weight of water (18.015) to molecular weight of dry air (28.966)
- 7000 = grains per pound (exact conversion)
The humidity ratio W (lb water/lb dry air) is the core quantity; multiplying by 7,000 converts it to grains. ASHRAE Fundamentals (Chapter 1) defines this relationship as the primary psychrometric property for moisture content.
What is a Grain of Moisture?
A grain is a unit of mass equal to 1/7,000 of a pound (0.0648 grams). The unit predates SI and was historically the weight of a single grain of barley. In psychrometrics, grains per pound of dry air (gr/lb or GPP) is the preferred imperial unit for moisture content because it avoids small decimal humidity ratios. The equivalent SI unit is grams per kilogram of dry air (g/kg), where 1 g/kg = 7.0 gr/lb.
Unlike relative humidity, which changes with temperature while moisture content stays constant, grains per pound is an absolute measure. Air at 75°F/50% RH and air that has been cooled to 60°F (now near 80% RH) can contain the same number of grains per pound if no moisture was added or removed. This makes GPP the operationally correct variable for tracking actual moisture loads in HVAC systems.
Reference Values at Sea Level (29.92 inHg)
The table below shows grains of moisture per pound of dry air at standard atmospheric pressure, calculated from the Magnus saturation pressure equation. These values apply at sea level; see the altitude section for corrections.
| Temp (°F) | 30% RH | 40% RH | 50% RH | 60% RH | 70% RH | 80% RH |
|---|---|---|---|---|---|---|
| 60°F | 22.9 | 30.6 | 38.3 | 46.0 | 53.8 | 61.6 |
| 65°F | 27.3 | 36.5 | 45.7 | 55.0 | 64.3 | 73.6 |
| 70°F | 32.5 | 43.5 | 54.5 | 65.5 | 76.6 | 87.8 |
| 75°F | 38.5 | 51.5 | 64.6 | 77.8 | 91.0 | 104.3 |
| 80°F | 45.5 | 60.9 | 76.4 | 92.1 | 107.8 | 123.6 |
| 85°F | 53.7 | 71.8 | 90.2 | 108.7 | 127.3 | 146.1 |
| 90°F | 63.0 | 84.5 | 106.1 | 127.9 | 150.0 | 172.2 |
Highlighted rows (70-75°F) represent the ASHRAE residential comfort design range. Values in gr/lb at P = 29.92 inHg.
Key reference points: the ASHRAE indoor design condition of 75°F / 50% RH equals approximately 64.6 gr/lb. ASHRAE Standard 55 sets maximum acceptable indoor humidity at 65% RH, which at 75°F corresponds to 77.8 gr/lb. Microbial growth risk rises sharply above 70 gr/lb at typical indoor temperatures.
Effect of Altitude on Grains of Moisture
Because barometric pressure appears in the denominator of the grains formula (P – Pw), lower atmospheric pressure at higher elevations increases the calculated GPP for the same temperature and relative humidity. This is a common source of error when contractors apply sea-level psychrometric charts in high-altitude locations.
| Elevation | Barometric Pressure | GPP at 75°F / 50% RH | Difference vs. Sea Level |
|---|---|---|---|
| Sea Level (0 ft) | 29.92 inHg | 64.6 gr/lb | baseline |
| 1,000 ft | 28.86 inHg | 67.0 gr/lb | +2.4 gr/lb |
| 2,500 ft | 27.32 inHg | 70.9 gr/lb | +6.3 gr/lb |
| 5,000 ft (Denver, CO) | 24.89 inHg | 77.9 gr/lb | +13.3 gr/lb |
| 7,000 ft | 23.09 inHg | 84.1 gr/lb | +19.5 gr/lb |
Barometric pressures from the International Standard Atmosphere (ISA) model. GPP computed at constant 75°F dry bulb / 50% RH.
At 5,000 ft elevation, the same 75°F / 50% RH air holds 13.3 more grains per pound than at sea level. A dehumidifier sized for Miami coastal conditions (P = 29.92 inHg) will be undersized by roughly 21% on a grain-removal basis when operated in Denver. The second calculator tab accounts for this automatically when you enter the local barometric pressure.
Grains of Moisture in HVAC Latent Load Calculations
HVAC engineers use grains per pound directly in latent heat calculations. The standard field formula for latent cooling capacity is:
Q_{latent} = 0.68 \times CFM \times \Delta GWhere Q is latent capacity in BTU/hr, CFM is airflow, and delta-G is the change in grains per pound across the coil. The factor 0.68 incorporates air density at standard conditions (0.075 lb/ft3), the heat of vaporization of water (1,076 BTU/lb), and the unit conversion from pounds to grains. A coil removing 20 grains/lb from 1,200 CFM of air is handling 0.68 x 1,200 x 20 = 16,320 BTU/hr of latent load.
Oversized air conditioning systems with short run cycles fail to remove adequate moisture even when they meet sensible cooling targets. An oversized unit may maintain 75°F but leave indoor GPP at 80+ gr/lb (above 65% RH at that temperature), creating mold risk despite the thermostat being satisfied. Monitoring GPP rather than temperature alone is the correct diagnostic for latent performance issues.
Grains of Moisture Formula
How to Calculate Grains of Moisture
- Determine the partial pressure of water vapor (Pw) in inHg. If you know temperature and RH, use Pw = (RH/100) x Ps, where Ps is the saturation pressure from the Magnus formula.
- Determine total barometric pressure (P) in inHg. Standard sea-level value is 29.92 inHg; adjust downward for altitude using the ISA lapse rate (~1 inHg per 1,000 ft gain).
- Substitute into G = 0.62198 x (Pw / (P – Pw)) x 7000.
- Verify your result against the reference table above for the relevant temperature and RH combination.
Example: At 75°F / 50% RH at sea level, the Magnus saturation pressure is approximately 0.876 inHg. Partial pressure Pw = 0.50 x 0.876 = 0.438 inHg. G = 0.62198 x (0.438 / (29.92 – 0.438)) x 7000 = 0.62198 x 0.01485 x 7000 = 64.6 gr/lb. This matches the ASHRAE standard indoor design value.
