Enter the temperature and relative humidity into the calculator to determine the humidity grains per pound (GPP). This calculator helps to assess the moisture content in the air.
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Humidity Grains Per Pound Formula
Grains per pound (gr/lb) is the mass of water vapor in one pound of dry air. The calculator uses the psychrometric humidity ratio and converts to grains, where 1 lb = 7000 grains.
GPP = 7000 * 0.621945 * Pw / (P - Pw)
Saturation vapor pressure (Magnus form, kPa) at temperature T in °C:
Pws = 0.61094 * exp(17.625 * T / (T + 243.04))
Vapor pressure from relative humidity:
Pw = Pws * RH / 100
Relative humidity from a known GPP:
RH = 100 * Pw / Pws, where Pw = (W * P) / (0.621945 + W) and W = GPP / 7000
Variables:
- GPP = grains of water vapor per pound of dry air (gr/lb)
- W = humidity ratio (lb water / lb dry air)
- P = total atmospheric pressure (kPa)
- Pw = partial pressure of water vapor (kPa)
- Pws = saturation vapor pressure at the dry-bulb or dew point temperature (kPa)
- T = temperature (°C)
- RH = relative humidity (%)
Calculator modes:
- Temp + RH: Computes Pws from dry-bulb temperature, multiplies by RH/100 to get Pw, then solves for W and converts to GPP.
- GPP + Temp: Converts GPP to W, back-solves for Pw, and divides by Pws at the dry-bulb temperature to get RH.
- Dew Point: Sets Pw equal to Pws at the dew point (because RH = 100% at the dew point) and converts directly to GPP. Dry-bulb temperature is not needed.
Pressure can come from the standard sea level value (101.325 kPa), an altitude (using the barometric formula P = 101.325 * (1 - 2.25577e-5 * h)^5.25588 with h in meters), or a direct pressure entry.
Reference Tables
Use the table below to sanity-check a result. Values assume standard sea level pressure.
| Dry-bulb (°F) | 30% RH | 50% RH | 70% RH | 90% RH |
|---|---|---|---|---|
| 50 | 16 | 27 | 38 | 49 |
| 60 | 23 | 38 | 54 | 69 |
| 70 | 32 | 54 | 76 | 98 |
| 75 | 38 | 64 | 90 | 116 |
| 80 | 45 | 76 | 107 | 138 |
| 90 | 63 | 106 | 150 | 194 |
| 100 | 87 | 147 | 208 | 270 |
Restoration and HVAC technicians often classify indoor air by GPP regardless of RH:
| GPP Range | Classification | Typical Use Case |
|---|---|---|
| Below 40 | Dry | Target for water-damage drying |
| 40 to 60 | Moderate | Comfortable conditioned space |
| 60 to 80 | Humid | Dehumidification recommended |
| Above 80 | Saturated load | Poor drying, mold risk |
Example Problems
Example 1: Find GPP from temperature and RH. Air is at 75°F and 50% RH at sea level.
- Convert temperature: 75°F = 23.89°C
- Pws = 0.61094 * exp(17.625 * 23.89 / (23.89 + 243.04)) = 2.985 kPa
- Pw = 2.985 * 0.50 = 1.493 kPa
- W = 0.621945 * 1.493 / (101.325 - 1.493) = 0.00930 lb/lb
- GPP = 0.00930 * 7000 = 65 gr/lb
Example 2: Find RH from GPP and temperature. Air is at 70°F with 55 gr/lb at sea level.
- W = 55 / 7000 = 0.007857 lb/lb
- Pw = 0.007857 * 101.325 / (0.621945 + 0.007857) = 1.264 kPa
- Pws at 21.11°C = 2.507 kPa
- RH = 100 * 1.264 / 2.507 = 50.4%
FAQ
Why grains instead of grams? Grains per pound is the legacy unit on psychrometric charts in the United States. One pound of water equals 7000 grains, so the unit gives convenient whole-number values for indoor air.
Does GPP change with temperature? No. GPP measures the actual mass of water vapor in the air. If you heat or cool the air without adding or removing moisture, GPP stays the same while RH changes.
Why does altitude matter? Total atmospheric pressure appears in the humidity ratio formula. At higher elevations, lower pressure raises the humidity ratio for the same vapor pressure, so GPP changes slightly even at identical temperature and RH.
What is the difference between dew point and GPP? Dew point is the temperature at which the current vapor would saturate the air. GPP is the mass of that vapor per pound of dry air. They carry the same moisture information in different units, which is why the dew point mode needs no RH input.
