Humidity and Dew Point Calculator for Seattle Climate
Calculate relative humidity and dew point temperature using the Magnus formula, calibrated for Seattle's temperate marine climate (average annual RH ~75%, temps 35–85°F).
Formulas Used
1. Saturation Vapor Pressure — Magnus Formula (Alduchov & Eskridge 1996):
es(T) = 6.1078 × exp(17.625 × T / (243.04 + T)) [hPa, T in °C]
2. Actual Vapor Pressure from Wet Bulb — Sprung Psychrometric Equation:
ea = es(Tw) − 0.000799 × P × (T − Tw)
where P = atmospheric pressure (hPa), T = dry bulb (°C), Tw = wet bulb (°C).
3. Relative Humidity:
RH = (ea / es(T)) × 100 [%]
4. Dew Point — Magnus Inversion:
Td = 243.04 × ln(ea/6.1078) / (17.625 − ln(ea/6.1078)) [°C]
5. Frost Point (when Td < 0°C) — WMO Magnus constants for ice:
Tf = 273.86 × ln(ea/6.1078) / (22.587 − ln(ea/6.1078)) [°C]
6. Absolute Humidity:
AH = 216.7 × ea / (T + 273.15) [g/m³]
7. Specific Humidity:
q = 622 × ea / (P − 0.378 × ea) [g/kg]
8. Atmospheric Pressure at Elevation (Barometric Formula):
P = 1013.25 × (1 − 2.25577×10⁻⁵ × h)5.25588 [hPa, h in meters]
9. Heat Index — NWS Rothfusz Regression (T ≥ 80°F, RH ≥ 40%):
HI = −42.379 + 2.049T + 10.143RH − 0.2248TRH − 0.00684T² − 0.05482RH² + 0.001229T²RH + 0.000853TRH² − 1.99×10⁻⁶T²RH²
Assumptions & References
- Magnus formula constants from Alduchov & Eskridge (1996), Journal of Applied Meteorology, 35(4): 601–609 — accurate to ±0.1% over −40°C to 60°C.
- Psychrometric coefficient A = 0.000799 °C⁻¹ applies to a ventilated (Assmann) psychrometer; sling psychrometers use A ≈ 0.000799–0.000802.
- Frost point uses WMO (2018) Technical Regulations Magnus constants for ice: a = 22.587, b = 273.86°C.
- Barometric formula per ICAO Standard Atmosphere (ISO 2533:1975).
- Heat Index regression from NWS (Rothfusz 1990, SR 90-23); valid for T ≥ 80°F and RH ≥ 40%.
- Seattle climate context: NOAA Climate Normals 1991–2020 for Seattle-Tacoma International Airport — mean annual RH ≈ 75%, mean annual temperature ≈ 52°F, elevation 433 ft.
- Mold growth risk threshold: sustained RH > 70% per ASHRAE Standard 160-2016.
- Condensation warning triggered when dew point is within 5°F of air temperature (surface condensation risk per ASHRAE Fundamentals Handbook).
- Inputs are validated: dry bulb −40°F to 140°F; wet bulb must not exceed dry bulb; RH 1–100%; elevation 0–14,000 ft.
Formulas Used
1. Saturation Vapor Pressure — Magnus Formula (Alduchov & Eskridge 1996):
es(T) = 6.1078 × exp(17.625 × T / (243.04 + T)) [hPa, T in °C]
2. Actual Vapor Pressure from Wet Bulb — Sprung Psychrometric Equation:
ea = es(Tw) − 0.000799 × P × (T − Tw)
where P = atmospheric pressure (hPa), T = dry bulb (°C), Tw = wet bulb (°C).
3. Relative Humidity:
RH = (ea / es(T)) × 100 [%]
4. Dew Point — Magnus Inversion:
Td = 243.04 × ln(ea/6.1078) / (17.625 − ln(ea/6.1078)) [°C]
5. Frost Point (when Td < 0°C) — WMO Magnus constants for ice:
Tf = 273.86 × ln(ea/6.1078) / (22.587 − ln(ea/6.1078)) [°C]
6. Absolute Humidity:
AH = 216.7 × ea / (T + 273.15) [g/m³]
7. Specific Humidity:
q = 622 × ea / (P − 0.378 × ea) [g/kg]
8. Atmospheric Pressure at Elevation (Barometric Formula):
P = 1013.25 × (1 − 2.25577×10⁻⁵ × h)5.25588 [hPa, h in meters]
9. Heat Index — NWS Rothfusz Regression (T ≥ 80°F, RH ≥ 40%):
HI = −42.379 + 2.049T + 10.143RH − 0.2248TRH − 0.00684T² − 0.05482RH² + 0.001229T²RH + 0.000853TRH² − 1.99×10⁻⁶T²RH²