Relative Humidity & Dew Point Calculator

ANA›Life Services Authority›National Calculator Authority›Relative Humidity & Dew Point Calculator

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Relative Humidity & Dew Point Calculator

Calculate relative humidity from dry-bulb and dew point temperatures, or compute the dew point from temperature and relative humidity using the Magnus–Tetens formula.

Calculation Mode

Find Relative Humidity (from T and T_d) Find Dew Point (from T and RH)

Air Temperature (T)

°C °F K

Dew Point Temperature (T_d)

°C °F K

Air Temperature (T)

°C °F K

Relative Humidity (RH)

%

Calculate

function relToggleMode() { var mode = document.getElementById('rel-mode').value; document.getElementById('rel-mode-rh').style.display = mode === 'rh' ? '' : 'none'; document.getElementById('rel-mode-dp').style.display = mode === 'dp' ? '' : 'none'; document.getElementById('rel-result').innerHTML = ''; }

function relToC(val, unit) { if (unit === 'C') return val; if (unit === 'F') return (val - 32) * 5 / 9; if (unit === 'K') return val - 273.15; }

// Magnus formula constants (August-Roche-Magnus approximation) // Valid for -40°C to +60°C var MAGNUS_A = 17.625; var MAGNUS_B = 243.04; // °C

function satVaporPressure(tc) { // e_s(T) = 6.1078 * exp(a*T / (b+T)) [hPa] return 6.1078 * Math.exp((MAGNUS_A * tc) / (MAGNUS_B + tc)); }

function relCalc() { var res = document.getElementById('rel-result'); var mode = document.getElementById('rel-mode').value;

if (mode === 'rh') { var tRaw = parseFloat(document.getElementById('rel-temp-a').value); var tdRaw = parseFloat(document.getElementById('rel-dewp-a').value); var tUnit = document.getElementById('rel-unit-a').value; var tdUnit = document.getElementById('rel-unit-da').value;

if (isNaN(tRaw) || isNaN(tdRaw)) { res.innerHTML = '⚠ Please enter valid numbers for both temperatures.'; return; }

var T = relToC(tRaw, tUnit); var Td = relToC(tdRaw, tdUnit);

if (T 60) { res.innerHTML = '⚠ Air temperature must be between -40°C and 60°C for the Magnus formula.'; return; } if (Td 60) { res.innerHTML = '⚠ Dew point must be between -40°C and 60°C for the Magnus formula.'; return; } if (Td > T) { res.innerHTML = '⚠ Dew point temperature cannot exceed air temperature.'; return; }

var es_T = satVaporPressure(T); var es_Td = satVaporPressure(Td); var RH = (es_Td / es_T) * 100;

// Heat index (Steadman, valid when T >= 27°C and RH >= 40%) var hiNote = ''; var hiVal = null; if (T >= 27 && RH >= 40) { var HI = -8.78469475556 + 1.61139411 * T + 2.33854883889 * RH - 0.14611605 * T * RH - 0.012308094 * T * T - 0.0164248277778 * RH * RH + 0.002211732 * T * T * RH + 0.00072546 * T * RH * RH - 0.000003582 * T * T * RH * RH; hiVal = HI; hiNote = 'Heat Index' + HI.toFixed(1) + ' °C / ' + (HI*9/5+32).toFixed(1) + ' °F'; }

res.innerHTML = '### Results ' + '' + 'ParameterValue' + 'Relative Humidity (RH)' + RH.toFixed(2) + ' %' + 'Saturation Vapor Pressure at T' + es_T.toFixed(4) + ' hPa' + 'Actual Vapor Pressure (at T_d)' + es_Td.toFixed(4) + ' hPa' + 'Air Temperature' + T.toFixed(2) + ' °C / ' + (T9/5+32).toFixed(2) + ' °F' + 'Dew Point Temperature' + Td.toFixed(2) + ' °C / ' + (Td9/5+32).toFixed(2) + ' °F' + hiNote + '' + '' + relComfortLabel(RH) + '

';

} else { var tRaw2 = parseFloat(document.getElementById('rel-temp-b').value); var rhRaw = parseFloat(document.getElementById('rel-rh-b').value); var tUnit2 = document.getElementById('rel-unit-b').value;

if (isNaN(tRaw2) || isNaN(rhRaw)) { res.innerHTML = '⚠ Please enter valid numbers for temperature and relative humidity.'; return; } if (rhRaw 100) { res.innerHTML = '⚠ Relative humidity must be between 0% and 100%.'; return; }

var T2 = relToC(tRaw2, tUnit2);

if (T2 60) { res.innerHTML = '⚠ Air temperature must be between -40°C and 60°C for the Magnus formula.'; return; } if (rhRaw === 0) { res.innerHTML = '⚠ Relative humidity of 0% yields an undefined dew point.'; return; }

// Dew point via Magnus inversion: // T_d = b * [ln(RH/100) + aT/(b+T)] / [a - ln(RH/100) - aT/(b+T)] var lnRH = Math.log(rhRaw / 100); var gamma = lnRH + (MAGNUS_A * T2) / (MAGNUS_B + T2); var Td2 = (MAGNUS_B * gamma) / (MAGNUS_A - gamma);

var es_T2 = satVaporPressure(T2); var es_Td2 = satVaporPressure(Td2); var spreadC = T2 - Td2;

res.innerHTML = '### Results ' + '' + 'ParameterValue' + 'Dew Point Temperature (T_d)' + Td2.toFixed(2) + ' °C / ' + (Td29/5+32).toFixed(2) + ' °F' + 'Dew Point Depression (T − T_d)' + spreadC.toFixed(2) + ' °C' + 'Saturation Vapor Pressure at T' + es_T2.toFixed(4) + ' hPa' + 'Actual Vapor Pressure' + es_Td2.toFixed(4) + ' hPa' + 'Air Temperature' + T2.toFixed(2) + ' °C / ' + (T29/5+32).toFixed(2) + ' °F' + 'Relative Humidity' + rhRaw.toFixed(1) + ' %' + '' + '' + relComfortLabel(rhRaw) + '

'; } }

function relComfortLabel(rh) { if (rh

#### Formulas Used

Magnus–Tetens Saturation Vapor Pressure:

e_s(T) = 6.1078 × exp( a·T / (b + T) )

a = 17.625 (dimensionless) b = 243.04 °C T in °C, e_s in hPa (≡ mbar)

Relative Humidity from T and T_d:

RH = 100 × e_s(T_d) / e_s(T)

Dew Point from T and RH (Magnus inversion):

γ(T, RH) = ln(RH/100) + a·T / (b + T)

T_d = b·γ / (a − γ)

Heat Index (Steadman / Rothfusz, T ≥ 27°C, RH ≥ 40%):

HI = −8.785 + 1.611·T + 2.339·RH − 0.146·T·RH − 0.0123·T² − 0.0164·RH² + 0.00221·T²·RH + 0.000725·T·RH² − 0.00000358·T²·RH²

#### Assumptions & References

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