Enclosure relative humidity calculation from ambient air

Air starting at 40°C and 95% relative humidity reaches approximately 35% RH when heated to 60°C at unchanged pressure. That result assumes no moisture enters, leaves or condenses. A sealed, rigid enclosure needs a pressure correction, giving approximately 37% RH instead. Use the calculation below to document the assumptions, then check the coldest surfaces rather than relying on the warm-air reading alone.

What you need for the calculation

Collect these inputs before choosing a formula:

• Ambient air temperature, measured away from enclosure exhaust and sun-heated surfaces.
• Ambient relative humidity, measured at the same location and time.
• Internal air temperature at the equipment location being assessed.
• Whether the enclosure exchanges air sufficiently to remain near ambient pressure.
• Whether moisture can enter through wet cables, conduit, leaks or damp materials.
• The lowest expected internal surface temperature, including shutdown and overnight conditions.

Use simultaneous temperature and humidity measurements. Combining an afternoon temperature with an overnight humidity maximum describes a different air condition.

For the worked example, the enclosure initially contains ambient air at 40°C and 95% RH. Electronics then raise its air temperature to 60°C. The enclosure heat calculation guide covers establishing that temperature from heat load and heat rejection.

Calculate the pressure-equalized result

Relative humidity compares actual water-vapor pressure with saturation vapor pressure at the same temperature. Heating lowers RH because saturation vapor pressure rises strongly with temperature.

1. Obtain saturation vapor pressure at both temperatures. Use a reputable psychrometric calculator or saturation-pressure table. Call the ambient value p_sat,out and the internal value p_sat,in. Keep both pressures in the same units.

2. Convert ambient RH to a fraction. Divide the percentage by 100. For example, 95% RH becomes 0.95.

3. Calculate the initial water-vapor partial pressure. Use p_v,out = (RH_out / 100) × p_sat,out. This establishes how much of the total air pressure comes from water vapor.

4. Apply the sensible-heating assumption. If total pressure and humidity ratio remain unchanged, use p_v,in = p_v,out. Humidity ratio means water-vapor mass per unit mass of dry air. This assumption excludes condensation, evaporation, moisture release and mixing with different air.

5. Calculate internal RH. Use RH_in = 100 × p_v,in / p_sat,in. Combining the equations gives RH_in = RH_out × p_sat,out / p_sat,in, with RH expressed as percentages on both sides.

Do not substitute temperature ratios for saturation-pressure ratios. Relative humidity does not change linearly with Celsius temperature.

Work through 40°C and 95% RH to 60°C

Using standard saturation vapor pressures over liquid water:

First calculate the actual water-vapor pressure:

p_v,out = 0.95 × 7.385 = 7.016 kPa

For unchanged total pressure and humidity ratio, that water-vapor pressure remains approximately constant during heating:

RH_in = 100 × 7.016 / 19.946 = 35.2%

The engineering result is therefore approximately 35% RH at 60°C, under the stated assumptions. Small differences between psychrometric calculators will not change that practical conclusion.

This is not moisture removal. The air still has essentially the same humidity ratio, despite its much lower RH. Cooling it again reverses the benefit unless moisture has actually been removed.

The corresponding dew point is approximately 39°C at the assumed pressure. A surface below that temperature can collect condensation while the surrounding air remains at 60°C. The condensation guide explains how that surface-temperature limit affects heaters, drains and shutdown conditions.

Correct for a sealed, rigid enclosure

A truly sealed, fixed-volume enclosure behaves differently. Its trapped gas cannot expand freely or escape as it warms. With unchanged water-vapor mass, vapor pressure rises in proportion to absolute temperature.

Use this correction before calculating RH:

p_v,in = p_v,out × (T_in + 273.15) / (T_out + 273.15)

Here, both temperature inputs are in degrees Celsius. Adding 273.15 converts them to kelvin for the pressure ratio.

For the same starting conditions:

p_v,in = 7.016 × 333.15 / 313.15 = 7.464 kPa

Then:

RH_in = 100 × 7.464 / 19.946 = 37.4%

The sealed, rigid result is therefore approximately 37% RH at 60°C, not 35%. Total absolute pressure also rises by approximately 6.4% for this idealized temperature change. This calculation does not establish an enclosure's pressure capability.

With bulk air still at 60°C, the higher vapor pressure corresponds to a dew point near 40.2°C. Use that value when checking a colder wall beside the warm air. During uniform cooling of the whole sealed volume, vapor pressure changes again; do not treat 40.2°C as a fixed dew point throughout that cycle.

These equations assume ideal-gas behavior, negligible volume change and no condensation or moisture exchange with materials. They do not include gasket movement, leakage or enclosure deformation.

Check whether the assumptions match the enclosure

A gasketed enclosure is not automatically a hermetic vessel. Conversely, an enclosure with a small membrane vent does not necessarily equalize pressure instantly.

The pressure equalization vent article explains why vent flow, humidity transport and heat removal are separate questions. A pressure-equalization device does not guarantee that internal moisture conditions immediately match ambient air.

Check the calculation against these conditions:

• Starting air: Was the enclosure closed under the stated ambient conditions, or during different weather?
• Moisture sources: Are there wet cable jackets, damp insulation, cleaning residues or moisture arriving through conduit?
• Moisture sinks: Is there desiccant, a dehumidifier or a cooling surface collecting condensate?
• Air exchange: Does leakage or ventilation replace the starting air during the heating period?
• Temperature distribution: Are the roof, door, backplate and cable entries colder than the measured air?

Ambient readings alone cannot determine internal RH when those effects are unknown. Report the calculated value as a conditional estimate, not a guaranteed enclosure condition.

Verify the result through operation and shutdown

Install suitable logging sensors with the equipment de-energized under your site's electrical safety procedure. Measure internal air temperature and RH together, then measure the surfaces most likely to become cold.

Keep the humidity sensor away from direct heater discharge and hot component surfaces. A locally heated sensor can report low RH without representing the rest of the enclosure. The humidity sensor placement article distinguishes internal enclosure measurements from measurements intended to represent outdoor air.

Log startup, normal operation, shutdown and the coolest expected period. Compare measured RH with the calculation at each matching air temperature. Investigate persistent differences before changing the enclosure design.

Check the calculated dew point against actual surface temperatures. Allow for sensor accuracy, response time and temperature gradients when setting a control margin. A single warm-air reading cannot demonstrate that every terminal, connector or door surface stays dry.

Also check component temperature limits independently. Lower RH at 60°C does not make 60°C acceptable for equipment rated for a lower ambient temperature.

Avoid mistakes that undermine the result

Do not call heating dehumidification. Heating reduces RH but does not remove water. A shutdown can restore high RH and create condensation on cooling surfaces.

Do not assume the current outdoor RH describes trapped air. A closed enclosure may retain moisture from installation or an earlier weather condition.

Do not use the 35% result for every sealed box. Document whether you assumed constant pressure or constant volume. Include any significant pressure difference in the calculation.

Do not drill ventilation holes to make the constant-pressure assumption true. Openings change ingress protection and can introduce wetter air. The ventilation holes article covers the protection lost through unqualified openings.

For an order or drawing review, specify operating and shutdown temperatures, starting moisture conditions, heat load and any pressure-equalization hardware. Include the required ingress protection, cable-entry arrangement and cold-surface assessment. For custom enclosures, put every opening and accessory location on the approved drawing rather than leaving the moisture-control arrangement to field changes.

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