Relative Humidity
Vapour pressure as a percentage of the saturation pressure.
Formula
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Example
p_v=1200, p_sat=2340: RH = 51%
How it works
Relative humidity compares how much water vapour is actually present in air to the maximum amount that air could hold at the same temperature. Because the saturation pressure is the vapour pressure at which air becomes fully saturated, dividing the actual vapour pressure by that limit gives a fraction of "how full" the air is, and multiplying by 100 converts it to a percentage. A value of 100% means the air is saturated, while lower values mean the air can still hold more moisture before condensation begins.
When to use it
Use this formula when you know the actual water-vapour pressure in air and the saturation pressure at the same temperature, and you need the humidity as a percentage. It is common in HVAC, refrigeration, weather, and indoor air-quality calculations.
Worked example, step by step
Given: Actual vapour pressure, p_v = 850 Pa Saturation pressure, p_sat = 1700 Pa Step 1: Substitute into the formula RH = (p_v / p_sat) × 100 Step 2: Divide the pressures RH = (850 / 1700) × 100 Step 3: Simplify the fraction RH = 0.5 × 100 Step 4: Convert to a percentage RH = 50% Final answer: The relative humidity is 50%.
Common mistakes to avoid
- Using vapour pressure and saturation pressure measured at different temperatures
- Forgetting to multiply by 100, leaving the answer as a decimal instead of a percent
- Reversing the ratio and calculating p_sat / p_v, which gives an incorrect humidity greater than 100%
Did You Know?
Warm air holds far more moisture, so the same water content gives a lower RH as temperature rises.
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