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UV Index from Erythemally Weighted Irradiance

Also known as UV index · UVI · ultraviolet index · UV index from radiometer reading · erythemal irradiance to UV index · CIE weighted irradiance times 40 · 25 mW per square metre per UV index · how the UV index is calculated · erythemally weighted UV · McKinlay Diffey weighted UV · sunburn index · UV index from microwatts per square centimetre

UVI=40 Eer\mathrm{UVI} = 40\,E_{er}
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Worked example: EPA example: 216.7 (read as mW/m²) → UV index 8.7. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

See also

Solar Elevation Angle (Height of the Sun above the Horizon): The Sun's height, which sets the UV at the ground more than anything else does.Relative Optical Air Mass (Kasten and Young): The amount of air the sunlight crosses at that height, which the ozone and the molecules scatter and absorb.Solar Azimuth Angle (Compass Bearing of the Sun): Which way the Sun lies, for deciding which side of a building or a beach is in the shade.
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UV Index from Erythemally Weighted Irradiance explained

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The UV index is a number on a scale, and this formula is the definition of that scale, not a law of nature. Take the ultraviolet irradiance, weight each wavelength by how strongly it burns human skin (the CIE erythema reference spectrum of McKinlay and Diffey, 1987), add it across the spectrum to get EerE_{er} in watts per square metre, and multiply by 40 square metres per watt. One unit of the index is therefore 25 milliwatts per square metre of erythemally weighted irradiance, and an index of 10 is 0.25 W/m². The index itself has no unit.

The 40 only fixes the scale; the weighting does the physical work. That is why the input must be the weighted irradiance, not a broadband UV-B or UV-A reading, which have different spectra and would give a different number. NOAA's Global Monitoring Laboratory states the definition for its Antarctic ultraviolet network and gives a shortcut for readings in microwatts per square centimetre: multiply by 0.4, since 1 μW/cm² is 0.01 W/m² and 40 times 0.01 is 0.4. The EPA's account of how the National Weather Service forecasts the index ends the same way: the total weighted effect, adjusted for elevation and cloud, is divided by 25.

The EPA's worked example uses hypothetical strengths. A weighted total of 280, adjusted by 1.06 for 1 km of elevation and 0.73 for broken cloud, gives 280×1.06×0.73=216.7280 \times 1.06 \times 0.73 = 216.7, and 216.7/25=8.7216.7 / 25 = 8.7, rounded to 9. The page, reading 216.7 as milliwatts per square metre, gives 40×0.2167=8.66840 \times 0.2167 = 8.668, which matches the printed 8.7 to its two figures. The limit here is that the EPA gives those strengths no unit; dividing by 25 equals multiplying by 40 square metres per watt only when they are in mW/m², which is how the page reads them. One more check: 25 μW/cm² gives an index of 10.

On the scale the EPA publishes, 1 to 2 is low, 3 to 7 moderate to high and 8 and above very high to extreme. NOAA says the index reaches 15 or 16 in the tropics at high elevation under clear skies. A published forecast is for solar noon, while a radiometer reading gives the index at the moment it was taken. The result is only as good as the weighted measurement behind it.

UV Index from Erythemally Weighted Irradiance formula

UVI=40 Eer\mathrm{UVI} = 40\,E_{er}
Where
  • UVI\mathrm{UVI}= UV index
  • EerE_{er}= Erythemally weighted irradiance (mW/m²)
Where this comes from
  • NOAA Global Monitoring Laboratory, Antarctic UV Monitoring Network, "Database 4 - Field Description" (a US federal work in the public domain), the entry for UVindex: "The UV index is defined as erythemally (CIE) weighted irradiance, expressed in the units W/m2, and multiplied by 40. Note that the UV Index is a dimensionless number"; and, because the column Dose3_CIE_Erythema is in microwatts per square centimetre, UV Index = Dose3_CIE_Erythema x 0.4. Read it
  • US Environmental Protection Agency, Sun Safety, "Learn About the UV Index", section "Calculating the UV Index" (a US federal work in the public domain): the National Weather Service's steps, with a worked example using hypothetical strengths (the weighted total of 280, adjusted by 1.06 for 1 km of elevation and 0.73 for broken cloud, 280 x 1.06 x 0.73 = 216.7, divided by 25: 216.7 / 25 = 8.7, rounded to 9). The EPA's scale page groups 1 to 2 as low, 3 to 7 as moderate to high and 8 and above as very high to extreme. Read it
  • NOAA Climate Prediction Center, Stratosphere, "UV Index: What is it?" (a US federal work in the public domain): the index is a next-day forecast for solar noon, from 0 at night to 15 or 16 in the tropics at high elevation under clear skies. Read it
Revised 31 October 2026
Cite this page

formula.expert. (2026, October 31). UV Index from Erythemally Weighted Irradiance Calculator. https://formula.expert/solvers/uv-index-from-erythemal-irradiance

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