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Calculator: from irradiance to joules and back

Short answer: the dose you give with a light therapy lamp is intensity multiplied by time. The formula is dose (J/cm²) = intensity (mW/cm²) × time (seconds) ÷ 1000. With the calculator below you can work it out both ways: from intensity and time to dose, or from intensity and the dose you want to the session length you need.

The calculator

Fill in both fields.
Fill in both fields.

How the formula works

Intensity is expressed in milliwatts per square centimetre: the power that falls on one square centimetre of skin. Multiply that by time and you get energy per square centimetre, expressed in joules per square centimetre. Because a milliwatt is a thousand times smaller than a watt, you divide by 1000.

What you want to knowFormula
DoseJ/cm² = mW/cm² × seconds ÷ 1000
Session lengthseconds = J/cm² × 1000 ÷ mW/cm²
Intensity neededmW/cm² = J/cm² × 1000 ÷ seconds
All three forms of the same equation.

Does your meter read in W/m² instead of mW/cm²? Then divide by ten: 300 W/m² is 30 mW/cm². That conversion is built into the calculator’s dropdown.

The most important limit of this calculator

The maths is always right. What you put into it usually is not.

The result depends entirely on the intensity figure you enter, and that is exactly the number that is rarely reliable in this industry. If you enter the value from the box, you are probably working with a figure measured with a solar meter, at the point with the highest reading, on a cold lamp, in the centre of the panel. A number like that is easily twice too high, and so is the calculated dose.

That is why the calculator has a checkbox that halves the value you enter. It is a rough rule of thumb, not a calibration: the real error of a solar meter is not linear and depends on the ratio of red to infrared. The background is in the article on the solar meter measurement error.

Three things the calculator does not solve for you:

  • The distance. Intensity drops quickly with distance. A dose calculation only applies to the distance at which the intensity was measured.
  • The spot on your body. The centre of a panel is much brighter than the edge. The calculated dose applies to the point where the measurement was taken, not to everything within the beam.
  • Which dose makes sense. That is a separate question, and the protocols going around are mostly taken from laser research. See the overview article on the lack of a gold standard.

So use the calculator mainly to see how sensitive a session length is to the intensity figure. Enter 100 mW/cm² and then 50, and see what happens to the time you need. That difference is exactly what is at stake with a measurement error of a factor of two.

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