Unpolarized light through polarizer calculator

Enter any nonnegative incident intensity, using watts per square meter or another consistent unit, and the result is exactly one half of that value. The calculation describes truly unpolarized light and an ideal polarizer, so it does not require a polarizer angle. It returns the original intensity, transmitted intensity, and the fixed transmission fraction for clear use in lessons, laboratory planning, and optical-system estimates.

Why an ideal polarizer transmits one half

Unpolarized light has no single preferred electric-field direction. Over time, its transverse field orientations are distributed uniformly around the direction of travel. An ideal linear polarizer selects the component along one transmission axis. For a field at an angle to that axis, the transmitted intensity follows the squared projection, represented by the cosine squared of the angle. Averaging that factor over all equally represented orientations gives exactly one half. Therefore, if the incident intensity is I, the transmitted intensity after one ideal polarizer is I divided by two. This result is not an approximation caused by rounding in the calculator; it is the ideal-model average. The output also reports a transmission fraction of 0.5 to make that relationship explicit. Because the incoming light is unpolarized, rotating the single polarizer does not change the average transmitted intensity. Its axis changes the polarization direction of the emerging light, but not the one-half intensity result under these assumptions.

How to enter and interpret intensity

Enter the incident intensity as a nonnegative finite number. You may use watts per square meter, milliwatts per square centimeter, or any other intensity unit appropriate to your work, because the calculation is a dimensionless scaling by one half. The transmitted result uses the same unit as the input, so you should record that unit alongside the value in your notes or application. For example, an input measured in watts per square meter produces an output in watts per square meter. Zero is valid and returns zero, while negative values are rejected because physical optical intensity cannot be negative. The calculator does not convert units, infer a unit, or reinterpret power as intensity. If you begin with total optical power rather than intensity, the same one-half factor applies in the ideal model when the beam is fully intercepted, but you should label the quantity as power. Automated API requests cost $0.002; the browser calculation uses the same deterministic formula.

Know when the one-half rule applies

Use this calculation when the incoming beam is unpolarized and passes through a single ideal linear polarizer. Those conditions matter. After the first polarizer, the emerging light is linearly polarized, so adding a second polarizer requires Malus's law and the angle between the two transmission axes. Likewise, partially polarized or already polarized incident light needs information about its polarization state and orientation; simply halving it can be wrong. A real polarizer also absorbs, reflects, or leaks some light beyond the ideal projection model. Its measured throughput may therefore be lower or otherwise differ from one half, and manufacturer transmission data should be used for engineering tolerances. This tool intentionally isolates the textbook baseline: no extinction ratio, spectral response, surface loss, beam geometry, or detector response is included. That narrow scope makes it useful for checking homework, establishing a reference value before adding component losses, and testing software that implements the standard unpolarized-light result.