Malus Law Calculator

Work out malus law instantly with clear inputs, formula shown and shareable results.

About Malus Law Calculator

Malus's law gives the intensity through a second polariser as I0 cos^2(theta). At 30 degrees, 75% gets through; at 45 degrees exactly half; at 90 degrees none at all. The cosine applies to amplitude and the square to intensity, which is why crossed polarisers go completely black.

Formulas

Malus's law

I = I0 cos^2(theta)

Amplitude

amplitude ratio = cos(theta)

Worked example

With the default values below, Malus Law Calculator returns Transmitted Intensity of 75.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Intensity reaching the analyserminimum 0 W/m2: 100 W/m2
Angle between the polariser axesaccepts 0–180 deg: 30 deg

Results

Transmitted Intensity: 75.000 W/m2
Fraction Transmitted: 75.00%
Intensity Absorbed: 25.000 W/m2
Amplitude Passed: 0.8660

Step by step

1Values used
2Malus's law
3Amplitude
4Transmitted Intensity= 75.000 W/m2
5Fraction Transmitted= 75.00
6Intensity Absorbed= 25.000 W/m2
7Amplitude Passed= 0.8660

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does 45 degrees pass exactly half?

Because cos^2(45) is 0.5. That is also why inserting a third polariser at 45 degrees between crossed ones lets light through again.

Does unpolarised light follow this law?

No. Unpolarised light loses half its intensity at the first polariser regardless of angle; Malus's law applies from the second onwards.