Optical Density Calculator (OD ↔ transmission %, stacked ND filters)

Understanding the optical density calculator — concept and principle

This calculator converts between optical density (OD) and transmission for neutral-density filters, laser eyewear and absorbing samples. It adds stacked filters, and gives the attenuation factor, decibels, photographic stops, the power after the filter and the share blocked. Photographers, laser users and lab technicians use it.

Each unit of OD cuts the light tenfold, so OD 2 passes 10⁻² = 1 %.

How it is calculated

OD = −log₁₀ T; T = 10^(−OD)

Stacked filters: OD_total = OD₁ + OD₂

Attenuation factor = 10^OD; decibels = 10 × OD; stops = OD ÷ log₁₀ 2 ≈ OD ÷ 0.301

Power after = power in × T

T is the transmitted fraction (shown in %).

The principle

Each layer of an absorbing filter removes the same fraction of the light reaching it, so transmission falls exponentially with thickness. Taking the logarithm turns this into a simple scale: each extra unit of OD cuts the light by another factor of ten. Logarithms turn products into sums, so stacking filters simply adds their ODs. Photographers count in stops, halvings of light, which is why ND 0.3 is one stop.

Worked example

Default inputs: OD 2, no extra filter, incoming power 50.

T = 10^(−2) = 1%; total OD = 2.
Attenuation factor = 10² = 100 (1 in 100).
Decibels = 10 × 2 = 20 dB; stops = 2 ÷ 0.301 = 6.64.
Power after = 50 × 0.01 = 0.5; blocked = 99%.

Each point is the calculator re-run with only “Optical density OD” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Optical density OD	Transmission (%)
0.5	31.62
1	10
1.5	3.162
2	1
2.5	0.3162
3	0.1
4	0.01

How to read the result

OD 1 passes 10%, OD 2 passes 1% and OD 3 passes 0.1%. Laser eyewear is rated by OD at the laser's wavelength, and filters are not neutral across the spectrum, so check the OD at your wavelength. In spectrophotometry, OD is the same quantity as absorbance.

Common mistakes

Treating OD as linear: OD 4 is not twice as dark as OD 2, but a hundred times darker.
Multiplying ODs of stacked filters instead of adding them.
Using visible-light OD for an infrared or ultraviolet laser.

Keep in mind: Laser eyewear must be rated for the specific wavelength and power by its maker. This calculator does not certify eye safety.

Frequently asked questions

How many stops is ND 0.9?

About 3 stops.

What OD gives 0.1% transmission?

OD 3.

Is optical density the same as absorbance?

In spectrophotometry they are the same logarithmic quantity, though OD can also include scattering.

Can OD be negative?

Not for a passive filter; OD 0 means full transmission.

Sources: Edmund Optics, application note "Understanding Neutral Density Filters"

Checked 9 Nov 2026. Definition OD = −log₁₀(transmittance): standard. Stacking rule (the OD of stacked filters add): Edmund Optics application note “Understanding Neutral Density Filters”.

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