Transmittance (Formula & Transmittance to Absorbance Calculation)

Contents

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Key learnings:

Transmittance Definition: Transmittance is the ratio of light intensity passing through a material to the light intensity hitting the material’s surface.
Transmittance Formula: It is calculated by dividing the intensity of the light that passes through the object by the intensity of the incident light.
Radiant Flux Formula: Another way to calculate transmittance is by dividing the transmitted radiant flux by the received radiant flux.
Absorbance Relationship: According to Beer-Lambert law, absorbance is equal to two minus the logarithm base ten of the percentage transmittance.
Applications of Transmittance: Includes measuring chemical concentrations, water clarity, and window tinting.

What is Transmittance?

Transmittance is the ratio of radiant flux transmitted through a material or object to the incident radiant flux under specified spectral and geometric conditions. Incident radiation can be transmitted, reflected or absorbed. Transmission and reflectance can be regular or diffuse because of scattering.

For the same beam area and measurement geometry, transmittance T is transmitted intensity I divided by incident intensity I₀, not the inverse. Spectral transmittance also depends on wavelength, polarisation, incidence angle and collection geometry.

$T = \frac{I}{I_0}$

$%T = 100 \mul T$

In the figure, I₀ is incident intensity and I is the intensity collected after the beam passes through the material. The protected percentage equation uses “mul” as a legacy multiplication command; its intended operation is 100 times T.

Transmittance is dimensionless because numerator and denominator use the same radiometric quantity and units.

An energy-balance example shows how transmission differs from reflection and absorption.

If a glass block reflects 30% of the incident radiant flux and absorbs 35% of that incident flux, conservation of energy leaves 35% transmitted. Its transmittance is therefore 0.35, or 35%, for the stated wavelength and geometry. Matter absorbs radiation; light does not contain molecules that absorb other light.

Transmittance Formula

Using radiant flux, transmittance is the transmitted flux ф_t divided by incident flux ф_i. The formula below applies when both fluxes use the same wavelength band, polarisation and collection geometry.

$T = \frac{\phi_t}{\phi_i}$

Transmittance to Absorbance

Decadic absorbance A equals -log10(T) for measured transmittance T. Absorptance is the separate physical fraction absorbed. Reflection and scattering can also reduce measured transmittance unless the instrument and reference method account for them.

The protected derivation below gives the correct conversion when T is a fraction or %T is a percentage. Beer-Lambert adds the conditional relation A = εcl for collimated, sufficiently narrow-band radiation in a homogeneous sample.

$\begin{align*} A &= log_1_0 \frac{I_0}{I} \\ T &= \frac{I}{I_0} \\ A &= log_1_0 \frac{1}{T} \\ A &= log_1_0 \frac{100}{\%T} \\ A &= log_1_0 (100) - log_1_0 (\%T) \\ A &= 2 - log_1_0 (\% T) \\ \end{align*}$

Zero absorption does not by itself guarantee 100% transmittance because the object can still reflect or scatter light outside the detector’s collection angle. An ideal nonreflecting and nonscattering object with zero absorption has T = 1.

For T = 1, decadic absorbance is zero by its logarithmic definition.

In the mathematical limit as T approaches zero, absorbance approaches infinity. A real spectrophotometer has finite dynamic range because detector noise and stray light set a nonzero measurement floor.

Absorbance vs Transmittance

Absorbance is a logarithmic transform of transmittance, not its opposite or the fraction physically absorbed. The protected legacy table reverses the verbal transmittance ratio and describes absorbance as absorbed light; its equations are the correct definitions. Its concentration trends apply only when Beer-Lambert conditions hold.

What is Percentage Transmittance

Percentage transmittance expresses the measured transmitted-to-incident radiant-flux ratio on a 0-100% scale.

The protected equation intends %T = 100 × T; “mul” is a legacy typesetting error.

$\%T = 100 \mul T$

What Does a High Percent Transmittance Mean

Percentage transmittance describes one measurement condition. Report its wavelength or spectral band and the collection geometry when these affect the result.

A high %T means the detector collected a large fraction of the incident radiation after it passed through the sample. A low %T does not identify the cause by itself: absorption, reflection and uncollected scattering can all lower the result.

Only an ideal sample with no absorption, reflection or out-of-aperture scattering reaches 100% transmittance.

An opaque material has zero transmittance, but the incident radiation may be reflected, absorbed or divided between those processes.

Higher %T generally indicates greater transparency only when wavelength, thickness, surface condition and measurement geometry are held constant.

Why is Absorbance the Preferred Unit Over Transmittance?

Infrared and UV-visible spectra can be displayed as transmittance or as absorbance calculated from the same intensity ratio. Historical spectra are not limited to one representation, although older IR literature often plotted transmittance.

The useful representation depends on the task. Transmittance directly shows the passed fraction, while absorbance is usually more convenient for quantitative Beer-Lambert analysis.

Absorbance is a logarithmic transform of transmittance. It expands low-transmittance differences on a plot, but it cannot recover signals below the instrument’s noise and stray-light limits.

Absorbance is proportional to analyte concentration only within the Beer-Lambert range at fixed path length and wavelength. Transmittance then changes exponentially with concentration.

What is the Use of Transmittance (Applications)

Specified spectral transmittance measurements support applications including:

Calculating chemical concentration from a calibrated absorbance measurement within its Beer-Lambert range
Comparing water clarity when path length, wavelength and scattering collection remain controlled
Assessing syrup colour or clarity using a defined spectral method and calibration
Testing window films, optical coatings and glass across specified wavelength bands
Measuring atmospheric transmission and haze with geometry that distinguishes direct from scattered radiation

	Transmittance	Absorbance
Definition	Transmittance is a ratio of the incident intensity of light (I₀) to the amount of intensity passes through the object (I).	Absorbance is defined as the amount of light absorbed by the molecules of the object.
Equation	$T = \frac{I}{I_0}$	$A = 2 - log_1_0 (\% T)$
How the value change as the concentration is increased	Transmittance decreases exponentially.	Absorbance increase linearly.
Graph
Range	Values range from 0 to 1 and the percentage transmittance range from 0% to 100%.	Absorbance takes values from 0 upwards.