A **Transmittance to Absorbance Calculator** is used in **spectroscopy** to convert between two related measurements of light interaction with a sample: **transmittance** and **absorbance**.

For example, if a solution allows

50%of light to pass through (transmittance of0.5or50%), the calculator would determine its absorbance as approximately0.301.

This conversion is particularly useful in fields like **biochemistry**, where absorbance measurements are often used to determine the **concentration** of substances in solution.

## Transmittance to Absorbance Calculator

Transmittance (%) | Transmittance (decimal) | Conversion Equation | Absorbance |
---|---|---|---|

100 | 1.000 | A = -log₁₀(1.000) | 0.000 |

50 | 0.500 | A = -log₁₀(0.500) | 0.301 |

25 | 0.250 | A = -log₁₀(0.250) | 0.602 |

10 | 0.100 | A = -log₁₀(0.100) | 1.000 |

5 | 0.050 | A = -log₁₀(0.050) | 1.301 |

1 | 0.010 | A = -log₁₀(0.010) | 2.000 |

0.1 | 0.001 | A = -log₁₀(0.001) | 3.000 |

## Transmittance to Absorbance Formula

The formula used to convert transmittance to absorbance is:

**A = -log₁₀(T)**

Where:

**A**is absorbance (unitless)**T**is transmittance (expressed as a decimal between 0 and 1)

For transmittance expressed as a percentage, the formula becomes:

**A = -log₁₀(%T / 100)**

This logarithmic relationship means that as transmittance decreases, absorbance increases, but not in a linear fashion. For instance:

- A transmittance of 100% (T = 1) yields an absorbance of 0
- A transmittance of 10% (T = 0.1) results in an absorbance of 1
- A transmittance of 1% (T = 0.01) gives an absorbance of 2

## What is the absorbance of 20% transmittance?

To calculate the absorbance of a sample with **20% transmittance**, we apply the formula:

A = -log₁₀(20 / 100) = -log₁₀(0.2)

Using a calculator or logarithm tables, we find that log₁₀(0.2) ≈ **-0.69897**.

Therefore, A = -(-0.69897) ≈ **0.69897**.

This result demonstrates that a sample allowing only **20%** of light to pass through (i.e., absorbing **80%** of the incident light) has an absorbance of approximately **0.699**.

## How to determine transmittance (% T) from Beer Lambert’s law?

**Beer-Lambert’s law** relates the attenuation of light to the properties of the material through which it is traveling.

The Beer-Lambert law is expressed as:

**A = εbc**

Where:

**A**is absorbance**ε**is the molar attenuation coefficient (L mol⁻¹ cm⁻¹)**b**is the path length of the sample (cm)**c**is the concentration of the absorbing species (mol L⁻¹)

To determine transmittance from Beer-Lambert’s law, we can use the relationship between absorbance and transmittance:

**T = 10⁻ᴬ**

Substituting the Beer-Lambert equation:

**T = 10⁻ᵋᵇᶜ**

To express this as a percentage:

**%T = 100 × 10⁻ᵋᵇᶜ**

This formula allows us to calculate transmittance if we know the molar attenuation coefficient, path length, and concentration of the sample.

For example, if ε = 1000 L mol⁻¹ cm⁻¹, b = 1 cm, and c = 0.001 mol L⁻¹, we can calculate:

%T = 100 × 10⁻¹⁰⁰⁰×¹×⁰·⁰⁰¹ ≈ 10%

## What is the relationship between transmittance and absorbance?

Transmittance and absorbance are **inversely related**, with absorbance being a **logarithmic function** of transmittance.

Their relationship can be expressed in several equivalent ways:

**A = -log₁₀(T)****T = 10⁻ᴬ****A = log₁₀(1/T)****T = 1/10ᴬ**

This relationship means that:

- As transmittance decreases, absorbance increases (and vice versa)
- The relationship is not linear; small changes in transmittance at low values correspond to large changes in absorbance
- Absorbance can theoretically range from 0 to infinity, while transmittance is bounded between 0 and 1 (or 0% to 100%)
- A transmittance of 100% corresponds to an absorbance of 0
- A transmittance of 10% corresponds to an absorbance of 1
- A transmittance of 1% corresponds to an absorbance of 2

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