How to use
- Type into whichever of the three boxes you have, and leave the other two empty.
- Transmittance goes in as a fraction between 0 and 1; percent transmission as 0 to 100.
- The other two appear underneath. A negative absorbance is accepted — it means the sample transmits more than the blank.
💡 Exponents can be entered with e — for example, 1.5×10⁻⁵ is entered as 1.5e-5.
Formula & notes
Transmittance is the fraction of light that got through, and absorbance is minus its logarithm. That is the whole conversion; what matters is which logarithm, and the answer is the common one.
One relation, written three ways.
- Absorbance from transmittance
- A = −log₁₀(T) = 2 − log₁₀(%T)
- Transmittance from absorbance
- T = 10^(−A) %T = 100 × 10^(−A)
The scale, in whole steps
| Absorbance | Transmittance | %T | Light through |
|---|---|---|---|
| 0 | 1 | 100 | all of it |
| 0.301 | 0.5 | 50 | half |
| 1 | 0.1 | 10 | a tenth |
| 2 | 0.01 | 1 | a hundredth |
| 3 | 0.001 | 0.1 | a thousandth |
0.301 for half the light is worth memorising: it is log₁₀ 2, and it turns up whenever a dilution halves an absorbance.
Practical notes
- ⚠️ Common logarithm, base 10. JIS K 0115:2020 3.1 defines absorbance as 常用対数 outright, and IUPAC Gold Book A00028 notes that a decadic and a napierian absorbance are both in use depending on the base. A spectrophotometer reports the decadic one. Confusing them is out by ln 10 = 2.303 — large enough to matter and small enough to look like a pipetting error.
- A = 1 means one tenth of the light gets through; A = 2 means one hundredth. Each unit of absorbance is a factor of ten, which is why the useful range on a spectrophotometer is so short.
- The linear range is roughly 0.1 to 1.0 absorbance on most instruments. Above it, stray light and detector limits make the reading understate the absorbance, so the honest move is to dilute and multiply back.
- A negative absorbance means the sample transmits more than the blank. It is not impossible, it is a blanking problem — usually the wrong reference or a mark on the cuvette — so the tool converts it rather than refusing.
- Transmittance of exactly zero is refused. −log₁₀(0) is infinite rather than large, and an instrument runs out of dynamic range long before it gets there.
FAQs
Base 10, the common logarithm. JIS K 0115 says 常用対数 in the definition and every laboratory spectrophotometer reports it. A napierian absorbance, on natural logarithms, exists in some optics literature and is larger by ln 10 = 2.303. If a conversion comes out 2.3-fold off, that is where to look.
That a tenth of the light reached the detector. A = 2 is a hundredth, A = 3 a thousandth. It is a logarithmic scale, so a small change in absorbance high up the range is an enormous change in how much light there is to measure — which is why the instrument stops being linear.
Probably not. A negative absorbance means the sample let more light through than the blank did, which usually means the blank was wrong — the wrong buffer, a fingerprint, or a cuvette put in the wrong way round. Re-blank and read again. The tool converts negative values rather than refusing them, because the number is real even when the measurement is not.
Because it implies infinite absorbance. In practice an instrument runs out of dynamic range somewhere around A = 3 or 4, and a reading of zero transmission means the light is below the detector floor rather than absent. Diluting is the answer, not a bigger number.
Absorbance, because it is proportional to concentration through Beer-Lambert and %T is not. %T is what the older instruments displayed and it survives on some readouts; converting it to absorbance is the first thing to do with it.
Yes — it is log₁₀ 2. Every halving of the transmitted light adds 0.301 to the absorbance, so a twofold dilution of an absorbing solution drops the reading by that much. It is a quick way to check a dilution series without a calculator.
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