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Optical Absorbance, Concentration & Transmission

Relate decadic absorbance, percent transmittance, concentration, optical path and molar absorption coefficient.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A molar coefficient of 100 M⁻¹cm⁻¹, concentration 0.01 mol/L and path 1 cm give absorbance 1 and transmittance 10%.

A = εlc = −log₁₀(T% / 100)

Worked example

Enter these known values and leave the other values blank.

Decadic molar absorption coefficient
100 / M / cm
Absorbing-species concentration
0.01 mol / L
Optical path length
1 cm
Decadic absorbance
1
Percent transmittance
10 %

Assumptions and limitations

  • Concentration and path length are positive; coefficient and absorbance are nonnegative. Percent transmittance must be greater than zero and at most 100.
  • The coefficient has reciprocal concentration and reciprocal length units. Both selectors matter; M⁻¹cm⁻¹ is equivalent to L/(mol·cm).
  • The model assumes suitable monochromatic light, a homogeneous sample and a coefficient applicable to the species, wavelength and conditions. Scattering and instrumental effects are excluded.
  • Zero absorption coefficient permits zero absorbance and 100% transmission but cannot determine an unknown concentration or path uniquely.

Common questions

Should I enter 0.1 or 10 for ten percent transmission?

Enter 10. This field is percent transmittance; the logarithm uses the fraction obtained by dividing by 100.

Why is zero transmission rejected?

Its negative logarithm is unbounded. A finite absorbance calculation requires strictly positive transmission.

References

Bookify requires positive percent transmittance because zero transmission has no finite logarithmic absorbance. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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