Optical Density Calculator — Beer-Lambert Law
Apply the Beer-Lambert law to spectrophotometric data: solve for absorbance (OD), transmittance, sample concentration, or molar absorptivity from the other three quantities. Supports cuvette path lengths other than 1 cm.
Solve for
L mol⁻¹ cm⁻¹
cm
mol/L
Optical density = log₁₀(I₀/I) = ε × l × c
- 1
ε × path length
1,000 × 1 = 1,000 - 2
Absorbance A = ε × l × c
1,000 × 0.001 = 1
How does this calculator work?
Beer-Lambert law: A = ε × l × c (absorbance = molar absorptivity × path length × concentration). Rearrange to find any one quantity from the other three. Transmittance T = 10^(−A) gives the fraction of light transmitted. Valid for A ≲ 1.5 with monochromatic light and homogeneous solutions.
Formula
How this is calculated
The Beer-Lambert law describes how light is attenuated as it passes through an absorbing medium: A = ε × l × c, where A is the absorbance (also called optical density or OD), ε is the molar absorptivity (a substance- and wavelength-specific constant in L mol⁻¹ cm⁻¹), l is the optical path length (the distance through the sample, usually 1 cm for a standard cuvette), and c is the molar concentration of the absorbing species. Absorbance is related to transmittance T by A = −log₁₀(T), where T = I/I₀ (the ratio of transmitted to incident light intensity).
The law is most reliable at absorbances below ~1.5; at higher values stray light, fluorescence, and detector non-linearity cause deviations. It also assumes a monochromatic light source, a homogeneous sample, no significant light scattering, and that the absorber does not change chemically at the concentrations being measured. In practice, a calibration curve is the gold standard for quantitative work.
Choose what you want to solve for in the dropdown — the calculator will use the Beer-Lambert relationship to determine the missing quantity from the values you provide. Molar absorptivity (ε) values vary widely by substance and wavelength; typical biological chromophores range from ~10³ to ~10⁵ L mol⁻¹ cm⁻¹.
Frequently asked questions
They are the same quantity — A = −log₁₀(T) = log₁₀(I₀/I). The term "optical density" (OD) is commonly used in microbiology (e.g. OD₆₀₀ for bacterial culture turbidity), while "absorbance" is the preferred IUPAC term in chemistry. They are numerically identical.
At A > ~1.5, very little light reaches the detector; stray light (a small fraction of the wrong wavelength) becomes a significant fraction of the measured signal, causing apparent absorbance to plateau. Detector noise, fluorescence from the sample, and molecular association at high concentrations also cause deviations.
Molar absorptivity is substance- and wavelength-specific. Common examples: NADH at 340 nm ε ≈ 6,220 L mol⁻¹ cm⁻¹; myoglobin at 410 nm ε ≈ 1.27 × 10⁵; DNA at 260 nm ε ≈ 50 mL μg⁻¹ cm⁻¹ (mass-based). Look up the value for your specific analyte and wavelength in a published reference.
Also known as
TG we-Calculate Editorial Team. (2026). Optical Density Calculator — Beer-Lambert Law [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/optical-density-calculator
TG we-Calculate Editorial Team. "Optical Density Calculator — Beer-Lambert Law." TG we-Calculate. 2026. https://we-calculate.com/calculator/optical-density-calculator.
TG we-Calculate Editorial Team, "Optical Density Calculator — Beer-Lambert Law," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/optical-density-calculator
@misc{wecalculate_optical_density_calculator, title = {Optical Density Calculator — Beer-Lambert Law}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/optical-density-calculator}}, year = {2026}, note = {TG we-Calculate} }
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