Biochemistry Calculators

Spectrophotometry is the workhorse measurement of the biochemistry bench: almost every assay — cofactors at 340 nm, dye-binding protein kits, enzyme kinetics followed by appearance or disappearance of color — ends as an absorbance reading that has to become a concentration. The bridge between the two is one equation, and doing it right means keeping its terms straight: which ε at which wavelength, what dilution stood between you and the reading, and what path length the light actually crossed. This collection starts with that general law; the polymer-specific conventions (A260 for nucleic acids, A280 for proteins) live in their own dedicated tools, linked below. Every page shows the method, works real numbers and cites its sources, and everything runs locally in your browser.

The Beer–Lambert Law, Solved for Anything Missing

The Beer-Lambert calculator takes A = ε·c·l and solves for whichever quantity you lack — absorbance, molar extinction coefficient, concentration or path length — with unit pickers for M/mM/µM/nM and cm/mm so nothing silently mixes scales. It is built for the bench rather than the textbook: the dilution you made before measuring is a first-class input (the result is reported both in the cuvette and as your original sample), a molecular weight turns the molar answer into µg/mL, and transmittance — fraction or percent — converts to absorbance on the spot. When your reading leaves the range a spectrophotometer can be trusted in, the result says so instead of presenting it as fact. The how to use the Beer–Lambert law guide walks the same steps by hand, including why solving for ε is a single-point calibration and when a multi-point slope is the sturdier number.

Enzyme Kinetics: From Rate Measurements to Km, Vmax and kcat

Absorbance becomes concentration, concentration over time becomes a rate, and a rate against substrate becomes kinetics. The Michaelis-Menten calculator solves v = Vmax·[S]/(Km + [S]) for any one of the four quantities, and goes where the generic equation solvers stop: supply the enzyme concentration and it reports the turnover number kcat and the catalytic efficiency kcat/Km with a check against the diffusion ceiling; supply an apparent Km/Vmax pair measured with inhibitor and it classifies the inhibition pattern — competitive, noncompetitive, uncompetitive, mixed — with the ratio changes printed. Every answer carries where you sit on the saturation curve, and impossible inputs (v above Vmax, a Km solved from a flat near-saturating point) are refused with an explanation instead of laundered into a number. The companion enzyme kinetics guide walks the same arithmetic by hand.

From a Rate Reading Back to the Buffer It Ran In

Every one of those measurements happens in a buffer, and making the buffer is its own calculation — one that most protocols shorten into “adjust the pH with NaOH”. The buffer calculator solves the charge-and-mass balance instead of the ratio: it returns the grams of the form on your bottle, the millimoles and millilitres of NaOH or HCl that reach the target, the sodium, potassium and chloride the recipe leaves behind, the capacity β at that pH and how much acid or base the design can actually absorb. That machinery is where the interesting differences show up. For 50 mM acetate at pH 4.756 it asks 24.98 mmol of NaOH where Henderson–Hasselbalch asks 25.00 — a tenth of a percent, so the shortcut is safe and the page proves it. For 100 mM citrate at pH 4.00 the two differ by 10.3 % of the titrant, because pKa 3.13 and 4.76 are both engaged at that pH and the equation can only see one bracket. For 10 mM phosphate pushed to pH 12.3 it prints no Henderson–Hasselbalch reading at all: the mixture needs more strong ion than the buffer can carry, and the remainder is free OH⁻. Choose a system by distance from its pKa (HEPES is 0.10 unit from pH 7.4; phosphate and MOPS 0.20), then set the concentration by the capacity you need — β is 57.6 mmol·L⁻¹·pH⁻¹ at 100 mM and 0.62 at 1 mM. The how to make a buffer solution guide walks the bench procedure with the same numbers.

From the General Law to Polymer Conventions

Nucleic acids and proteins are heterogeneous polymers: nobody quotes a meaningful single ε for a plasmid, so their fields compressed the law into conventions — a fixed µg/mL-per-A260 factor for DNA and RNA, sequence-derived ε280 for proteins. Those conventions are deliberately kept out of the general solver and given their own pages, so no constant is maintained in two places:

• DNA and RNA at 260 nm → the DNA concentration calculator applies the standard 50/33/40 µg/mL factors with dilution and path-length correction, and reports purity ratios when you enter A280 and A230.
• Proteins at 280 nm → the protein concentration calculator builds ε280 from the sequence (or takes a measured one) and returns molar and mg/mL concentrations.
• Defined compounds, dyes, cofactors, assay standards → the Beer-Lambert calculator, where you bring the real ε.

Planning the Measurement Around the Math

An absorbance number is only as good as the sample in the light path, and the two most common fixes are dilution problems, which the suite handles end to end: use the Beer-Lambert result to see you are outside the linear band, the dilution calculator to plan the dilution that brings you into it, and the molarity calculator to turn a weighed mass into the standard concentration your ε-mode calibration needs.

Which calculator do I need?

Start from what your instrument gave you:

• An absorbance (or %T) for a defined compound with a known ε → Beer-Lambert calculator for concentration in molar and mass units, with the dilution folded in.
• A trustworthy standard and you need its ε → Beer-Lambert calculator in ε mode — a single-point calibration, with the slope method explained in the guide.
• An A260 reading of a DNA or RNA prep → DNA concentration calculator for the conventional factors plus purity ratios.
• An A280 reading of a purified protein → protein concentration calculator for sequence-derived ε280.
• Rates at several substrate levels, or an inhibitor to characterise → Michaelis-Menten calculator for v/Km/Vmax/[S] arithmetic, kcat and the inhibition-pattern read.
• Nothing measured yet — you are making the standards → molarity calculator and dilution calculator from the laboratory suite.
• A buffer to make, or a pH to reach → buffer calculator for the mass, the mmol and mL of NaOH or HCl, the co-ions left behind and the capacity at that pH.

Biochemistry Tools

• Beer-Lambert Law Calculator — solve A = ε·c·l for any quantity, with dilution factor, transmittance conversion, mass output and reliability warnings.
• Michaelis-Menten Calculator — solve the saturation equation for v, Vmax, Km or [S], with kcat and catalytic efficiency from an enzyme concentration, and inhibitor pattern classification.
• Buffer Calculator — formulate a buffer from the charge-and-mass balance: grams to weigh, mmol and mL of NaOH or HCl, the Henderson–Hasselbalch comparison, capacity, reserve and co-ion load, across ten systems with cited pKa values.