Laboratory calculations without the spreadsheet.

Solution preparation

n = c × V, m = n × M

Mass of solid needed for a target concentration and final volume.

Dilution

C1 × V1 = C2 × V2

Solve C1 × V1 = C2 × V2 for any missing variable.

Serial dilution

f = (C₀ / Cₙ)^(1/n)

Step-by-step transfer and diluent volumes for a dilution series.

Molarity

n = m / M, c = n / V

Relate mass, amount of substance, molecular weight, volume and concentration.

Percentage solutions

% = (solute / total) × 100

% w/v, % v/v and % w/w in both directions.

Buffer pH & preparation

pH = pKa + log₁₀([A⁻]/[HA])

Solve pH, pKa or the base/acid ratio, then get the amounts, masses and stock volumes to prepare the buffer.

pH / acid–base

pH = −log₁₀[H⁺], pH + pOH = 14 (25 °C)

Convert between pH, pOH, [H⁺] and [OH⁻], including strong acids and bases.

Solution mixing

C(final) = Σ(CᵢVᵢ) / ΣVᵢ

Final concentration when two or more solutions of the same solute are combined.

Osmolarity

osmolarity = Σ (i × c)

Ideal osmolarity from each solute's concentration and van 't Hoff factor.

DNA / RNA molarity & copies

M ≈ length × MW per base, c = ρ / M, N = n × Nₐ

Approximate nucleic-acid molarity, ng ↔ pmol conversions and copy number from length.

Master mix

total = per reaction × n × (1 + excess)

Scale any per-reaction component list to a batch with explicit excess.

PCR setup

V(component) = C(final) × V(rxn) / C(stock)

Per-reaction PCR component volumes scaled to a run, with water to volume.

Cell seeding

V(stock) = cells required / stock concentration

Suspension and medium volumes for a target number of cells per well.

Enzyme activity

1 U = 1 µmol product per minute

Units, activity concentration and specific activity from a measured rate.

CFU / plating

CFU/mL = colonies / (V × dilution fraction)

Colony counts to CFU/mL, with explicit dilution and plated volume.

Stoichiometry

n = m / M, equivalents = n / n(limiting)

Equivalents, limiting reagent and required amounts across a reaction table.

Reaction yield

% yield = actual / theoretical × 100

Theoretical yield and percentage yield from the limiting reagent.

Beer–Lambert

A = ε × l × c

Solve A = ε × l × c for absorbance, concentration, path length or ε.

Calibration curve

y = m·x + b, x = (y − b) / m

Linear least-squares fit with optional weighting and back-calculated unknowns.

Standard addition

c(sample) = |b / m| × V(final) / V(sample)

Determine a sample concentration from spiked aliquots, with explicit volumes.

Spike recovery

Recovery % = (spiked − unspiked) / added × 100

Recovery percentage from unspiked, spiked and added amounts.

LOD / LOQ

LOD = k·σ / S

Detection and quantitation limits from σ and the calibration slope.

Replicate statistics

RSD % = s / |x̄| × 100

Mean, standard deviation, variance and RSD % for replicate measurements.

Unit converter

Dimensional conversion

Mass, volume, amount and concentration units with explicit conversion rules.

Molecular weight

M = Σ (nᵢ × Aᵢ)

Formula mass from a chemical formula, with an element breakdown.

Density

ρ = m / V

Solve ρ = m / V for density, mass or volume.

ppm / ppb

ρ = w × d

Mass fractions to mass concentration, with an explicitly entered density.

RCF / RPM

RCF = 1.118 × 10⁻⁵ × r(cm) × RPM²

Convert between centrifuge speed and relative centrifugal force using the rotor radius.

Ideal gas law

P V = n R T

Solve PV = nRT for pressure, volume, amount of substance or temperature.

Gas mixture

xᵢ = Pᵢ / ΣP, P(total) = Σ Pᵢ

Composition of a gas mixture from ratios, mol%, vol%, flows or partial pressures.