Biology & Life Sciences

Genetics, ecology, physiology and cellular biology formulae

This Biology & Life Sciences formula collection brings together the key equations used to study genetics, ecology, physiology, and cell biology, from Hardy-Weinberg and allele frequency calculations to population growth, diversity indices, and microscope magnification. It’s designed to help students, exam candidates, and professionals quickly find the formulas they need, making complex biological relationships easier to understand, apply, and interpret in real-world research and analysis.

Hardy-Weinberg Equilibrium

p^2 + 2pq + q^2 = 1

Genotype frequencies in a non-evolving population.

Allele Frequency Sum

p + q = 1

The two allele frequencies must total 1.

Exponential Population Growth

N_t = N_0 e^{rt}

Unlimited growth of a population over time.

Logistic Growth

\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)

Population growth limited by carrying capacity.

Per Capita Growth Rate

r = b - d

Net growth rate from birth and death rates.

Population Doubling Time

t_d = \frac{\ln 2}{r}

Time for a population to double.

Surface Area to Volume

SA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cellular exchange efficiency.

Microscope Magnification

M = \frac{\text{image size}}{\text{actual size}}

How much larger an image appears than the object.

GC Content

\%GC = \frac{G + C}{A + T + G + C} \times 100

Proportion of G and C bases in DNA.

Shannon Diversity Index

H = -\sum p_i \ln p_i

Measures species diversity in a community.

Simpson Diversity Index

D = 1 - \sum p_i^2

Probability two random individuals differ in species.

Lincoln-Petersen Estimate

N = \frac{M \times C}{R}

Population size from mark-and-recapture sampling.

Net Primary Production

NPP = GPP - R

Energy stored by producers after respiration.

Cardiac Output

CO = HR \times SV

Blood pumped by the heart per minute.

Respiratory Quotient

RQ = \frac{CO_2\ produced}{O_2\ consumed}

Ratio revealing which fuel is being metabolised.

Michaelis-Menten Kinetics

v = \frac{V_{max}[S]}{K_m + [S]}

Rate of an enzyme-catalysed reaction.

Cell Dilution Factor

DF = \frac{V_{final}}{V_{sample}}

Factor by which a sample is diluted.

Hemocytometer Cell Count

C = \bar{n} \times DF \times 10^4

Cells per mL from a counting-chamber average.

Bacterial Generations

n = \frac{\log N_t - \log N_0}{\log 2}

Number of divisions over a growth period.

Bacterial Growth Count

N_t = N_0 \times 2^n

Cell count after n binary fissions.

Kleiber's Law

q_0 = 70\,M^{0.75}

Metabolic rate scales with body mass to the ¾ power.

Osmolarity

\text{Osm} = n \times C

Solute particle concentration in solution.

Monohybrid Cross Ratio

3 : 1

Phenotype ratio from a heterozygous monohybrid cross.

Dihybrid Cross Ratio

9 : 3 : 3 : 1

Phenotype ratio from a dihybrid cross.

Recombination Frequency

RF = \frac{\text{recombinants}}{\text{total offspring}} \times 100

Genetic map distance in centimorgans.

Enzyme Activity Unit

U = \frac{\mu mol\ product}{min}

One unit converts 1 µmol of substrate per minute.

Ecological Efficiency

E = \frac{\text{energy at level } n+1}{\text{energy at level } n} \times 100

Energy transfer between trophic levels (~10%).

Biochemical Oxygen Demand

BOD = \frac{D_1 - D_2}{P}

Oxygen consumed by microbes decomposing organic matter.

Total Magnification

M = M_{obj}\times M_{eye}

Total magnification of a compound microscope.

Surface-to-Volume Ratio

SA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cell exchange efficiency.

Net Primary Productivity

NPP = GPP - R

Energy available to an ecosystem after respiration.

Population Growth Rate

r = \frac{B - D}{N}

Per-capita growth from births and deaths.

Allele Frequency

p + q = 1

Frequencies of two alleles sum to one.

Bacterial Doubling

N = N_0\times 2^{t/g}

Exponential bacterial growth by generations.

Respiratory Quotient

RQ = \frac{CO_2\text{ produced}}{O_2\text{ consumed}}

Ratio revealing which fuel is being metabolized.

Enzyme Turnover Number

k_{cat} = \frac{V_{max}}{[E]}

Reactions catalyzed per enzyme per second.