biology formulas

magnification

image size / actual size

actual size

image size / M

Enzyme rate

V depends on [S], temperature, pH.

Michaelis–Menten: V = V_max [S] / (K_m + [S])

Photosynthesis efficiency

(energy stored chemically / incident light energy) × 100%

Selection coefficient

s relative fitness reduction.

w = 1 − s (relative fitness)

Lincoln index

M marked first sample, C second capture, R marked in second.

N ≈ (M × C) / R

Simpson’s index of diversity

n total individuals, n_i in category i.

D = 1 − Σ (n_i / n)²

Net primary production

Energy available to consumers.

NPP = GPP − R_plant

Energy transfer efficiency

(energy at trophic level n+1) / (energy at trophic level n) × 100%

Cardiac output

SV × HR (stroke volume x heart rate)

Ventilation rate

Per minute.

tidal volume × respiratory rate

Filtration rate idea

Kidney.

GFR links plasma flow and filtration pressure (qualitative + given data calculations)

Standard deviation (sample)

s = √( Σ(x − x̄)² / (n − 1) )

Standard error

s / √n

95% CI (large n, normal approx.)

≈ mean ± 1.96 SE

Chi-squared

Goodness of fit / contingency

χ² = Σ (O − E)² / E

Eyepiece Graticule Calibration

actual size of object= number of graticule units x calibration factor per unit

Fick’s Law of Diffusion

surface area x concentration difference / diffusion distance

volume of a sphere

4/3 pi r3

surface area of a sphere

4pir2

Allele frequency

p + q = 1 (where p is frequency of dominant allele, q is frequency of recessive allele)

Genotype frequency equation:

p2 + 2pq + q2 = 1 (where p2 = homozygous dominant, 2pq = heterozygous, q2 = homozygous recessive

Genetic Ratios:

Expected Mendelian ratios (e.g., 3:1 for monohybrid cross, 9:3:3:1 for dihybrid cross)

Percentage Change

final value - initial value / initual value x 100

Rate of Reaction / Growth

change in quantity / time taken