Magnification
Image size measured from micrograph, actual size measured/estimated from scale bar.
Magnification = Image size / Actual size IB Diploma Programme 2026
🧬 IBDP Biology Formula Sheet
Cell magnification, genetics ratios, ecology indices, and HL biochemistry relationships explained in concise variables.
Genetics Ecology HL Biochemistry
Quantify Biological Relationships
Although Biology is concept-heavy, the IB exams still expect precise ratios, rate equations, and statistical tests. This sheet keeps them consolidated for quick recall.
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Magnification & scale bars
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Population diversity indices
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Enzyme & transport equations
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HL statistical tests
Cells & Transport (SL Core)
Microscopy, SA:V discussion, and osmosis language used in Paper 1/2 short answer responses.
Surface Area to Volume Ratio
For cube of side length l.
SA:V = (6l²) / (l³) = 6 / l Water Potential
Ψ total water potential, Ψ_s solute potential, Ψ_p pressure potential.
Ψ = Ψ_s + Ψ_p Topic Focus
Microscopy & Scale
- Always include units when quoting image vs. actual size to avoid losing communication marks.
- Explain whether you are estimating based on scale-bar or converting magnification when asked for dimensions.
Surface Area to Volume
- Link high SA:V to diffusion efficiency when explaining cell size limits.
- Mention structural adaptations (microvilli, alveoli) to tie calculations to biology.
Water Potential
- Clarify sign conventions (solute potential is negative) when comparing ψ inside vs. outside cells.
- State whether pressure potential is zero/open when dealing with animal vs. plant cells.
Genetics & Enzymes (SL Core)
Population genetics, inheritance ratios, and enzyme kinetics that support Paper 2 structured questions.
Hardy-Weinberg Frequencies
p frequency of dominant allele, q recessive allele, p + q = 1.
p² + 2pq + q² = 1 p = √(dominant phenotype proportion) Chi-squared Test
O observed counts, E expected counts.
χ² = Σ (O − E)² / E Michaelis-Menten Kinetics
v reaction rate, V_max maximum rate, [S] substrate concentration, K_m is substrate concentration at ½ V_max.
v = (V_max [S]) / (K_m + [S]) Topic Focus
Hardy-Weinberg Usage
- List assumptions (large population, random mating, no migration) before applying the equation.
- Clarify whether you are solving for allele vs. genotype frequencies in each step.
Chi-squared Interpretation
- Quote degrees of freedom and critical value when concluding if data matches expected ratio.
- State whether deviation is likely due to chance or another biological reason.
Enzyme Kinetics
- Use the Michaelis-Menten graph to explain what V_max and K_m represent physically.
- Discuss how inhibitors change apparent K_m or V_max when relevant.
Ecology & Statistics (SL Core)
Population indices, growth calculations, and rate proxies that frequently appear in data-response items.
Simpson's Diversity Index
N total number of organisms, n_i number of individuals of species i.
D = 1 − [Σ n_i (n_i − 1)] / [N (N − 1)] Population Growth Rate
Births, deaths, immigration, emigration measured over same interval.
Growth rate = (Births + Immigration − Deaths − Emigration) / Population Photosynthetic Rate Proxy
m mass of oxygen produced, t time, A leaf area.
Rate = (Δm O₂) / (A · Δt) Topic Focus
Diversity Metrics
- Mention sampling method (quadrats, transects) when presenting Simpson's index to add context.
- Explain that higher D indicates more diverse communities and what that implies ecologically.
Population Change
- Clearly identify time intervals and whether values are absolute numbers or rates.
- Discuss limiting factors when growth deviates from calculated rate.
Photosynthesis/Respiration Rates
- Normalize by area or mass (as shown) when comparing across experimental setups.
- State measurement method (e.g., oxygen production, CO₂ uptake) before analyzing trends.
Higher Level Biochemistry & Physiology
HL-specific transport, neurobiology, and water potential relationships that extend Paper 3 calculations.
Nernst Potential (neurons)
E_ion equilibrium potential (mV), R gas constant, T temperature (K), z charge, F Faraday constant, [out]/[in] ion concentrations.
E_ion = (RT / zF) ln([ion]_out / [ion]_in) Bohr Shift Relationship
Shows how CO₂ concentration (k) and pH affect oxygen saturation S.
S = S_max / [1 + (k · [CO₂])^n] Water Potential for Solute
Ψ_s = −i C R T, where i ionisation constant, C molar concentration, R gas constant, T Kelvin.
Ψ_s = −i C R T Topic Focus
Neurobiology Calculations
- Explain physiological meaning of each term in the Nernst equation (temperature, charge, concentration).
- Compare calculated equilibrium potentials to actual membrane potential when discussing ion movement.
HL Transport & Respiration
- Use Bohr shift expression to explain affinity changes with CO₂ concentration/pH.
- Relate solute potential equation to osmoregulatory strategies in different tissues.
Data-Linking
- When given experimental data, mention how these equations justify observed physiological responses.
- Tie calculations back to IB syllabus subtopics (e.g., HL 11.2 Muscles, 11.3 Kidney) to improve explanation depth.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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State Assumptions
Mention constant temperature or closed population when applying Hardy-Weinberg or Simpson's index for clarity.
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Link to Practicals
Pair formulas (e.g., magnification) with the practical they came from so Paper 3 questions feel familiar.
Boost IB Biology Quant Skills
Tutors emphasise data handling, IA statistics, and HL biochemical calculations so you move confidently between qualitative and quantitative tasks.
Formulas reference the IB Biology data booklet plus HL emphasis topics such as membrane transport and neurobiology.
Units: use mol dm⁻³ for concentration, kPa for pressure, and Kelvin for gas/solute calculations unless stated otherwise.