AP Biology Formula Sheet 2026 — Equations & Reference Guide
AP Biology is not a heavily math-based exam, but it does provide a formula sheet and expects you to use several equations. Here is the complete AP Bio equation reference with explanations for every formula.
AP Biology Formula Sheet (Provided on Exam Day)
The College Board provides a formula and equation sheet with four sections: Statistical Analysis, Hardy-Weinberg, Surface Area and Volume, and Water Potential.
Statistical Analysis
Mean (average): $$\bar{x} = \frac{\sum x_i}{n}$$
Standard deviation: $$s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$$
Standard error of the mean: $$SE = \frac{s}{\sqrt{n}}$$
Chi-square statistic: $$\chi^2 = \sum\frac{(O - E)^2}{E}$$
where O = observed frequency, E = expected frequency
Hardy-Weinberg Equilibrium
Allele frequencies: $$p + q = 1$$
Genotype frequencies: $$p^2 + 2pq + q^2 = 1$$
Where:
- p = frequency of dominant allele
- q = frequency of recessive allele
- p² = frequency of homozygous dominant (AA)
- 2pq = frequency of heterozygous (Aa)
- q² = frequency of homozygous recessive (aa)
How to use Hardy-Weinberg:
- Identify q² from the frequency of the recessive phenotype
- Take the square root to find q
- Calculate p = 1 − q
- Calculate p², 2pq from there
Hardy-Weinberg conditions (all must be met for equilibrium):
- No mutation
- No gene flow (no migration)
- Random mating
- No natural selection
- Large population size
If a population is evolving, at least one condition is violated.
Surface Area and Volume
| Shape | Surface Area | Volume |
|---|---|---|
| Sphere | $4\pi r^2$ | $\frac{4}{3}\pi r^3$ |
| Cube | $6s^2$ | $s^3$ |
| Rectangular solid | $2(lw + lh + wh)$ | $lwh$ |
| Cylinder | $2\pi r^2 + 2\pi rh$ | $\pi r^2 h$ |
SA:V ratio = Surface Area ÷ Volume
As cell size increases, SA:V ratio decreases — this limits how large a cell can grow because nutrient/waste exchange becomes inefficient.
Water Potential
$$\Psi = \Psi_s + \Psi_p$$
where:
- Ψ (Psi) = water potential
- Ψ_s = solute potential (always negative or zero)
- Ψ_p = pressure potential
Solute potential: $$\Psi_s = -iCRT$$
where:
- i = ionization constant (1 for non-electrolytes like glucose; 2 for NaCl)
- C = molar concentration (mol/L)
- R = pressure constant = 0.0831 L·bar/(mol·K)
- T = temperature in Kelvin (°C + 273)
Water movement rule: Water always moves from higher water potential (less negative) to lower water potential (more negative).
Chi-Square: How to Use It in AP Biology
Chi-square tests are used to determine whether observed ratios differ significantly from expected Mendelian ratios.
Step-by-step:
- State H₀: the observed ratio matches the expected (e.g., 3:1)
- Calculate E for each class: E = (total) × (expected frequency)
- Calculate χ² = Σ(O−E)²/E
- Find degrees of freedom: df = number of classes − 1
- Compare χ² to critical value at p = 0.05 (provided in table)
- If χ² > critical value → reject H₀ (significant deviation)
Common critical values (p = 0.05):
| df | Critical value |
|---|---|
| 1 | 3.84 |
| 2 | 5.99 |
| 3 | 7.82 |
| 4 | 9.49 |
What's NOT on the Formula Sheet (Must Memorize)
| Topic | What to Know |
|---|---|
| Photosynthesis equation | 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂ |
| Cellular respiration equation | C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP |
| ATP yield per glucose | ~30–32 ATP (aerobic); 2 ATP net (glycolysis only) |
| Light reactions products | ATP, NADPH, O₂ |
| Calvin cycle inputs | CO₂, ATP, NADPH |
| Calvin cycle outputs | G3P (used to make glucose) |
| ETC location | Inner mitochondrial membrane |
| Lac operon logic | On when lactose present + glucose absent |
| DNA replication direction | 5' → 3' (new strand synthesis) |
| Transcription product | mRNA (pre-mRNA → mature mRNA after splicing) |
| Translation codons | AUG = start; UAA, UAG, UGA = stop |
| Meiosis outcome | 4 haploid cells (gametes) |
AP Biology Math Tips
- Hardy-Weinberg appears on almost every exam — practice all 5 steps until automatic
- Chi-square is the most likely FRQ statistical question — know df = classes − 1
- Water potential problems involve turgor pressure in plant cells — Ψ_p = 0 when cell is flaccid
- Standard error bars in data questions: overlapping error bars do NOT mean results are not significant; they just suggest it
AP Biology Key Numbers
| Value | Context |
|---|---|
| 6.02 × 10²³ | Avogadro's number (moles) |
| pH 7.4 | Normal human blood pH |
| 37°C | Normal human body temperature |
| -0.9 MPa | Typical solute potential of a plant cell |
| 10% rule | Energy transfer between trophic levels |
| 3 billion bp | Human genome size |