---
title: "Ultimate AP Biology Equation Sheets"
description: "Every AP Biology equation you need to know, straight from the official reference sheet, to help you get a 5 on the AP Biology Exam."
url: "https://nerd-notes.com/ap-biology-formula-sheets/"
date_modified: "2026-10-02T05:49:07+00:00"
---

# Ultimate AP Biology Equation Sheets

Every equation and constant on the official AP Biology exam reference sheet, in one interactive digital sheet with each formula tagged by unit.

- [View Digital Equation Sheet](https://nerd-notes.com/ap-biology-formula-sheets/#eq-official) (jumps to the digital sheet at the bottom of this page)

## And even more free resources to help you get a 5

- Use Phy to solve and explain hard questions. [Try here.](https://nerd-notes.com/ai/)

## Official 2026 Digital Equation Sheet

[Download the official PDF](https://apcentral.collegeboard.org/media/pdf/ap-biology-equations-and-formulas-sheet.pdf).

On the page this is an interactive sheet: a sticky tab bar jumps between its sections, and hovering (or focusing) an equation shows its name and the AP Biology unit it belongs to. Its full content follows: College Board's "AP Biology 2026 Equations and Formulas", transcribed, with each equation's name and CED unit as the page shows them on hover.

AP Biology units: 1 Chemistry of Life · 2 Cells · 3 Cellular Energetics · 4 Cell Communication and Cell Cycle · 5 Heredity · 6 Gene Expression and Regulation · 7 Natural Selection · 8 Ecology.

### Statistical Analysis and Probability

**Mean**

- Sample mean: $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$

**Standard Deviation**

- Sample standard deviation: $s = \sqrt{\frac{\sum\left(x_i - \bar{x}\right)^2}{n-1}}$

**Standard Error of the Mean**

- Standard error of the mean: $SE_{\bar{x}} = \frac{s}{\sqrt{n}}$

**Chi-Square**

- Chi-square: $\chi^2 = \sum\frac{(o-e)^2}{e}$

Variables: $\bar{x}$ sample mean; $n$ sample size; $s$ sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population); $o$ observed results; $e$ expected results; $\Sigma$ sum of all

### Degrees of Freedom

- Degrees of freedom are equal to the number of distinct possible outcomes minus one.

### Chi-Square Table

| $p$ value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 0.05 | 3.84 | 5.99 | 7.81 | 9.49 | 11.07 | 12.59 | 14.07 | 15.51 |
| 0.01 | 6.63 | 9.21 | 11.34 | 13.28 | 15.09 | 16.81 | 18.48 | 20.09 |

### Laws of Probability

- Addition rule (mutually exclusive events) (Unit 5: Heredity): $P(\text{A or B}) = P(\text{A}) + P(\text{B})$
- Multiplication rule (independent events) (Unit 5: Heredity): $P(\text{A and B}) = P(\text{A}) \times P(\text{B})$

### Hardy–Weinberg Equations

- Hardy–Weinberg genotype frequencies (Unit 7: Natural Selection): $p^2 + 2pq + q^2 = 1$
- Hardy–Weinberg allele frequencies (Unit 7: Natural Selection): $p + q = 1$

Variables: $p$ frequency of allele 1 in a population; $q$ frequency of allele 2 in a population

### Metric Prefixes

| Factor | Prefix | Symbol |
|---|---|---|
| $10^{9}$ | giga | $\mathrm{G}$ |
| $10^{6}$ | mega | $\mathrm{M}$ |
| $10^{3}$ | kilo | $\mathrm{k}$ |
| $10^{-1}$ | deci | $\mathrm{d}$ |
| $10^{-2}$ | centi | $\mathrm{c}$ |
| $10^{-3}$ | milli | $\mathrm{m}$ |
| $10^{-6}$ | micro | $\mu$ |
| $10^{-9}$ | nano | $\mathrm{n}$ |
| $10^{-12}$ | pico | $\mathrm{p}$ |

### Mode, Median, Mean, and Range

- Mode = value that occurs most frequently in a data set
- Median = middle value that separates the greater and lesser halves of a data set
- Mean = sum of all data points divided by number of data points
- Range = value obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum)

### Rate and Growth

**Rate**

- Rate: $\frac{dY}{dt}$

**Population Growth**

- Population growth (Unit 8: Ecology): $\frac{dN}{dt} = B - D$

**Exponential Growth**

- Exponential growth (Unit 8: Ecology): $\frac{dN}{dt} = r_{\max}N$

**Logistic Growth**

- Logistic growth (Unit 8: Ecology): $\frac{dN}{dt} = r_{\max}N\left(\frac{K-N}{K}\right)$

Variables: $dY$ amount of change; $dt$ change in time; $dN$ change in population size; $B$ birth rate; $D$ death rate; $N$ population size; $K$ carrying capacity; $r_{\max}$ maximum per capita growth rate of population

### Simpson’s Diversity Index

- Simpson's diversity index (Unit 8: Ecology): $\text{Diversity Index} = 1 - \sum\left(\frac{n}{N}\right)^2$

Variables: $n$ total number of organisms of a particular species; $N$ total number of organisms of all species

### Water Potential (ψ)

**Water Potential (ψ)**

- Water potential (Unit 2: Cells): $\psi = \psi_{\mathrm{P}} + \psi_{\mathrm{S}}$

**The Solute Potential of a Solution**

- Solute potential of a solution (Unit 2: Cells): $\psi_{\mathrm{S}} = -iCRT$

Variables: $\psi_{\mathrm{P}}$ pressure potential; $\psi_{\mathrm{S}}$ solute potential; $i$ ionization constant (1.0 for sucrose because sucrose does not ionize in water); $C$ molar concentration; $R$ pressure constant (R = 0.0831 liter bars/mole K); $T$ temperature in Kelvin (°C + 273)

### Water Potential in an Open Container

- The water potential will be equal to the solute potential of a solution in an open container because the pressure potential of the solution in an open container is zero.

### Surface Area and Volume

**Surface Area of a Sphere**

- Surface area of a sphere (Unit 2: Cells): $SA = 4\pi r^2$

**Surface Area of a Rectangular Solid**

- Surface area of a rectangular solid (Unit 2: Cells): $SA = 2lh + 2lw + 2wh$

**Surface Area of a Cylinder**

- Surface area of a cylinder (Unit 2: Cells): $SA = 2\pi rh + 2\pi r^2$

**Surface Area of a Cube**

- Surface area of a cube (Unit 2: Cells): $SA = 6s^2$

**Volume of a Sphere**

- Volume of a sphere (Unit 2: Cells): $V = \frac{4}{3}\pi r^3$

**Volume of a Rectangular Solid**

- Volume of a rectangular solid (Unit 2: Cells): $V = lwh$

**Volume of a Cylinder**

- Volume of a cylinder (Unit 2: Cells): $V = \pi r^2 h$

**Volume of a Cube**

- Volume of a cube (Unit 2: Cells): $V = s^3$

Variables: $r$ radius; $l$ length; $h$ height; $w$ width; $s$ length of one side of a cube; $SA$ surface area; $V$ volume

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The resources above are plain links; the digital sheet is an interactive JavaScript component whose data loads from the Nerd Notes API — its full content is reproduced above for automated readers.