AP Biology formula sheet: every equation by topic.
You are not tested on remembering these formulas. College Board prints them and gives them to you for the whole exam, which moves the difficulty somewhere else: knowing which relationship a question is asking for, and running it without fumbling the units. Every line of the AP Biology formula sheet is set out below in searchable text with its variable key, checked against the sheet College Board publishes for 2026. If you need the wider picture first, start with the full AP Bio exam guide.
Is the formula sheet provided on the AP Biology exam?
Yes. College Board supplies a two-sided Equations and Formulas sheet, formally called the AP Biology Exam Reference Information, and you have it for the whole exam. In 2026 the exam is a hybrid: you answer the multiple-choice questions and read the free-response questions in Bluebook, then handwrite your free-response answers in a paper booklet. The reference information is printed and mailed to schools and is also built into Bluebook, in test preview and on exam day. A calculator is allowed on both sections. A four-function (with square root) or scientific, non-graphing calculator is safe, a Desmos scientific calculator is built into Bluebook, and from the 2027 exam handheld calculators with storage capabilities, such as graphing calculators, are not allowed.
The AP Biology reference sheet is mostly statistics plus a handful of biology relationships: mean, standard deviation, standard error, chi-square, the laws of probability, Hardy–Weinberg, rate and growth, Simpson’s diversity index, water potential, and surface area and volume. It holds about 23 equations, alongside the variable keys, a chi-square table and a table of metric prefixes. Because the math is handed to you, the exam tests whether you can pick the right relationship and apply it, not whether you memorized it.
That matters more than it sounds. The course framework puts Statistical Tests and Data Analysis at 8–14% of the multiple-choice section, and on the free response it is the calculation parts of questions 1 and 2 that are scored on your setup as much as your answer.
Every equation on the AP Biology equation sheet
Every relationship on the sheet, with its variable key and a one-line note on when the exam asks for it. These are the AP Biology equations and constants you are handed on test day. Nothing here is a screenshot — it is all on-page text you can search, copy, and study from.
Statistics and probability
Compare your χ² value to the critical value for your degrees of freedom. If χ² is greater than the critical value at p = 0.05, the difference is significant and you reject the null hypothesis.
| Degrees of freedom (df) | p = 0.05 | p = 0.01 |
|---|---|---|
| 1 | 3.84 | 6.63 |
| 2 | 5.99 | 9.21 |
| 3 | 7.81 | 11.34 |
| 4 | 9.49 | 13.28 |
| 5 | 11.07 | 15.09 |
| 6 | 12.59 | 16.81 |
| 7 | 14.07 | 18.48 |
| 8 | 15.51 | 20.09 |
The sheet also defines the mode (most frequent value), median (middle value), mean, and range (largest observation minus smallest), and it prints the laws of probability: multiply probabilities for independent events, add them for mutually exclusive events.
Hardy–Weinberg (population genetics)
The reason this pair earns a place on a biology sheet is that it describes a population in which nothing is happening. Departure from those predicted frequencies is the standard evidence that something is acting on the population, which is why questions built on it so often turn into questions about natural selection ap biology covers in more depth.
Rate and population growth
Simpson’s diversity index
Water potential
A worked example, since this is the calculation students most often set up wrongly. For a 0.15 M sucrose solution in an open beaker at 22 °C: T = 22 + 273 = 295 K, and Ψs = −(1.0)(0.15)(0.0831)(295) = −3.68 bars. The beaker is open, so Ψp = 0 and Ψ = −3.68 bars. Place a potato core of Ψ = −2.0 bars in it and water leaves the core, because water moves toward the lower (more negative) potential. Show that substitution line in a free response; it carries the point even when the arithmetic slips.
Metric prefixes
The sheet prints the standard SI prefixes for converting between units of measurement.
| Factor | Prefix | Symbol |
|---|---|---|
| 109 | giga | G |
| 106 | mega | M |
| 103 | kilo | k |
| 10−1 | deci | d |
| 10−2 | centi | c |
| 10−3 | milli | m |
| 10−6 | micro | µ |
| 10−9 | nano | n |
| 10−12 | pico | p |
Surface area and volume (cell size)
All four solids appear on the sheet, for both surface area and volume. Dividing surface area by volume gives the surface-area-to-volume ratio (SA:V). As a cell grows, volume rises faster than surface area, so the ratio falls, which is why cells stay small enough to exchange materials efficiently.
What’s NOT on the sheet (what you must still know)
The sheet gives you equations — it does not give you the biology. You still have to supply everything the formulas operate on, and several relationships students expect to find are not printed at all.
Two are worth naming, because most study guides get this wrong. Gibbs free energy (ΔG = ΔH − TΔS) and pH (pH = −log[H+]) are widely listed as being on the AP Biology formula sheet. They are not. ΔG is on the AP Chemistry reference tables, which is where the confusion starts, and the AP Biology sheet carries neither the pH nor the pOH rules. You still need both ideas. Free energy runs through the whole energetics unit, where ΔG < 0 is spontaneous and exergonic and ΔG > 0 is not; pH turns up in enzyme and membrane questions. You simply will not find either printed on your desk.
Also absent: the photosynthesis and cellular-respiration equations, the shapes of the exponential J-curve and logistic S-curve (you get the growth equations, not the graphs), the Q10 temperature logic, and every bit of biological content, from processes and vocabulary to the diagrams you read and label.
The two shapes the sheet does not draw for you. Both come from equations that are on it: unlimited growth from dN/dt = rmaxN, and resource-limited growth from dN/dt = rmaxN (K − N) / K. The term that makes the difference is (K − N) / K, which shrinks toward zero as N approaches K and flattens the curve. Original diagram, drawn for this page; College Board prints the equations, not the graphs.
In short, the sheet hands you the math, and you bring the mechanism: knowing when chi-square applies, what each Hardy–Weinberg term means, or why a cell with a low surface-area-to-volume ratio struggles to exchange materials fast enough. That reasoning is exactly what the free response rewards.
How to use the formula sheet on exam day
Treat the sheet as a map, not a safety net. It is only fast if you already know your way around it, so work with it open all year, long before the clock is running. You can meet the real thing early, too: the reference information sits inside Bluebook’s test preview, so the version you open in the exam is one you have already navigated.
On test day, name the relationship a question is asking for, pull it off the sheet, and use the variable key to match every symbol to a value before you compute. Watch the units, which is where most of the lost marks are: Kelvin rather than Celsius for water potential, and the right p-value column for chi-square. Show the setup, since the free response scores your reasoning and not just the final number.
Drill the math one unit at a time with the AP Biology Progress Check answers, then pressure-test it on the free-response guide.
Get the official College Board sheet
To work from the same equations you will have in the exam, open the official Equations and Formulas sheet (PDF), or the College Board’s AP Biology exam page for the rest of the exam-day detail. The printed booklet reproduces that PDF; Bluebook shows the same information on screen. Everything on this page is checked line by line against that document and against the equations appendix of the AP Biology Course and Exam Description, which is why a few entries here differ from other study guides.
Frequently asked questions
Quick answers, checked against College Board.
Can I write on the AP Biology formula sheet during the exam?
Yes. The printed reference booklet tells you that any blank space in it may be used for scratch work during the exam, so you can annotate it, rearrange an equation, or note the values you have pulled out of a question. It is collected by the proctor at the end, so nothing you write on it is scored.
Is Gibbs free energy on the AP Biology formula sheet?
No, and this is the most common thing study guides get wrong about it. The equation for Gibbs free energy sits on the AP Chemistry reference tables, not the AP Biology one, which is where the confusion comes from. You are still expected to know what it means for a reaction to be spontaneous, you just will not find the equation in front of you.
Is the AP Biology formula sheet the same every year?
Not permanently. The content is stable from one year to the next, but it has changed across course revisions, and lists that circulate online often describe an older version. Check the current year’s Exam Reference Information on AP Central rather than a study guide’s summary.
Why is R on the AP Biology formula sheet different from the gas constant in chemistry?
It is the same constant wearing different units. R = 8.314 joules per mole per kelvin is identical to 0.0831 liter bars per mole per kelvin, because one liter bar equals 100 joules. College Board prints the liter-bar version so that solute potential comes out in bars, which is the unit water potential questions are asked in.
Is a cram sheet the same as the AP Biology reference sheet?
No. A cram sheet is something you build yourself while revising, and you cannot take it into the exam. The reference sheet is the document College Board provides, and it is the only one on your desk on exam day. Anything you want on paper beyond it has to be in your head.