How to Memorize Formulas (and When You Shouldn't)

Every math and science course comes with a list of formulas, and sooner or later you have to decide what to do with it. Memorize all of them? Rely on the formula sheet? Derive everything on the spot?

The honest answer is a mix. Some formulas are worth knowing cold, some are better derived, and some can stay on the sheet. This guide covers how to tell them apart, and how to make the ones you choose actually stick.

Should You Memorize Formulas at All?

"Understand it, don't memorize it" is good advice, but it sets up a false choice. Knowing a formula by heart doesn't stop you from understanding it, and it has real benefits:

Speed. On a timed exam, looking up or deriving a formula you use constantly costs minutes you don't have.

Choosing the right tool. You can only recognize that a problem needs a particular formula if that formula is already in your head.

Catching mistakes. If you know KE = ½mv², you'll notice when an answer comes out in the wrong units or doubles when it should quadruple.

There are also formulas you shouldn't spend effort on. A good rule of thumb: memorize the formulas you use every week, the ones other formulas are built from, and anything your exam won't give you. Skip the ones you can derive in a line from something you already know, and rarely used ones that will be on the formula sheet. For example, if you know sin²θ + cos²θ = 1 and cos 2θ = cos²θ − sin²θ, the other two forms of cos 2θ follow in one step.

Understand It Before You Memorize It

A formula you don't understand is just a string of symbols, and strings of symbols are hard to remember. Before you make a card, make sure you can answer three questions: what does each symbol stand for, what units does it have, and when does the formula apply?

Derek Sivers, writing about memorizing a programming language with spaced repetition, put it simply: "Create the flash card after you've really understood." The same holds for formulas. Understanding first makes the memorizing faster, and it means the formula comes back with its meaning attached.

Split Each Formula Into Small Cards

One formula often hides several things worth knowing. Instead of one card that asks for everything, write a few small ones. Physicist and writer Michael Nielsen, in his essay Augmenting Long-term Memory, recommends making questions and answers "as atomic as possible": small cards are easier to answer, easier to rate honestly, and easier for a spaced repetition schedule to handle.

For the quadratic formula, that might look like this:

Test Yourself Instead of Copying It Out

Writing a formula out ten times feels like work, but most of it is copying: the formula is in front of you, so your memory never has to produce it. Trying to recall it from a prompt is what builds the memory. In a large review of study techniques, Dunlosky and colleagues (2013) rated practice testing as one of only two techniques with high utility.

So look at the prompt, write the formula from memory on paper (or type it: in Space Repeat the W key opens a box to write your answer before you flip the card), then check. If you got it wrong, that's useful: the card will come back sooner.

Space Out the Reviews

Distributed practice, spreading reviews over days and weeks, was the other technique Dunlosky's team rated high utility. Cramming a formula list the night before can get you through the next morning, but most of it is gone a week later, just when the next unit needs it.

A spaced repetition app handles the timing for you. You see a new formula again after about a day, then after a few days, then after weeks, and each successful review pushes the next one further out. Ten minutes a day keeps a whole course's formulas fresh. How Spaced Repetition Algorithms Work explains the scheduling.

Use Them in Problems

Cards make formulas easy to recall. Problems make them easy to use. Do both: review your cards, then pick problems that need those formulas. Each time you apply a formula in context, you strengthen the link between the formula and the kind of situation that calls for it, which is the part a card on its own can't teach.

A Few Formulas Worth Knowing by Heart

Every course has its own list, but these come up again and again across math and science:

Other common ones: the Pythagorean theorem, the area and circumference of a circle, Newton's second law, Ohm's law, and the formulas for mean and standard deviation.

Writing Formulas on Cards

Formulas are easier to remember when you see them the way they're written in your textbook. In Space Repeat you put math between dollar signs, like $\frac{a}{b}$ or $x^2$, and it's rendered properly; chemistry goes inside \ce{}, like $\ce{H2SO4}$. The Math & code toolbar under each card field inserts the common pieces and shows a preview, so you don't need to know LaTeX to start. New accounts can also add ready-made decks for math, physics and chemistry. For more on studying math this way, see How to Study Math with Flashcards.

The Bottom Line

Memorize the formulas you use often, the ones other formulas are built from, and the ones you won't be given. Understand each one first, split it into small cards, test yourself instead of copying, space the reviews out, and use the formulas in real problems. That's far less work than cramming the whole list before every exam, and it lasts.