How to Memorize Formulas (Math, Physics, Chemistry)

To memorize formulas, shrink the list before you drill it: derive the ones that come from something simpler, learn what every symbol stands for so you can rebuild the arrangement, and check the units to catch a wrong version. Then drill the small remainder with blank-page recall, spaced over days.

That order matters, because most of a formula sheet is not arbitrary and does not need raw memorization. What follows is seven techniques that work across math, physics, and chemistry, each with a worked example, plus the one self-check that formulas have and vocabulary lists do not.

Why do formulas fall out of your head?

A formula memorized as a bare string of symbols has nothing holding it in place. There is no meaning to reconstruct it from, no internal logic that flags a letter drifting to the wrong side of the fraction bar, and no way to tell a correct memory from a confident wrong one. That is why the classic exam failure is not a blank page. It is writing F = m/a instead of F = ma and never noticing.

Rereading a formula sheet makes this worse, because it builds recognition rather than recall. Every formula looks right while it is sitting in front of you. The exam asks you to produce it from nothing, which is a completely different task. The techniques below attack both problems at once: they give each formula something meaningful to hang on, and they replace rereading with retrieval you can check.

Derive what you can, then hand the rest to memory

Some formulas are not separate facts at all, they are consequences of something simpler you already know. The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), is what falls out of completing the square on ax² + bx + c = 0. The kinematics equations for constant acceleration fall out of the definitions of velocity and acceleration as rates of change. Work through a derivation once, on paper, and the formula stops being a line to store and becomes a line you can regenerate.

Do not stretch this further than it goes. Plenty of formulas have no derivation available at your level, and pretending otherwise is how students end up staring at a blank page. Derive what genuinely derives, then be honest about the remainder and give it to the six techniques below. For where derivation fits inside a whole revision plan, the fuller subject guides go deeper than this post does: see the full guide to studying for a math test and the full physics study guide. This post stays on the formulas themselves.

Learn what every symbol means before the arrangement

A formula is an arrangement of quantities, and arrangements are easy to scramble. Meanings are not. If you know that the m in F = ma is inertia, the property that makes a heavy object hard to get moving, then F = m/a is not merely wrong, it is absurd: it would claim a heavier object accelerates more easily under the same push. The meaning polices the arrangement, which is why this technique is worth more than any number of extra repetitions.

Do it deliberately. Write each symbol down the left of a page and its physical or mathematical meaning on the right, in your own words, before you attempt to memorize the line. The same move works in every subject:

• Math. In the quadratic formula, -b / (2a) is the axis of symmetry of the parabola, and the √(b² - 4ac) / (2a) term is how far each root sits from that axis. The discriminant, b² - 4ac, decides how many real roots exist. Read the formula as centre, plus or minus a spread, and the order of the pieces stops being arbitrary.
• Physics. In T = 2π√(L/g), the period of a simple pendulum at small swings, L is the length and g is gravitational acceleration. A longer pendulum swings more slowly, so L belongs on top. Stronger gravity yanks it back faster, so g belongs underneath. The physical story fixes the fraction for you.
• Chemistry. The dilution formula M1V1 = M2V2 says nothing more than that adding solvent does not change the number of moles of solute, because moles equal concentration times volume. Once you read it as a conservation statement, there is almost nothing left to memorize.

Unit-check every formula you are unsure of

Here is the technique that formula memorization has and vocabulary memorization does not: a formula carries its own error check. Both sides of a correct equation must carry the same units, so a scrambled arrangement usually breaks the units in an obvious way, and you can catch it in seconds without opening anything. Dimensional analysis is normally taught as a problem-solving habit, but it is just as useful as a memory aid, because it lets you verify a recalled formula instead of trusting it.

Physics, a missing exponent. Suppose you half-remember kinetic energy as KE = ½mv rather than KE = ½mv². Energy is measured in joules, and a joule is kg·m²/s². Mass times velocity gives kg·m/s, which is momentum, not energy. Mass times velocity squared gives kg·m²/s², which matches. The version with the square is right, and you have proved it rather than guessed it.

Physics, an inverted fraction. If you cannot recall whether the pendulum period is T = 2π√(L/g) or T = 2π√(g/L), put the units in. L is in metres and g is in m/s², so L/g has units of s² and its square root is seconds, which is a time. The flipped version gives 1/s, which is a frequency, not a period. The correct form is the one that produces seconds.

Chemistry, a bad rearrangement. Rearranging PV = nRT to find the amount of gas gives n = PV / (RT). With R expressed in L·atm/(mol·K), the numerator carries L·atm and the denominator carries L·atm/mol, so the whole expression comes out in moles, which is exactly what n means. If your rearrangement produces anything other than moles, you rearranged it wrong.

Two habits make this pay. First, memorize the unit of the quantity on the left of each formula, not just the symbols on the right, because that is the target your check aims at. Second, run the check on your own recall during practice, not only when an answer looks strange under exam pressure. A formula you have unit-checked yourself is one you will trust at minute 40 of a test.

Use mnemonics only for the formulas that refuse to stick

After deriving, decoding, and unit-checking, you will be left with a short list of genuinely arbitrary formulas. That is what mnemonics are for, and the reason to keep the list short is that a mnemonic buys retrieval without buying understanding.

The well-known formula mnemonics earn their place. SOHCAHTOA packs the three trig ratios into one word: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent. PEMDAS, remembered as Please Excuse My Dear Aunt Sally, encodes the order of operations: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction. That second one is a procedure rather than a formula, but it shows the pattern clearly, which is that a fixed order becomes a phrase.

For everything else, build your own instead of hunting for a famous one. A cue you invented beats a cue you were handed, because building it forces you to look hard at the material and because the image already means something to you. Take the first letters of the symbols in the order they appear, make a sentence you would struggle to forget, then test it once against the real formula so you are not drilling a broken cue. The wider toolkit, including where mnemonics stop helping, is in the guide to mnemonic devices for studying. For a worked example of a formula-heavy set where structure plus a single mnemonic replaces sixteen memorized lines, see how to memorize the unit circle.

One caution worth taking seriously. In the large 2013 review of study techniques by Dunlosky and colleagues, the keyword mnemonic, the technique in that review closest to this kind of memory cue, was rated low utility for durable learning, while practice testing and distributed practice were rated the most useful of the ten reviewed. Mnemonics hand you the label, not the understanding. Use them as the last resort for the stubborn few, never as the plan.

How do you drill formulas so they actually stick?

With a blank page, not a formula sheet. Blank-page reconstruction is the highest-value drill for formulas because it matches what the exam demands: produce the line from nothing, correctly, under time. Rereading the sheet rehearses the wrong skill.

The routine is short. Close every book. On a blank sheet, write out every formula for the topic you can recall, with the meaning of each symbol beside it. Then open your real sheet and mark yourself: correct, wrong, or missing. Do not simply reread the ones you got wrong. Cover them again and rewrite them until they come out right from memory, then return to those specific formulas the next day rather than restarting the whole list.

Two details do a lot of work. Group the formulas by topic as you write, so you also rehearse which formulas belong together, and write the units alongside each one, so the unit check above becomes part of the drill instead of a separate habit. Ten minutes of this is worth an hour of staring at the sheet.

Practice applying the formula, not just writing it

Recalling a formula and knowing when to reach for it are two separate skills, and exams test the second one far more than the first. A student who can write out every kinematics equation for constant acceleration but cannot tell which one to use when a problem gives a distance and asks for a time has memorized the wrong half of the job.

So pair every recall drill with application. After you reconstruct a formula, work one problem that uses it and one that looks similar but needs a different formula, so you rehearse the choice and not only the recall. Then write the trigger next to the formula on your sheet: the condition or the given quantities that mark it as the right tool. For PV = nRT, the trigger is a gas problem where pressure, volume, temperature, or amount is changing. For an energy method in mechanics, the trigger is a problem that hands you positions and speeds but never mentions time. Those triggers are what turn a memorized list into a toolkit you can actually use.

Space the reviews for the pile that is pure memorization

Whatever survives derivation, decoding, and unit checking still has to be maintained, and maintenance means spacing. Revisit the memorized pile after a day, then after a few days, then after a week, so each review lands just as the formula starts to slip. Spacing is what moves a formula from something you knew last Tuesday to something you still have on exam day.

Make every one of those reviews a retrieval rather than a reread, because the pairing is where the gain is: practice testing and distributed practice were the two highest-rated techniques in the same 2013 review cited above, so a spaced schedule of blank-page reconstruction is not guesswork. For how the two halves fit into one schedule, see how active recall and spaced repetition work together.

How GeniusPal helps

The method above has one expensive step: turning a formula sheet into something you can actually be tested on. Writing a prompt for every formula, with the symbol meanings and the units on the back, is exactly the chore students skip right before they go back to rereading the sheet. That is the gap GeniusPal closes. Upload your formula sheet, a problem set, or your class notes, and it turns the content into flashcards, a quiz, or a recall set, so drilling formulas becomes retrieval practice instead of staring at a page. The free plan includes two study-set generations for the lifetime of the account, which is enough to build a set for one unit and see whether the routine suits you.

Be clear about the limits. GeniusPal will not derive a formula for you, invent your mnemonics, or decide which formulas your exam will supply on the day. Those judgments are yours, and they are the part that makes the method work. What it removes is the transcription work sitting between having a formula sheet and having the reps.