Arbitrary Meaning: What Arbitrary Means in Everyday Language, Law, Computing, and Maths

Short answer

• Arbitrary means based on personal choice, chance, or whim rather than on a rule, a reason, or a system that someone else could follow and check. If a choice is arbitrary, it could have gone a different way without breaking any rule, because no rule governed it in the first place. That one idea explains almost every use of the word, but the tone changes sharply with context. In everyday speech and in law, arbitrary is usually a criticism. It says a decision that affected people was made without a reason those people could examine. In math and computing, arbitrary is usually neutral. It simply means that any value or any member of a set will do, because the result does not depend on which one you pick. In linguistics, it means something more specific again: the link between a word and what it stands for is set by convention, not by nature. Three examples show the range. "The teacher set an arbitrary deadline of Tuesday" criticizes a date chosen with no reason why Tuesday was better than Wednesday. "Pick an arbitrary number between 1 and 100" is a neutral instruction, because any number in the range works. "Let x be an arbitrary real number" is a math instruction with a promise: the argument that follows must work for every real number, not just a convenient one.

Arbitrary in Everyday Language

In everyday speech, arbitrary most often describes a decision, a rule, a distinction, or a limit that feels random or unjustified. Oxford Advanced Learner’s Dictionary captures this core sense as an action, decision, or rule that does not seem to be based on a reason, system, or plan and sometimes seems unfair. Merriam-Webster gives the same idea in two parts: chosen seemingly at random or on a whim rather than in a reasoned way, and based on individual preference or convenience rather than on necessity or the value of the thing itself.

Four everyday uses come up again and again. An arbitrary rule exists because someone decided it, not because it follows from a principle anyone can see: a ban on hats in a hall might be a sensible safety rule, or arbitrary if no reason is given and no safety issue exists. An arbitrary distinction is a line drawn between two similar things without a clear basis, as when two nearly identical cases are treated differently with no relevant difference to explain the gap. An arbitrary limit is a number chosen for convenience rather than from evidence, such as a 500 word essay limit presented as if it came from the topic itself. Arbitrary power is power exercised without clear limits or accountability, as when a ruler can imprison people on a whim because no law constrains the choice. Merriam-Webster records this as a separate sense: power that is not restrained or limited.

The common thread is accountability. An arbitrary decision is hard to challenge on its own terms because there are no stated terms to challenge. You cannot argue that a different choice would have been more consistent with the rule, because there was no rule. That is why arbitrary is such a strong word in complaints about fairness. It says more than “I disagree with this decision.” It says “this decision was not made by a process I can understand or test.” Readers who enjoy pinning down words this way may also find our guide to 100 difficult words with meanings useful for building the same habit across a wider vocabulary.

Arbitrary versus random

Arbitrary and random are close, but they are not identical, and keeping them apart makes your own writing more precise. Random usually means governed by chance, as in a lottery draw or a shuffled deck. Arbitrary usually means governed by a person’s choice, where whim plays a part but a person still chose.

A lottery winner is chosen at random: no one decided who would win. A manager who promotes a friend over a better qualified colleague, for no stated reason connected to the job, has made an arbitrary choice: someone did decide, and that is the point of the criticism. In practice the words overlap, and Merriam-Webster lists random as part of the first sense. If precision matters, use random for chance and arbitrary for personal choice without a governing reason.

Arbitrary versus subjective

Subjective means based on personal feeling or opinion. Arbitrary can be subjective, but in its critical sense it is stronger. A subjective judgment can still be explained: “this painting is beautiful because of how it uses light” gives reasons another person can follow or dispute. Grading essays by the color of the cover is arbitrary, because the basis has no connection to the work being graded. Calling a judgment subjective says it came from a person. Calling it arbitrary says the person owed a relevant reason and did not provide one.

The Word Itself: Forms, Spelling, and Origin

Arbitrary is an adjective. It describes a noun: an arbitrary decision, an arbitrary rule, an arbitrary cutoff, an arbitrary value. Its related forms are worth separating, because two of them look similar and mean something quite different.

Arbitrarily is the adverb, meaning in an arbitrary way: “the cases were divided arbitrarily between the two teams” means no rule governed the division. Arbitrariness is the noun, meaning the quality of being arbitrary. Arbitrate, by contrast, is a verb with a different job: to settle a dispute as an arbitrator, a person chosen to hear both sides and decide. Arbitration is that process, used rather than a court. An arbitrator is supposed to decide by reasons and fairness, which makes good arbitration almost the opposite of an arbitrary decision, even though the words share a root.

That shared root is Latin arbiter, meaning a judge. Merriam-Webster traces arbitrary through Latin arbitrarius, relating to or depending on the discretion of an arbiter, and notes that the word first meant depending on individual discretion, in particular the kind of decision left to a judge rather than fixed by law. Over time the emphasis shifted from the wisdom of the judge to the unguided, personal side of a judgment made without a fixed rule. Oxford gives a similar origin.

The spelling also trips people up. The correct spelling is a-r-b-i-t-r-a-r-y. Common errors drop or swap letters in the middle, producing forms such as arbitary or arbitray. Breaking the word into arbit, as in arbitrate, plus rary helps. If you are building the wider skill of choosing precise wording, our explainer on another word for motivation shows how near synonyms differ in tone, and another word for accessible does the same for a word often used too loosely.

How to use arbitrary in a sentence

In a sentence, arbitrary normally sits directly before the noun it describes. You can also use the adverb form after a verb. These examples cover the main patterns, from everyday criticism to neutral technical use.

• “The cutoff score seemed arbitrary, because students just one point below it had done almost identical work.”
• “We picked an arbitrary meeting point, the fountain in the square, because any central place would do.”
• “The new dress code felt arbitrary to staff who had worked there for years without a complaint.”
• “She chose an arbitrary example to illustrate the point, because the principle mattered more than the example itself.”
• “The study used an arbitrary threshold for success, which the authors acknowledged as a limitation.”
• “Historians debate whether the period boundary is meaningful or arbitrary, since change rarely happens in a single year.”

Notice the defensive pattern in the last two examples. Saying a distinction is not arbitrary defends it: it claims the distinction follows from a reason or evidence, rather than from whim.

Arbitrary in Linguistics: Words and Meanings

Linguistics gives arbitrary a technical meaning that is related to the everyday sense but must not be confused with it. When linguists say language is arbitrary, they do not mean that speakers choose words at random each time they talk, and they do not mean that word meanings are unfair. They mean that the link between a word’s form and its meaning is unmotivated: there is no natural connection that forces that form to carry that meaning.

The classic statement comes from Ferdinand de Saussure in the Course in General Linguistics, first published in 1916 from his lecture notes. Saussure argued that a linguistic sign does not link a thing to a name. It links a concept, which he called the signified, to a sound image, which he called the signifier. His first principle was that the bond between signifier and signified is arbitrary. His proof was simple: the same concept is carried by different sound sequences in different languages, which shows that no one sequence is required by the concept itself.

Saussure added a clarification that prevents the most common misunderstanding. Arbitrary does not mean an individual speaker is free to change a sign at will. Once a pairing is established in a language community, speakers inherit it and use it consistently, and that consistency is what makes communication possible. The pairing is arbitrary in origin, but fixed by convention in use.

Saussure himself discussed two apparent exceptions. Onomatopoeia covers words that imitate a sound, such as glug or tick tock, and interjections cover expressions such as ouch. He treated both as limited and partly conventional rather than as refutations: imitative words differ across languages, change over time like other words, and make up only a small part of any vocabulary.

Keep this sense separate. In linguistics, arbitrary describes a relationship between form and meaning. In everyday criticism, it describes a decision without a reason. A language can be arbitrary in the linguistics sense and perfectly orderly in everyday use at the same time.

Arbitrary in Law

In law, arbitrary is a term of criticism with real consequences. A law, a decision, or an exercise of power is called arbitrary when it lacks a rational basis, when it treats similar cases differently without justification, or when it depends on the unchecked discretion of an official.

Merriam-Webster records a specifically legal sense: depending on individual discretion, as of a judge, and not fixed by law. The concern is not discretion itself, which judges, officials, and agencies must exercise every day. The concern is discretion without a reasoned, rule based basis that a court or reviewer can examine. Our explainer on the rule of law meaning covers the wider principle behind that concern: power exercised under law rather than by personal will.

Arbitrary and capricious in United States administrative law

The best known legal use is the phrase arbitrary and capricious. In United States federal administrative law, it is a standard courts use when they review decisions by government agencies. The Administrative Procedure Act, at 5 U.S.C. section 706(2)(A), directs a reviewing court to hold unlawful and set aside agency action found to be “arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law.”

Cornell Law Institute’s Legal Information Institute summarizes how that standard works in practice: for informal agency determinations, a court will typically leave the decision in place unless there is no reasonable basis for the finding. The court does not simply substitute its own preferred decision. It asks whether the agency gave a reasoned explanation connecting the facts it found to the choice it made. A decision can fail that test if it ignores important evidence, changes position without explaining why, or offers an explanation that runs against the record.

So when a lawyer calls an agency decision arbitrary and capricious, the claim is specific, not just that the decision seems unfair: the reasoning record lacks a rational, examinable basis. Legal explainers work best read this way, one phrase and one test at a time, in the same spirit as our guide to what pro bono means.

Arbitrary detention, discrimination, and power

Three other legal uses appear often in news and human rights reporting. Arbitrary detention means detention without a lawful basis, or without a fair process that lets the detained person challenge the reason. Arbitrary discrimination means treating people differently on grounds with no reasonable connection to the decision, such as favoring one applicant over another for no stated, relevant reason. Arbitrary power means power not limited by law, procedure, or accountability; constitutional systems are designed in part to prevent it, by requiring laws in advance, reasons for decisions, and a route of review.

In each case, arbitrary points to the same failure from a different angle: a missing reason, a missing rule, or a missing check. Legal meanings vary by jurisdiction, so check the law of the relevant place for any decision that affects you directly.

Arbitrary in Computing

In computing, arbitrary usually loses its negative tone and becomes a neutral technical term. It means any value, any choice, or any case that will do, because the system does not require a particular one. Context still matters, because one security use carries a warning rather than an invitation.

An arbitrary value is a value chosen for testing or illustration, where the exact value does not matter. “Enter an arbitrary value to test the form” means enter any suitable value; the test will work either way.

Arbitrary input is input a user can supply freely, without the system prescribing it in advance. That freedom is normal in forms, files, and data feeds, and systems are expected to handle it safely. The related security phrase arbitrary code execution is much more serious: it describes a flaw that lets an attacker run code of the attacker’s own choosing. Here arbitrary means not limited by the system, and that lack of limit is exactly the danger.

Arbitrary precision describes a number format that can hold as many digits as a calculation needs, rather than a fixed number set in advance. For very large numbers or very exact decimal results, that flexibility is a strength, not a flaw.

An arbitrary choice in an algorithm appears in instructions such as “pick an arbitrary element from the set.” That instruction carries a promise: the result does not depend on which element you pick first, so you do not need to search for a special one.

When a computing task says “choose arbitrarily,” it is normally telling you the outcome is safe under any allowed choice. That is almost the opposite of a legal decision about a person, where the outcome does depend on the choice and therefore needs a reason.

Arbitrary in Math

In math, arbitrary is also neutral, and it is more precise than in everyday speech. It is used to talk about a general member of a set, without specifying which one, so that an argument covers every member at once.

“Let x be an arbitrary real number” means x can be any real number, and the argument that follows must work for every real number, not just for a convenient example such as 2 or 10. Choosing an arbitrary member and reasoning only from properties every member shares is how a proof earns its generality. “For arbitrary n” works the same way: for any whole number n you choose, within the stated conditions, the statement holds, and no special property of a particular n is being used.

Two related phrases use the adverb form. Arbitrarily large means larger than any bound you care to set: no matter how large a target you name, the quantity can exceed it. Arbitrarily small means smaller than any positive amount you name, yet still positive. That second idea sits at the center of limits, where careful claims about closeness never claim that a positive quantity has reached zero.

A short comparison helps keep the math and everyday senses from blurring:

The table shows why context matters. Asking what arbitrary means with no sentence attached has no single complete answer. Asking what it means in “an arbitrary cutoff” or “let k be arbitrary” does.

Arbitrary in Work and Everyday Decisions

At work, arbitrary usually returns to its critical sense. A price, a fee, a target, or a deadline is called arbitrary when it is set without a clear basis in cost, workload, demand, or evidence.

An arbitrary price is set by habit or by copying a competitor, rather than by working from cost and value. An arbitrary target is chosen as a round number rather than from an analysis of capacity and demand. Convenience alone does not make a target wrong. It becomes a problem when it is presented as if it were derived from the work itself, and the people asked to meet it cannot see how it was reached.

An arbitrary deadline is a date chosen because it sounds tidy rather than because the work needs that date. Such deadlines are common and not always harmful, since a team sometimes needs a line in the calendar simply to coordinate. They become harmful when missing the tidy date is treated as a failure of the work, rather than as information that the original guess was wrong. An arbitrary workplace rule is one staff cannot connect to a purpose, such as a ban on a harmless practice offered with no explanation. People can accept a rule they disagree with more easily than a rule they cannot understand.

The practical lesson cuts both ways. If a decision affects other people, give a reason, even a brief one: a reason turns an arbitrary choice into a reasoned choice that can be discussed or improved. If you are on the receiving end, asking “what was this based on” is a fair question, and the answer, or its absence, tells you which kind of decision you face. Readers working through texting shorthand face the same task in miniature, and our explainer on HMU meaning in text shows how much work a few surrounding words can do.

When Arbitrary Is Fair Criticism and When It Is Not

Arbitrary is a strong word, so it helps to know when the charge fits and when it does not. The test is not whether a choice had a deep reason. Many good choices have shallow, practical reasons. The test is whether a reason was owed.

Arbitrary is fair criticism when a decision affects people and no reason or consistent criteria are given, when similar cases are treated differently without a relevant difference, when a cutoff is presented as if it followed from evidence when it was chosen for convenience, or when power is exercised with no process for challenging it.

Arbitrary is not fair criticism when a choice genuinely does not affect the outcome, as with an arbitrary example in math or a test value in computing, when a convention is arbitrary by nature and understood as one, as with a meeting point or the words of a language themselves, when a round number is used openly for convenience, or where personal taste is at stake and no rule is expected, as with a favorite color.

Used carefully, the word separates choices that merely lack a reason you like from choices that lack a reason anyone was given. That separation makes criticism sharper and your own decisions easier to defend.

Frequently Asked Questions

What does arbitrary mean in simple terms?

Arbitrary means based on personal choice or chance rather than on a rule or a clear reason. An arbitrary decision could easily have gone another way, because no rule or stated reason forced the choice that was made.

Is arbitrary a negative word?

Often, yes, in everyday and legal use, where it suggests unfairness or a lack of justification. In math, computing, and linguistics, it is usually neutral. Tone comes from context, not from the word alone.

What is an example of an arbitrary decision?

An arbitrary deadline is a date chosen with no reason why that date is better than another, then treated as if it were fixed by the work itself. An arbitrary cutoff works the same way: similar cases fall on either side of a line, and no relevant difference explains why the line sits where it does.

What does arbitrarily mean?

Arbitrarily is the adverb form of arbitrary. It means in an arbitrary way, as in “the groups were divided arbitrarily,” meaning no rule governed the division. Its noun form is arbitrariness, meaning the quality of being arbitrary.

What is the difference between arbitrary and random?

Random usually means governed by chance, as in a lottery draw. Arbitrary usually means governed by personal choice without a governing reason, as in a manager deciding on a whim. Random stresses chance; arbitrary stresses unguided choice.

What does arbitrary mean in law?

In law, arbitrary describes action that lacks a rational basis, treats similar cases differently without justification, or depends on unchecked discretion. In United States administrative law, arbitrary and capricious is the standard courts use to set aside agency action that lacks a reasoned explanation, under the Administrative Procedure Act.

What does arbitrary mean in computing?

In computing, arbitrary usually means any value or choice that will do, because the system does not require a particular one. It also appears in security language, where arbitrary code means code of an attacker’s choosing. That second use is dangerous precisely because the code is not limited by the system.

What does arbitrary mean in math?

In math, arbitrary means any member of a set, taken without specifying which one, so an argument applies generally. “Let x be an arbitrary real number” means the reasoning must work for every real number. Arbitrarily large and arbitrarily small describe quantities that can pass any bound you name.

What does arbitrary mean in language and linguistics?

In linguistics, arbitrary means the link between a word’s form and its meaning is set by convention rather than by nature, which is why different languages use different words for the same concept. Once a community settles on a word, speakers still use it consistently.

How do you use arbitrary in a sentence?

Place it before a noun naming a decision, rule, choice, or limit: “The cutoff seemed arbitrary.” Or use the adverb form: “The cases were split arbitrarily.” When you criticize a choice as arbitrary, name the missing rule or reason, so the reader can judge the charge.

Sources & references

• Merriam-Webster, "arbitrary." Senses covering choice at random or on a whim, choice based on preference or convenience, unrestrained power, and the legal sense of depending on individual discretion and not fixed by law; also the word history from Latin arbiter and arbitrarius. https://www.merriam-webster.com/dictionary/arbitrary
• Oxford Advanced Learner's Dictionary, "arbitrary adjective." Sense 1: an action, decision, or rule not seeming to be based on a reason, system, or plan and sometimes seeming unfair; sense 2: using power without limits; word origin from Latin arbitrarius, from arbiter. https://www.oxfordlearnersdictionaries.com/us/definition/english/arbitrary
• Cambridge English Dictionary, "arbitrary." English entry consulted alongside the Oxford and Merriam-Webster entries for the core everyday sense and the adverb and noun forms. http://dictionary.cambridge.org/us/dictionary/english/arbitrary?a=british
• Ferdinand de Saussure, Course in General Linguistics, excerpt on the nature of the linguistic sign, hosted by the University of Missouri-St. Louis. Principle I: the bond between the signifier and the signified is arbitrary and unmotivated, proved by differences across languages, with onomatopoeia and interjections treated as limited exceptions. https://www.umsl.edu/~gradyf/theory/CourseinGeneralLinguistics.htm
• Cornell Law Institute, Legal Information Institute, "standard of review." Arbitrary and capricious is typically used for informal agency determinations, which courts typically leave in place unless there is no reasonable basis for the finding. https://www.law.cornell.edu/wex/standard_of_review
• 5 U.S. Code section 706, Scope of review, via Cornell Law Institute. Subsection (2)(A) directs courts to hold unlawful and set aside agency action found to be arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law. https://www.law.cornell.edu/uscode/text/5/706