Precision, Accuracy and Resolution

Three words get thrown around as if they mean the same thing — accurate, precise, high-resolution — and in everyday chat they roughly do. In science they mean three completely different things, and muddling them is one of the classic ways to fool yourself in the lab.

Picture throwing darts at a board. Some throws land close to the bullseye (the answer you were aiming for). Some land in a tight little cluster (all near each other). And the board itself is marked with rings so fine — or so coarse — that they set how precisely you can even describe where a dart landed. Those are exactly the three ideas:

Accuracy — how close a measurement is to the true value.
Precision — how close repeated measurements are to each other.
Resolution — the smallest change an instrument can actually show.

A great measurement is all three. But you can have any one without the others — and the whole point of this page is to feel, in your bones, why they come apart.

Accuracy: hitting the true value

A measurement is accurate when it lands close to the true value — the real answer nature is holding behind its back. Weigh a mass that is genuinely 50.0 g and read "50.1 g": accurate. Read "47.3 g": not accurate — something has pushed your reading away from the truth.

What pushes it away? Usually a systematic error — a fault that tugs every reading the same way. The classic culprit is a zero error: a balance that already shows "2 g" with nothing on the pan, or a ruler read from the 1 cm end instead of 0. Every single reading then comes out 2 g too big, or 1 cm too long. You could be extremely careful and still be wrong, because the tool itself is lying by the same amount every time.

The tell-tale sign is that accuracy is about the truth — so you can only judge it if you know (or can look up) what the right answer should be. That's why we calibrate instruments against a known standard: to check they are telling the truth before we trust them.

Precision: agreeing with yourself

A measurement is precise when you can repeat it and the readings come out close to each other — a tight cluster, a small spread. Notice what's missing from that sentence: any mention of the true value. Precision is only about consistency, not correctness. You can be beautifully, reliably, repeatably wrong.

Because precision is about spread, the only way to see it is to repeat the measurement. A single reading tells you nothing about precision. Take a few and look at how far apart they are:

Student A times a swinging pendulum five times: 2.11 s, 2.10 s, 2.12 s, 2.11 s, 2.10 s — a spread of just 0.02 s. Very precise.
Student B times it: 2.4 s, 1.9 s, 2.2 s, 2.6 s, 1.8 s — a spread of 0.8 s. Not precise, even though the readings scatter around the right value.

Curiously, Student B's average might land closer to the truth than Student A's — scattered readings can average out to something accurate. So a scatter-gun can be accurate-on-average yet imprecise, and a tight cluster can be precise yet miss the target completely. They really are independent.

Accuracy, precision and resolution

Accuracy — closeness of a measurement to the true value. Spoiled by systematic errors (e.g. a zero error). Judged against a known standard.
Precision — closeness of repeated measurements to one another (their spread), regardless of whether they are right. Revealed only by repeating.
Resolution — the smallest change in the quantity that the instrument can display. A property of the tool, not of any one reading.

The dartboard: four ways to throw

This is the picture that makes it click. The bullseye at the centre is the true value. Each dart is one measurement. Two knobs control the throws:

Spread sets precision — small spread means the darts land in a tight cluster (precise); large spread scatters them (imprecise).
Cluster off the bullseye sets accuracy — how far the whole cluster's centre sits from the bullseye. On the bullseye is accurate; off to one side is inaccurate (a systematic error nudging every dart the same way).

Dial in each of the four famous combinations and watch the readout: precise and accurate (small spread, on centre — the goal), precise but not accurate (small spread, off to one side — a tight cluster in the wrong place), accurate-ish but not precise (big spread, centred — scattered but balanced around the truth), and neither (big spread, off-centre).

Resolution: the smallest change you can see

The third idea belongs to the instrument, not to any single throw. Resolution is the smallest change in a quantity that the tool can actually display — the size of its finest step.

A ruler marked only in centimetres can tell 7 cm from 8 cm, but not 7.4 from 7.5. A ruler marked in millimetres has ten times finer resolution — it reads to the nearest mm.
A kitchen scale reading to the nearest 1 g has coarser resolution than a lab balance reading 0.01 g. The lab balance can notice a change a hundred times smaller.
A stopclock ticking whole seconds has coarser resolution than a stopwatch showing 0.01 s.

Choosing an instrument is largely about matching its resolution (and its range) to the job. To measure the thickness of a coin you want a tool whose steps are much smaller than the coin — centimetre marks are useless; you reach for something reading tenths of a millimetre. But here comes the trap that catches everyone…

The three ideas hide three of the most common mistakes in all of science:

Precise does not mean accurate. A tight cluster of readings that all agree can still be dead wrong — think of a balance with a zero error, giving "52.3, 52.3, 52.4 g" for a true 50 g. Consistent, but consistently wrong.
More decimal places is not more accurate. Resolution is not accuracy. A cheap scale can display "49.7382 g" and be nowhere near the truth — those extra digits are precision of display, not correctness. Fine resolution just lets a wrong answer be wrong in more detail.
A systematic (zero) error hurts accuracy, not precision. A tool that reads 2 g high every time shifts every reading the same way — the cluster stays just as tight (still precise) but the whole cluster slides off the bullseye (now inaccurate). Repeating the measurement will never reveal it, because it hides in every repeat equally. Only calibration catches it.

An atomic clock is a wonder of precision: the best ones would drift by less than a second over the whole age of the universe. Their ticks are almost unimaginably consistent — that is why they define the second and keep GPS working.

But suppose someone set that magnificent clock one hour fast. Now it is still fantastically precise — every tick still spaced with atomic perfection — yet every time you read it, it is wrong by an hour. Precise, but not accurate. A cheap wristwatch set correctly would tell you the right time better. Precision buys you consistency; only getting the starting point right (calibration) buys you accuracy. The two really are separate powers.