Uncertainty & Measurement
Virtual ruler with limited precision. Builds on Powers of Ten & Units.
A dart thrower throws 10 darts at a dartboard. All 10 land in a tight cluster — but the cluster is in the bottom-left corner, far from the bullseye.
How would you describe this performance?
Precision means how tightly clustered your results are (low spread). Accuracy means how close to the true value. A tight cluster far from the bullseye is PRECISE but NOT ACCURATE.
Loading simulation…
Try all four combinations: high/low accuracy × high/low precision. See the patterns.
x = x̄ ± δx
The ± tells you the PRECISION. Whether x̄ is close to the true value tells you the ACCURACY. You need both numbers to evaluate a measurement.
If your scale always reads 2 kg too high, it's precise (consistent) but inaccurate. You can fix accuracy by calibrating — but you can't fix precision without a better scale.
A player who always hits the left rim is precise but inaccurate. Adjusting their aim fixes accuracy. A player who hits randomly is neither.
The Higgs boson mass was measured as 125.35 ± 0.15 GeV. The ±0.15 is the precision — it took thousands of scientists and billions of dollars to get that small.
“Every number in science has an uncertainty. If you see a measurement without ±, it's incomplete — like a sentence without a period.”
Measurement Lab
Measure objects with different instruments and see how uncertainty propagates through calculations.
Loading simulation…
Measure the same object with the ruler vs the caliper. Then calculate area — watch how uncertainties multiply!
When you multiply measurements, their RELATIVE uncertainties add. A 1% error in length becomes 2% error in area and 3% in volume.