Library / Foundations: Chemistry / FCH-20
Foundations: Chemistry
Percentage uncertainty
Size of a measurement’s uncertainty compared with the measurement itself.
- Ref
- FCH-20
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- %u [%]
U is the absolute uncertainty and x the measured value. Absolute uncertainty is the ± value of the instrument (for example ±0.05 cm³ per burette reading). For a difference of two readings, add the absolute uncertainties.
It shows how big the possible error is compared with what you measured. A small uncertainty on a large measurement is better.
Calculator
- Lower limit19.95 cm³
- Upper limit20.05 cm³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Using larger quantities reduces the percentage uncertainty from the same instrument.
- For a titre from two burette readings the absolute uncertainty is ±0.10 cm³, not ±0.05.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| x Measured value | 0.1 to 1,000 cm³ | 0.005 | 50 | 49.99 | +10% | −9.09 % |
| U Absolute uncertainty | 1e-6 to 5 cm³ | 5e-6 | 25 | 25 | +10% | +10 % |
Sweep of Measured value
| Measured value (cm³) | Percentage uncertainty (%) |
|---|---|
| 0.1 | 50 |
| 0.3162 | 15.81 |
| 1 | 5 |
| 3.162 | 1.581 |
| 10 | 0.5 |
| 31.62 | 0.1581 |
| 100 | 0.05 |
| 316.2 | 0.01581 |
| 1,000 | 0.005 |
Sweep one variable
Variables and how each one contributes
Percentage uncertainty
What the equation gives you. Everything else feeds it.
Absolute uncertainty
The ± uncertainty of the measurement. Directly proportional.
Measured value
The measured quantity. Inversely proportional.
Worked example with the values above
- Ratio: 0.05 / 20 = 0.0025.
- Multiply by 100.
- Percentage uncertainty = 0.25 %.
Assumptions and limits
- Uncertainty is from the instrument only.
- Random error treated as symmetrical.
Common mistakes
- Forgetting that a difference of two readings doubles the uncertainty.
- Using the instrument range instead of its uncertainty.
Statistics and uncertainty
Percentage uncertainties from separate measurements are added when quantities are multiplied or divided.
Where it is used
- Practical write-ups and error analysis.
- Choosing instruments for a required precision.
Maths you need
- Percentages: part over whole
- Measurement: instrument precision