Measurement uncertainty and percentage uncertainty

Uncertainty of a reading

The uncertainty is the range either side of a reading within which the true value probably lies.

• Burette: ±0.05 cm³ per reading. A titre uses two readings, so its uncertainty is ±0.10 cm³.
• Balance (2 d.p.): ±0.005 g per weighing. Weighing by difference uses two weighings: ±0.01 g.
• Thermometer: a temperature change uses two readings, so double the uncertainty of one reading.
• Pipette, volumetric flask, measuring cylinder: one value, usually given in the question (for example a 25.0 cm³ pipette ±0.06 cm³).

When a quantity is a difference of two readings, add the two uncertainties.

Percentage uncertainty

Percentage uncertainty = (uncertainty / measured value) x 100

Example from Pearson's guide: a titre of 24.50 cm³ has uncertainty 2 x 0.05 = 0.10 cm³, so 0.10 / 24.50 x 100 = 0.41%.

The smaller the measured value, the larger the percentage uncertainty.

Combining and reducing

• When results are multiplied or divided (as in almost every chemistry calculation), add the percentage uncertainties of the measurements to get the total.
• Absolute uncertainty in the result = total % / 100 x result.
• To reduce the percentage uncertainty: measure a larger quantity (larger mass, larger titre by using a more dilute solution in the burette, larger temperature change) or use higher-resolution apparatus (a 3 d.p. balance cuts a 0.05 g mass's uncertainty from 20% to 2%).
• Repeating does not change the uncertainty of each reading, but it reduces the effect of random errors.

Worked example

A titre is 24.50 cm³. Calculate its percentage uncertainty.

1. Two burette readings, each ±0.05 cm³: total ±0.10 cm³.
2. % uncertainty = 0.10 / 24.50 x 100 = 0.41%

Answer: 0.41%

Check yourself

1. A titre is 22.40 cm³. Each burette reading has an uncertainty of ±0.05 cm³. Calculate the percentage uncertainty in the titre.
   Show answer

   0.45 %. Uncertainty = 2 x 0.05 = 0.10 cm³; 0.10 / 22.40 x 100 = 0.45%.

2. 0.50 g of solid is weighed by difference on a balance with an uncertainty of ±0.005 g per weighing. Calculate the percentage uncertainty in the mass.
   Show answer

   2.0 %. Two weighings: ±0.01 g. 0.01 / 0.50 x 100 = 2.0%.

3. The same 0.50 g is weighed by difference on a balance with an uncertainty of ±0.0005 g per weighing. Calculate the new percentage uncertainty.
   Show answer

   0.2 %. Two weighings: ±0.001 g. 0.001 / 0.500 x 100 = 0.2%.

4. A temperature rises by 5.6 °C. Each thermometer reading has an uncertainty of ±0.05 °C. Calculate the percentage uncertainty in the temperature rise.
   Show answer

   1.79 %. Two readings: ±0.10 °C. 0.10 / 5.6 x 100 = 1.79%.

5. In an experiment the percentage uncertainties are: pipette 0.24%, burette 0.41% and balance 1.0%. What is the total percentage uncertainty in the result?
   Show answer

   1.65 %. Add them: 0.24 + 0.41 + 1.0 = 1.65%.

6. A molar mass is calculated as 126.0 g mol^-1 with a total percentage uncertainty of 0.91%. Calculate the absolute uncertainty in g mol^-1.
   Show answer

   1.15 g mol^-1. 0.91 / 100 x 126.0 = 1.15 g mol^-1, so 126.0 ± 1.1 g mol^-1.

7. Which change reduces the percentage uncertainty in a titre?
   • Using a larger conical flask
   • Using a more dilute solution in the burette so that the titre is larger
   • Reading the meniscus from a higher eye position
   • Adding more indicator
   Show answer

   Using a more dilute solution in the burette so that the titre is larger. The ±0.10 cm³ is the same, but it is a smaller fraction of a larger titre.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson IAL Chemistry teacher practical guide

Last updated 8 November 2026. Spotted a mistake? Tell us.