All subjects · Chemistry · WCH13 Practical Skills in Chemistry I

Accuracy, precision, errors and percentage error

Edexcel IAL Chemistry · WCH13 Practical Skills in Chemistry I

Uncertainty belongs to the apparatus; error is how far your answer is from the accepted value. Comparing the two tells you whether your method, not just your measuring, is at fault.

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Key words

Accurate: close to the true (accepted) value.
Precise: repeated results are close to each other.
Repeatable: the same person with the same method gets similar results; reproducible: other people or methods get similar results.
Valid: the method measures what it claims to, with other variables controlled.

Results can be precise but not accurate, if every reading is off in the same direction.

Random and systematic errors

Random errors scatter results either side of the true value (judging an end point, timing by hand, reading a scale). Reduce their effect by repeating and taking a mean.
Systematic errors shift every result the same way (heat loss to the surroundings, gas escaping, a balance not zeroed, reading the top of a meniscus). Repeating does not help; you must improve the method or apparatus.

Percentage error and what it shows

Percentage error = (accepted value - experimental value) / accepted value x 100 (ignore the sign).

Then compare it with the total percentage uncertainty from the apparatus:

% error within the % uncertainty: the difference can be explained by the measuring equipment.
% error much bigger than the % uncertainty: there are systematic errors in the method (such as heat loss), so improving the apparatus alone will not fix it.

Worked example

An enthalpy change is measured as -200 kJ mol^-1. The data-book value is -220 kJ mol^-1, and the total apparatus uncertainty is 3.03%. Comment.

% error = (220 - 200) / 220 x 100 = 9.1%
This is much larger than 3.03%.
So the main problem is a systematic error in the method, most likely heat loss to the surroundings.

Answer: 9.1% error; mostly systematic (heat loss)

Key idea: Accurate = close to the true value; precise = close together. Repeats reduce random error but not systematic error. If % error is far bigger than % uncertainty, the method has a systematic error.

Check yourself

An enthalpy of neutralisation is measured as -51.2 kJ mol^-1. The data-book value is -57.1 kJ mol^-1. Calculate the percentage error.
Show answer
10.3 %. (57.1 - 51.2) / 57.1 x 100 = 10.3%.
A student measures the molar volume of a gas as 22.8 dm³ mol^-1. The accepted value at the conditions used is 24.0 dm³ mol^-1. Calculate the percentage error.
Show answer
5.0 %. (24.0 - 22.8) / 24.0 x 100 = 5.0%.
Three titres are 24.30, 24.35 and 24.30 cm³, but the true titre is 25.00 cm³. How are the results best described?
- Accurate but not precise
- Precise but not accurate
- Accurate and precise
- Neither accurate nor precise
Show answer
Precise but not accurate. They agree closely with each other, but all are well below the true value.
Which is a systematic error?
- Misjudging one end point slightly
- Starting a stopwatch a little late on one run
- Heat lost to the surroundings in a calorimetry experiment
- A single misread thermometer
Show answer
Heat lost to the surroundings in a calorimetry experiment. Heat loss always makes the temperature rise too small.
How is the effect of random errors reduced?
- Repeating the measurement and calculating a mean
- Using the same faulty apparatus every time
- Recording fewer readings
- Rounding the answer to 1 significant figure
Show answer
Repeating the measurement and calculating a mean. Random errors scatter both ways, so they partly cancel in a mean.
The percentage error in a result is 12% and the total apparatus uncertainty is 2%. What does this suggest?
- The apparatus resolution is the main problem
- The result is as good as the apparatus allows
- There is a significant systematic error in the method
- The calculation must be wrong
Show answer
There is a significant systematic error in the method. The apparatus can explain only 2%, so the method itself loses accuracy.
Define the term precise as applied to a set of repeated results.
Show answer
The repeated results are close to each other (little spread).. Precision is about agreement between repeats, not closeness to the true value.

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